Prospect balancing theory: Bounded rationality of drivers’ speed choice

Accident Analysis and Prevention 63 (2014) 49–64

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Prospect balancing theory: Bounded rationality of drivers’ speed choice Martin Schmidt-Daffy ∗ Department for Psychology and Ergonomics, Berlin Institute of Technology, Germany

a r t i c l e

i n f o

Article history: Received 22 April 2013 Received in revised form 29 August 2013 Accepted 21 October 2013 Keywords: Decision-making Driving behaviour Loss aversion Motivational conflict Traffic safety

a b s t r a c t This paper introduces a new approach to model the psychological determinants of drivers’ speed choice: prospect-balancing theory. The theory transfers psychological insight into the bounded rationality of human decision-making to the field of driving behaviour. Speed choice is conceptualized as a trade-off between two options for action: the option to drive slower and the option to drive faster. Each option is weighted according to a subjective value and a subjectively weighted probability attributed to the achievement of the associated action goal; e.g. to avoid an accident by driving more slowly. The theory proposes that the subjective values and weightings of probability differ systematically from the objective conditions and thereby usually favour a cautious speed choice. A driving simulation study with 24 male participants supports this assumption. In a conflict between a monetary gain in case of fast arrival and a monetary loss in case of a collision with a deer, participants chose a velocity lower than that which would maximize their pay-out. Participants’ subjective certainty of arriving in time and of avoiding a deer collision assessed at different driving speeds diverged from the respective objective probabilities in accordance with the observed bias in choice of speed. Results suggest that the bounded rationality of drivers’ speed choice might be used to support attempts to improve road safety. Thus, understanding the motivational and perceptual determinants of this intuitive mode of decision-making might be a worthwhile focus of future research. © 2013 Elsevier Ltd. All rights reserved.

1. Introduction It is widely accepted that choices under risk are usually not guided by pure rationality but are often based on intuition which is better described in terms of emotions rather than cognitions (e.g., Kahneman, 2003; Gigerenzer, 2007). Since Simon (1955) called for a modification of the theory of “economic man”, research has accumulated considerable knowledge about the principles that rule the bounded rationality of human decision-making. A reliable finding from psychology, economics, and finance is that people often tend to avoid risks and losses (Kahneman et al., 1991; Rabin and Thaler, 2001). Thus, they prefer decision options with more predictable consequences and are reluctant to accept options involving a potential loss even if the alternative option would promise a higher payoff. The present paper transfers this knowledge to the field of drivers’ speed choice. The approach aims to improve the comprehension of the psychological factors that favour careful driving behaviour.

∗ Correspondence address: Biopsychology/Neuroergonomics, Technische Universität Berlin MAR 3-2, Marchstr. 23 10587 Berlin, Germany. Tel.: +49 30 314 25294; fax: +49 30 314 25274. E-mail address: [email protected] 0001-4575/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.aap.2013.10.028

An intuitive mode of decision making is particularly required in situations in which not all relevant information is available and the processing time is limited (Sivak, 2002). This characterization applies to many driving situations. The interplay of vehicle, road, weather, and other road users forms a complex and rapidly changing environment that is often not totally predictable for the driver. Accordingly, the concept of bounded rationality has already been discussed in the context of merging into traffic (Sivak, 2002) and car following (Lubashevsky et al., 2003). However, drivers’ speed choice is a particularly interesting field of application because velocity is one of the most important factors in accident risk (Aarts and Van Schagen, 2006). Therefore, it is paramount to understand drivers’ decision making related to speed.

1.1. Outline of the prospect balancing theory Tarko (2009) proposed a model of drivers’ speed choice in which the preferred speed results from a trade-off between three disutilities: crash risk, time loss and risk of a speeding fine. Because these disutilities are assumed to depend on drivers’ preferences and perceptual abilities, the model claims to comprise the concept of bounded rationality (in contrast to O’Neill, 1977). The present paper advances this idea by outlining a decision theory of drivers’

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speed choice. However, instead of focusing on a limited set of disutilities, the theory claims to be valid for the high diversity of goals that might guide drivers’ speed choice. Therefore, the theory concentrates more on the basic psychological principles that determine how the pursuit of an action goal is implemented in the choice of speed. These principles are derived from general knowledge about human decision-making. Prospect theory (Kahneman and Tversky, 1979; Tversky and Kahneman, 1992) is one of the most prominent approaches to describe the bounded rationality of judgments and choices in uncertain situations. Therefore, this theory is used as a frame of reference to conceptualize drivers’ decision-making. Applying prospect theory to the field of driving behaviour requires acknowledging that speed choice differs from common decision problems investigated in psychological research. In contrast to the discrete decision alternatives, e.g. of a lottery, driving speed is a continuous dimension. Given that information processing capacities are limited, it is not realistic that drivers consider the full range of different speeds and their potential outcomes in their decision-making. However, from a given driving speed, drivers have two options for altering velocity: accelerate or decelerate. It is assumed here, that only these two options are considered in speed choice. Usually accelerating increases the probability of a positive outcome (e.g. arriving in time) whereas decelerating decreases the probability of a negative outcome (e.g. a speeding fine). Thus driving requires a trade-off between these two desirable prospects rather than a discrete choice. Accordingly, the application of prospect theory to drivers’ speed choice is called prospect balancing theory. Prospect balancing theory proposes that a driver attributes a subjective total value to each of the two speed change options. With increasing velocity the total value of the acceleration option decreases whereas the total value of the deceleration option increases. The model predicts that the driver chooses a speed at which both total values are equal. Each total value is defined by the product of two variables: the subjective value and the subjective efficacy of the respective speed-change option. In terms of prospect theory, these variables correspond to the subjective weight and the subjectively weighted probability with which potential outcomes are considered in the evaluation of a decision option. The following sections describe these concepts. 1.1.1. Subjective values Drivers execute the driving task with certain aims and tendencies to reach these aims: drivers’ action goals. In respect to velocity many different goals might be involved. Most of these goals split into those that tend to be achieved by driving quickly (e.g. thrill of speed, fast arrival, impressing others) and those that are favoured by driving slowly (e.g. accident prevention, speeding fine avoidance). Because of the well-known tendency to simplify decision problems (editing phase, Kahneman and Tversky, 1979) it is proposed that drivers usually reduce their speed choice to a trade-off between two action goals: the most prominent goal related to fast driving and the most prominent goal related to slow driving. Which goals come to the fore depends on the driver and the driving situation and therefore might be influenced by personality traits on the one hand and the current task demands on the other hand. The achievement of an action goal has a particular value to the driver. One way to quantify this value would be to describe it by means of objective parameters (utilization worth of the vehicle, number of passengers, number of heart beats per minute); however, these parameters are hardly comparable. Moreover, it is reasonable to doubt that there is a linear relationship between these parameters and their subjective importance (e.g. relation between the number of passengers and drivers’ sense of responsibility). In line with prospect theory, it is therefore assumed that drivers attribute subjective values to the achievement of their action goals. These subjective values provide a common basis for the

comparison of different kinds of action goals. However, they diverge systematically from the numeric values of the respective objective parameters. The direction of these deviations can be deduced from prospect theory (e.g., Kahneman and Tversky, 1979). Fig. 1a illustrates two characteristics of the proposed relationship. First, an increase in objective value has a declining impact on the increase in subjective value. This implies, for example, that an increase in speeding fine from D 50 to D 100 should have a stronger impact on the re-evaluation of the speed options than an increase from D 200 to D 250. A second characteristic of the relationship is that the subjective value depends on whether an outcome is perceived as a loss or a gain. Thereby a loss is usually attributed a substantially higher subjective value than an equivalent gain. For instance, this implies that D 100 which are lost in case of late arrival should act as a stronger motivator for speeding than D 100 which are gained in case of arriving in time. Prospect balancing theory is in line with many models of driving behaviour in assuming that speed choice depends on conflicting action goals or motivations (e.g., Wilde, 1982; Fuller, 2005; Zuckerman, 2007; Koornstra, 2009). However, in contrast to most of these models the theory does not propose that drivers’ perceived risk of having an accident or of losing control is always involved in speed choice. 1.1.2. Subjective efficacy Drivers favour the achievement of one of their two dominant action goals by either decelerating or accelerating. Thus, if they only considered the subjective value of these goals they would either stop driving or choose the maximum speed, depending on which goal’s value prevails. Usually the benefit of further acceleration or deceleration decreases, however, the more the speed has been already changed. Thus, prospect balancing theory proposes that drivers’ evaluations of the speed-change options additionally include the subjective estimation of each option’s potential effectiveness in achieving the associated action goal. This is called the subjective efficacy. In line with the assumption that speed choice is determined by two predominant action goals, it is assumed that two kinds of subjective efficacies are considered: one related to acceleration and one related to deceleration. The subjective efficacy of a speed-change option depends on the parameters of the driving task. For instance, for a driver seeking to arrive on time, the subjective efficacy of the acceleration option might depend on the perceived ratio between the distance to the destination and the available time. If all other parameters of the driving task are constant, the subjective efficacy predominantly varies with the driving speed. Fig. 1b shows a hypothetical example of how the relationship between velocity and subjective efficacies might look for a given driver and driving situation. It is proposed that the subjective efficacy of a speed-change option correlates negatively with drivers’ current certainty of achieving the associated action goal. This involves some general assumptions about the relationship between efficacy and speed. • Usually the subjective certainty of achieving a velocity-related action goal increases with velocity. Thus, the subjective efficacy of the acceleration option decreases with the driving speed. On the other hand, the subjective certainty of achieving a safetyrelated action goal decreases with increasing velocity. Therefore, the subjective efficacy of deceleration option increases with driving speed. • Subjective efficacy varies between a value of zero and a particular maximum value. A zero efficacy is reached at speeds at which further acceleration or deceleration does not increase the subjective confidence of goal achievement (e.g. beneath the speed limit deceleration has zero efficacy for avoiding a speeding fine). The maximum subjective efficacy is reached at speeds at which

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Fig. 1. Central components of prospect balancing theory: the relationship between objective and subjective values in prospect theory (a), example curve progression of subjective efficacies (b) and subjective total values (c).

the driver perceives the highest possible benefit in choosing the respective speed option. However, the achievement of drivers’ goals usually does not only depend on speed choice but also on relevant circumstances outside drivers’ influence. The subjectively weighted probability of these circumstances limits the maximum efficacy of a speed option. For example, if the dominant action goal is the avoidance of a speeding fine, the subjective efficacy of deceleration might increase with velocity until it reaches a value that corresponds to the subjectively weighted probability of a radar speed check. • In line with actual probabilities of missing the action goal (e.g. injury risk, Richards and Cuerden, 2009) and subjective correlates (e.g. comfort, Lewis-Evans and Rothengatter, 2009), the subjective efficacy varies in a non-linear fashion with the driving speed. In particular it is proposed that the subjective efficacy asymptotically approximates its minimum and maximum value. In between there is a range of speeds in which the subjective efficacy substantially increases or decreases. The location and width of this speed range depends on the perceived extent to which characteristics of the driving task favour or hinder the achievement of the predominant action goal. Drivers’ estimated sight distance, for example, could determine at which speeds the efficacy of decelerating substantially increases. In this way, a drop in sight distance should shift the range in the direction of lower speeds, while an increase in variability of sight should cause the increase in efficacy to extend over a wider range of speeds. • Although the subjective efficacy of a speed option correlates with the risk of missing the respective action goal, drivers’ corresponding subjective certainties deviate systematically from the respective objective probabilities. The proposed deviation resembles the subjective weighting of probabilities stated by prospect theory (Kahneman and Tversky, 1979) or by its extension: cumulative prospect theory (Tversky and Kahneman, 1992). It follows, therefore, that drivers usually give low probabilities too much weight when evaluating their speed options, whereas they assign high probabilities a weight that is too low (e.g. at low speeds, drivers overestimate the efficacy of avoiding a collision by decelerating whereas they underestimate the efficacy of this option at high speeds). Previous models of driving behaviour already put forward the idea that internal determinants of drivers’ speed choice vary in a non-linear fashion with velocity (Tarko, 2009) or risk sensation (Zuckerman, 2007; Koornstra, 2009). In a similar way to these models the subjective efficacy ensures that the translation of drivers’ action goals into driving speed is adapted to the current requirements of the driving task. It is important to note, however, that, according to prospect balancing theory, only those requirements of

the driving task are considered which the driver regards as relevant for the achievement of the currently dominant action goals. The chance of achieving a travel-related action goal often does not depend on external task demands alone but also on the driver’s capabilities. For instance, avoiding a collision requires – amongst others – visual attention and fast reactions. Inspired by the taskcapability-interface model (Fuller, 2005) it is therefore assumed that the subjective efficacy of a speed option is usually based on the driver’s perception of both the relevant task demands and of his or her own capabilities to cope with these demands. A divergence between self-attributed and objective capabilities might contribute to the bounded rationality of driving behaviour (Sivak, 2002). Moreover, this implies that to some extent drivers might be capable of controlling the chance of achieving a travel-related action goal not only by choosing another driving speed but also by altering the effort they dedicate to the driving task (e.g. the subjective efficacy of deceleration decreases if drivers pay more attention to the road). It is important to note though that prospect balancing theory proposes that the evaluation of efficacies is predominantly an intuitive process. Thus, this evaluation might be experienced by the driver as affect-laden perceptions of the driving situation (similar to the field of safe travel, Gibson and Crooks, 1938) rather than as a deliberate cognitive calculation. 1.1.3. Subjective total value Prospect balancing theory proposes that the product of subjective value and subjective efficacy constitutes the subjective total value, which drivers attribute to their speed-change option. Because the total values depend on both the motivational conditions and the current task demands they can be allocated to the operational level of the hierarchical model of behavioural adaptation (Summala, 1997). The total value of a speed option resembles drivers’ strength of motivation to change speed accordingly. Drivers choose a speed at which neither the motivation to accelerate nor the motivation to decelerate prevails. Thus, it is predicted that they prefer a speed at which the subjective total values are balanced. Fig. 1c shows hypothetical curve progressions illustrating the functional relationship between the subjective total values and the driving speed. The curves indicate for each velocity how much drivers are motivated to decelerate on the one hand and to accelerate on the other hand. At the intersection point of the two curves the subjective prospects of both speed options are balanced. Along the speed axis this intersection point marks the predicted driving speed. The curve progressions illustrate how prospect balancing theory explains drivers’ selection of speed. It is important to note, however, that the theory does not state that the curves are internally represented by the driver. Representing the curves is not necessary for

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selecting a speed at which the total values of both speed-change options are balanced. Instead, drivers only need to code the two values for the current driving condition and change their speed accordingly if one value prevails. Moreover, the computation and comparison of the two total values is not considered to be a conscious process. On the contrary, it is assumed that these tasks are usually managed by an intuitive system which operates in a nonconscious automatic processing mode. Thus speed choice decisions are experienced as being guided by feelings rather than reasoning (like other intuitive decisions, Kahneman, 2003; Gigerenzer, 2007). An imbalance between both total values might be experienced as a feeling of being uncomfortable with the current velocity (Summala, 2007). Depending on which action goal is dominant, drivers may experience other feelings, such as fear, boredom, or impatience. Thus, introspectively, changing the driving speed might be motivated by the attempt to achieve the best possible feeling for the current driving situation (Vaa, 2007). In the evaluation of the speed options, bodily responses might play a role (Taylor, 1964). Vaa (2007) has proposed that these so called somatic markers (Damasio, 1994) indicate whether a decision alternative is either a good or a bad choice. 1.2. An example driving situation Prospect balancing theory can be illustrated by considering a driver who sets off on a journey to a business appointment. Let us assume that he has little time to cover the distance so that his dominant velocity-related action goal is arriving in time. On setting off, he perceives acceleration as a very effective action option. However, the perceived efficacy is probably not 100% because it is limited by the subjectively weighted probability that potential traffic congestion will impede a timely arrival anyway. As the driver accelerates, the subjective efficacy of this option decreases the more certain he is that the current speed is high enough to arrive on time. At the same time, the driver perceives increasing difficulty staying on the road or avoiding a collision in the case of a required braking response. Let us assume that the action goal which begins to dominate the driver’s safety-related considerations is the avoidance of damage to the car. With increasing vehicle speed, the certainty of achieving this goal decreases and therefore the subjective efficacy of deceleration increases. If the driver were to only consider the probabilities of goal achievement he would choose a speed at which both efficacies are balanced (e.g. the intersection point of the curve progressions in Fig. 1b). However, the driver additionally considers subjective values associated with the achievement of his action goals. For convenience, let us assume that both damaging the car and arriving in time are associated with objective values of the same magnitude (e.g. an excess payment of D 100 to the insurance company and a business deal worth D 100, respectively). Given that the driver codes the value of the safety-relevant goal as a loss and the value of the velocity-related goal as a gain, prospect theory (e.g., Kahneman et al., 1991; Abdellaoui et al., 2007) suggests that he attributes the avoidance of damage to the car a subjective value which is approximately twice as high as the subjective value of arriving in time (Fig. 1a). The products of these subjective values with the respective subjective efficacies constitute the subjective total values (Fig. 1c). The driver stops accelerating at a speed where the subjective total value of acceleration equals the subjective total value of deceleration. This speed is lower than suggested by the subjective efficacy alone (Fig. 1b). During stable driving conditions the driver maintains his speed, however if relevant conditions change, the balance point of the subjective total values shifts along the velocity dimension. This adaptation is mainly due to the impact of the perceived change in driving conditions on the subjective efficacies of the speed change options. For instance, the subjective efficacy of acceleration might

increase after a delay (e.g. a closed railway crossing). This would shift the balance point towards a faster driving speed. On the other hand, a warning sign might increase the subjective efficacy of deceleration and thus lead to the choice of a slower speed. It is important to note, though, that the driver bases his decision on subjectively weighted probabilities rather than objective likelihoods of goal achievement. Thus, a speed adjustment might be insufficient or excessive depending on how the subjective efficacies differ from the objective chances of goal achievement. Arriving in time and avoiding accidents represent common driving-related goals. Because these goals are frequently associated with financial gains or losses they are particularly suitable for illustrating the bounded rationality of drivers’ decision making. However, prospect balancing theory claims to apply to other goals as well. For instance losing the approval of one passenger might outweigh an equivalent gain in approval of another passenger; avoiding boredom might be a stronger motivator than an increased thrill. 1.3. Prospect balancing and traffic safety Prospect balancing theory postulates that drivers’ choice of speed differs systematically from a choice that conforms to the requirements of utility maximization. This difference is attributed to a divergence between drivers’ subjective values and objective gains or losses on the one hand and subjective efficacies and objective probabilities on the other hand. In particular, it is expected that drivers have a tendency to overvalue a potential loss (such as the costs of an accident) and to overweight low probabilities (e.g. the likelihood of an accident). Therefore, the theory predicts that drivers’ bounded rationality usually favours the selection of a safe driving speed. At first sight, this conclusion might appear dubious because we tend to mistrust intuitive decisions—at least if they are not made by ourselves. However, the assumption that intuition allows for highly advantageous behaviour is consistent with findings from general decision-making research (Kahneman, 2003). Gigerenzer (2007) pointed out that the results of intuitive decisions are often even more satisfying than a purely rational choice. Transferred to the field of traffic behaviour Sivak (2002, p. 262) concluded similarly that “. . . bounded rationality is adaptive. Or at least it is most of the time”. Results of previous studies (Schmidt-Daffy, 2012, 2013; Schmidt-Daffy et al., 2013) provided hints that drivers’ choice of speed is subjected to bounded rationality. In a driving simulation participants opted for lower speeds if the monetary gain for fast trip completion and the monetary loss in the case of an accident were increased by the same amount. Findings from general decision experiments (Harinck et al., 2007) suggest that this behaviour was mediated by loss aversion which increases with the stakes. In a follow up study (Schmidt-Daffy et al., 2013) no evidence was found that varying the ratio between gains and losses influenced the speed choice. It was speculated that loss aversion concealed the expected effect. However, previous studies did not assess the extent to which the chosen speeds deviated from a choice that would have optimized the pay-out. Therefore, they do not provide clear support for prospect balancing theory. In addition, the studies did not assess how participants evaluated their speed options. According to the concept of subjective efficacies, biased evaluations related to the likelihood of a gain or loss might have contributed to the bounded rationality of the observed speed choice. 1.4. Objectives Prospect balancing theory predicts that the concept of bounded rationality applies to drivers’ speed choice. The aim of the present study was to prove this prediction with behavioural and self-report

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data assessed in a driving simulator. In particular the study had two objectives: The first objective was to confirm that drivers’ speed choice is subject to the proposed preference of avoiding losses and risks compared to the achievement of a gain. In particular, it was predicted that in a safety-velocity conflict participants reduce their driving speed. In contrast to previous studies, the bounded rationality of this choice should be determined as the difference between the chosen speed and the speed that would promise the highest pay-out. The second objective was to provide empirical support for the new construct introduced by prospect balancing theory: the subjective efficacy. It was expected that participants’ feelings of certainty about the achievement of their action goals vary with the driving speed in accordance with the postulated changes in subjective efficacies. In particular, it was predicted that self-report data accord with the assumption that decision-makers tend to overweight low probabilities and tend to underweight high probabilities. Finally, it was explored whether physiological recordings provide additional information about the psychological processes that underlie decision-making. 2. Method 2.1. Participants A sample of 25 male volunteers with German as a first language was recruited using flyers posted at the Berlin Institute of Technology campus. One participant’s data had to be excluded from analysis due to non-compliance with the task instructions (deviation from prescribed speed ranges). The 24 participants, whose data were analyzed, were between 19 and 30 years old (M = 25.92, SD = 2.55), had a valid driver’s license for at least 2 years (M = 8.00, SD = 2.40) and had normal or corrected-to-normal vision. They had no alcohol, drug, or caffeine intake before participation and did not smoke more cigarettes than usual. The experiment was undertaken with the understanding and written consent of each participant and in compliance with the October 2008 version of the 1964 Declaration of Helsinki. As a reward for their attendance at the 2-h study, they received an 8 GB USB memory stick. In addition each participant earned a variable amount of money, which depended on their individual task performance (M = D 8.34, SD = D 1.10). 2.2. Driving simulation The study used an enhanced version of a driving simulator that proved of value in a previous study to explore the motivational determinants of speed choice in a highly standardized laboratory setting (Schmidt-Daffy et al., 2013). The simulator consisted of a car seat with an integrated cushioned forearm splint for recording peripheral-physiological variables from the left hand. Participants used their right foot to depress the accelerator and brake pedals (MOMO Racing Force Feedback Wheel by Logitech) and selected from four gears by pressing one of two keys (gear up and gear down) with their right hand. The maximum speed was 108 km/h. In order to limit the number of factors that could influence the choice of speed and the physiological variables, no steering wheel was used. Instead, the simulated car remained on the right-hand lane of a straight road automatically. In contrast to previous studies, reflector posts and trees at the roadside were added to provide more visual speed feedback (Fig. 2). The noise of a simulated car engine served as auditory feedback. The visual presentation was made by rear projection onto a transparent screen (94 cm × 79 cm) which was tilted in accordance with the front window of a real car, with the projected picture compensated for the tilt.

Fig. 2. Screenshots of the driving simulation with distance indicator (a), finish line (b), and a deer (c).

Three digital displays (Fig. 2) were projected side by side onto the lower part of the transparent screen. The right-hand display showed the current speed in km/h, the display in the centre indicated the present gear, and the left display provided information on the number of seconds that have elapsed since the beginning of the journey. Every 200 m a blue sign on the right-hand side of the road showed the distance covered in km (Fig. 2a). In addition, participants were informed that the distance between consecutive reflector posts is 50 m. The simulation was programmed using the Blender 2.49b 3D content creation software suite in Python programming language version 2.6.2.

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2.3. Driving tasks Each participant accomplished four different driving tasks which consisted of several trips. The trip could end in one of four different ways: either the finish line was crossed (Fig. 2b), the maximum journey time was reached before reaching the finish line, a deer was hit (Fig. 2c), or a collision with a deer was prevented by a braking response. The maximum journey time was 60 s for all trips. The distance to the finish line varied between trips. Instead of a finish line, in some of the trips a deer appeared at a variable time. At the end of each trip the simulated road and environment was blanked but the current values on the digital displays remained visible. This allowed participants to ascertain the travel time at which they crossed the finish line or to check the impact speed in case of a deer collision. Additionally, a green background of the displays signalled the timely crossing of the finish line and a red background a deer collision. If the finish line was missed or the deer collision was avoided the background colour was grey. Passing the finish line within the predefined journey time served to induce a velocity-related action goal. Avoiding a deer collision served to induce a safety-related action goal. In the first half of the study these action goals were pursued separately within two sub-tasks: • Task: reaching the finish line at the correct time. In this task participants had to choose a speed at which they would cross the finish line after exactly 60 s. The distance to the finish line was announced at the beginning of each trip. Nine trips were completed, in which the distances to the finish line varied in a random order: 1 × 0.8 km; 2 × 0.9 km; 3 × 1.0 km; 2 × 1.1 km; 1 × 1.2 km. No warning of a possible deer on the road was given and no deer appeared in these trips. Participants were instructed to accelerate as quickly as possible at the beginning of the trip and maintain their desired speed as soon as it was reached. The task familiarized participants with the frequencies of the different distances to the finish line and the required driving speed for each distance. Moreover, the task was used to determine the objective probability with which the finish was reached at different speeds. • Task: responding quickly to a traffic hazard. In this task participants had to brake as fast as possible once a deer appeared. They were informed that in each of the trips a deer would occur at an unpredictable time. Before starting a trip, a prescribed speed range was announced that was defined by a minimum speed and a maximum speed which were 5 km/h apart from each other. Participants were instructed to accelerate as quickly as possible until they reached the prescribed range. Each of them undertook five trips with different speed ranges. The speed ranges were either 50–55 km/h, 60–65 km/h, 70–75 km/h, 80–85 km/h and 90–95 km/h or 55–60 km/h, 65–70 km/h, 75–80 km/h, 85–90 km/h and 95–100 km/h. To avoid sequence effects, six different permutations of the order of the prescribed speed ranges across runs were implemented and completed by an equal number of participants. The task familiarized participants with the likelihood of a deer collision and the impact speed at different driving speeds. In addition, the collision frequencies and impact speeds were used to determine the respective objective probabilities and severities of a deer collision. In the second part of the study participants processed two sub-tasks that required the simultaneous pursuit of both goals. Participants accomplished each trip without knowing the particular distance of the finish line or whether there would be a deer on the road. However, they were informed that the frequencies of the distances would correspond to those of the previous task and that the probability of a deer encounter was 25% in each trip. In contrast to the previous tasks they could win or lose money depending on

the outcome of the trip. If they passed the finish line within 60 s, they won D 1. If they ran into a deer they lost at least D 1. This loss increased by 2 cents for each km/h impact speed. At the beginning of each sub-task a starting asset of D 1 was guaranteed to produce a fixed reference point for the potential gains and losses (Tversky and Kahneman, 1981). The order, in which the two sub-tasks were carried out, was balanced across participants. • Conflict task with free choice of speed. In this task, participants completed eight trips in which they were allowed to freely choose their driving speed. In two of these trips a deer appeared on the road after either 22 or 47 s. In the other trips the distance of the finish line varied in a random order: 1 × 0.8 km, 1 × 0.9 km, 2 × 1.0 km, 1 × 1.1 km and 1 × 1 × 1.2 km. The trips served to determine the preferred driving speed under the given motivational conditions and task demands. The first two trips were treated as practice trials and thus not analyzed. • Conflict task with prescribed speed ranges. In this task, participants’ choice of speed was restricted to prescribed ranges of 5 km/h. The same ten ranges were examined that had been implemented in the previous task of responding quickly to a traffic hazard. For each speed range, participants first accomplished a trial run of 30 s in which neither a finish line nor a deer appeared. Each trial run was followed by a main run in which participants could win or lose money depending on the outcome. The trial runs provided the opportunity to evaluate the driving speeds in respect to the chances of achieving the two action goals. The respective subjective certainties were assessed by a short questionnaire after each trial run. This ensured that the answers preferably reflect intuitive and perception-based evaluations without being biased by the outcome of the main run. In addition to the self-report data the speed choice within the prescribed ranges and the accompanying physiological arousal was recorded. Overall, the task consisted of 12 pairs of trial and main runs. The deer appeared in three main runs after either 18, 47, or 52 s. In the remaining main runs the distances to the finish line were the same as for the task of reaching the finish line at the correct time. The order of the trips (speed range, deer occurrence, and finish line distance) was balanced across participants using six different sequences. The first two trips were treated as practice runs. 2.4. Data recording and analysis 2.4.1. Objective measures of probability, utility, and disutility Driving speed was recorded at a rate of 60 Hz to the nearest 1 km/h and averaged to determine the speed within a particular trip. In order to skip the acceleration phase the first 17 s were not considered. In the task with free choice of speed and in the task with prescribed speed ranges an identical temporal basis for the analyses was guaranteed by limiting the averaging to the following 30 s. Trips in which the deer appeared before 47 s were excluded from analysis. The speed data in the task of reaching the finish line at the correct time were used to determine the distance participants covered at different driving speeds. Based on this analysis the objective probabilities of passing the finish line were estimated for each successive 5 km/h range of speeds between 50 and 100 km/h. These values were used as indicators of the objective likelihood of achieving the velocity-related action goal if no deer appears (conditional probability). The calculation of the probabilities considered the different distances of the finish lines and their predetermined frequencies. The calculation was based on behavioural data that account for participants’ way of accelerating at the beginning of the trips. Thus, the estimated probabilities mapped how frequently participants actually passed the finish line at the respective speeds.

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In the task of responding quickly to a traffic hazard it was determined how frequently the simulated car ran into a deer. Based on this analysis the objective collision probability was calculated for each of the ten prescribed speed ranges. In addition the average impact speed was assessed. Trips in which the participants avoided a deer collision were considered to have an impact speed of zero. For each of the ten speed ranges, these analyses provided objective values for the conditional probability and severity of missing the safety-related action goal if a deer appears. Just as for the velocity-related action goal, the respective values were based on observational data and accorded with participants’ actual experience. The conditional probabilities of passing the finish line and the probabilities of colliding with a deer were used to estimate the utility and disutility of the driving speeds in the conflict task with free choice of speed (Fig. 3). Estimates were computed for each of the ten speed ranges. The utility of a range of speeds was calculated by multiplying the respective probability of a gain with the magnitude of the gain. The probability of a gain was determined as the product of the conditional probability of passing the finish line at that range and the base rate probability of a finish line, which was 0.75 in all trips. The magnitude of the gain was always fixed at a value of D 1. The disutility of a range of speeds was calculated by multiplying the respective probability of a loss with the amount of loss. The probability of a loss was computed as the product of the conditional probability of colliding with a deer and the base rate probability of a deer encounter, which was 0.25. The amount of loss included at a particular speed range was D 1 plus 2 cents per km/h of the impact speed. The impact speed at a particular speed range was adopted from the average impact speed observed in the task of responding quickly to a traffic hazard. 2.4.2. Subjective measures of certainty, efficacy, and total value In the conflict task with prescribed speed ranges, participants rated on a 9-point scale (Fig. 4) how certain they were that: • they would be able to reach the finish line with no deer on the road; • they would be able to avoid a collision if they encountered a deer on the road; and • they would encounter a deer on the road. The first two questions aimed to assess the subjective equivalents of the conditional probabilities of goal achievement. The third question targeted the subjective equivalent of the base rate. However, by requesting a bipolar rating of certainty instead of a unipolar rating of probability or frequency, the answers should indicate the emotional evaluation of the probabilities (subjective weightings) rather than a mere cognitive estimation. After the main trials, participants additionally reported their estimate of the speed of impact had they encountered a deer on the road. Only trips in which no deer appeared were considered in the analysis of these data. Participants’ self-report data were used to estimate parameters for the subjective efficacies they attributed to the speed change options at each of the ten speed ranges (Fig. 5). The subjective efficacy of the acceleration option was estimated for each speed range by multiplying together two values: the subjective certainty that no deer would appear and the subjective certainty that the speed would be insufficient to pass the finish line (the complement values of the subjective certainty of a deer encounter and the subjective certainty of passing the finish line with no deer encounter). Correspondingly, the subjective efficacy of the deceleration option was computed by multiplying the subjective certainty that a deer would appear with the subjective certainty that the driving speed is too high to avoid a collision (the complement value of the subjective certainty of avoiding a collision in case of an encounter with a deer).

55

The total values of the speed-change options were calculated for each range of speeds by multiplying the calculated subjective efficacies with estimates of the subjective values. Findings from Harinck et al. (2007) suggest that a loss of D 1 is usually attributed a subjective value that is 1.21 times higher than the subjective value attributed to an equivalent gain. Accordingly, the subjective value of avoiding a deer collision was computed by multiplying the expected loss with a factor of 1.21. The expected loss was calculated at D 1 plus 2 cents per km/h expected impact speed. The expected impact speed was the average estimation of the participants at that speed range. For the acceleration option, the calculation of the total values considered the subjective value of reaching the finish line with a constant weight of 1 in all examined speed ranges. 2.4.3. Curve progressions Curve progressions were determined to illustrate how the analyzed parameters vary with driving speed and to provide a mathematical description of the relationship. For the objective probabilities and subjective certainties of reaching the finish line and colliding with a deer, as well as for all derived parameters, a cumulative normal distribution was fitted to the progression of the values across the ten speed ranges. The fitting was based on the distribution of differences between successive speed ranges which provided the mean and standard deviation of the normal distribution. For the deer collision, the speed-dependent increase in objective impact speed (objective loss) and participants’ expected impact speed (subjective loss) was described with an exponential curve progression. To illustrate the progression of disutility and the progression of subjective total values for the deceleration option, a cumulative normal distribution and an exponential function were combined, which depended on the speed-related progressions of the two kinds of values that constitute these measures respectively. 2.4.4. Maximum pay-out and actual speed selection The two functions that described speed-dependent utility and disutility were used for estimating the speed at which participants had the best chance of receiving the maximum pay-out during the task with free choice of speed. This speed was determined using the value at which the difference between the utility and the disutility was the highest. The determined value resembles the optimal choice if participants’ decision were solely based on objective values regarding the previously experienced probabilities and the announced gains and losses. In addition, based on the two functions that described the subjective total values, a speed was determined at which the total value attributed to the acceleration option resembles the total value attributed to the deceleration option. This speed is optimal with respect to participants’ self-reported feelings of certainty and the estimated subjective values attributed to the gains and losses. In the conflict task with free choice of speed participants’ actually chosen driving speed was calculated by averaging the mean speed in the six trips. In the conflict task with prescribed speed ranges, however, the average driving speed was analyzed separately for each trip. 2.4.5. Physiological data The electrodermal activity and the finger pulse volume were recorded to assess bodily arousal parameters while completing the task with prescribed driving speeds. In analysis of the main trials, the same assessment phase was applied as for the speed analysis. In order to assess the baseline activity for each speed range, the physiological arousal in the trial runs was analyzed between 17 and 27 s. The electrodermal activity was measured with two electrodes attached to the thenar and hypothenar of the left hand. In contrast to previous studies, the average level of electrodermal activity (EDL)

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M. Schmidt-Daffy / Accident Analysis and Prevention 63 (2014) 49–64

Conditional probability of finish line crossing

Conditional probability of a deer collision

Probability of a deer encounter (.25)

Probability of a gain

Probability of a loss

Utility of speed

Disutility of speed

Amount of gain

Amount of loss

2 cents loss per 1km/h observed impact speed

1 gain in case of passing the finish line

Multiplication of values

1 loss in case of a deer collision

Computation with complement value

Addition of values

Fig. 3. Calculation of the utility and disutility of a particular speed.

Fig. 4. Rating scale for the assessment of subjective certainty (translated from German).

Certainty of crossing the finish line, if no deer appears

Certainty of avoiding a deer collision, if a deer appears

Certainty of encountering a deer

Subjective efficacy ACCELERATION OPTION

Subjective total value

Subjective efficacy

Subjective value

1 1 gain in case of passing the finish line

Multiplication of values

DECELERATION OPTION

Subjective total value

Subjective value

Weighting factor according to Harinck et al. (2007) 2 Cents loss per 1km/h expected impact speed

Addition of values

1.21 1 loss in case of a deer collision

Computation with complement value

Fig. 5. Estimation of the proposed internal determinants of speed choice at a particular speed.

M. Schmidt-Daffy / Accident Analysis and Prevention 63 (2014) 49–64

utility of speed (probability -weighted gain)

(a)

certainty

chosen speed

disutility of speed (probability -weighted loss)

0.4 0.2

probability

8

utility minus disutility

0.0 55 60 65 70 75 80 85 90 95 speed in km/h Fig. 6. Estimated utility and speed selection while driving with free choice of speed.

subjective certainty

euro

0.8 0.6

PASSING THE FINISH LINE

1.0 0.8

6

0.6 4 0.4 2

0.2

0

3.1. Maximum pay-out and speed selection during free choice of speed Based on the estimated utilities and disutilities, the chance of achieving the maximum monetary pay-out was highest at 83.57 km/h (Fig. 6). Actually, however, in the task with free choice of speed participants drove with a mean speed of 78.40 km/h (SD = 3.80 km/h). A one sample t-test revealed that the chosen speeds were significantly lower than the speed that would have been required to maximize the pay-out t(23) = −6.66, p < 0.001. Participants received an average pay-out of D 3.00 (SD = D 1.01) in the task with free choice of speed. The pay-out correlated positively with the chosen driving speed (Pearson’s r = 0.44, p = 0.034). This indicates that participants would have received more money if they had driven faster. To sum up, results were in line with the bounded rationality that was predicted for drivers’ speed choice. In particular they confirmed their preference for safe driving speeds that was suggested by previous findings (Schmidt-Daffy, 2012, 2013; Schmidt-Daffy et al., 2013). 3.2. Objective probabilities and subjective evaluations within prescribed speed ranges Fig. 7a and b illustrates how participants’ certainty ratings deviated from the conditional probabilities for passing the finish line or avoiding a deer collision. Fig. 7c contrasts participants’ expectations with the actual impact speed. One sample t-tests analyzed the difference for each of the ten speed ranges (Table 1). For these comparisons the ratings on the 9-point rating scale were divided by 8 to accord with the probability scale. A Holm-correction counteracted the problem of multiple comparisons within each pair of variables. At low and moderate speeds the subjective certainty of reaching the finish line was significantly higher than the objective probability (Fig. 7a). At speeds faster than 85 km/h, at which the finish line was most likely to be passed, the subjective certainty was lower than the objective value. A partially opposite relationship was found for the chance of avoiding a collision with a deer (Fig. 7b). At low and moderate speed ranges, the subjective certainty was

speed in km/h

(b) AVOIDING A DEER COLLISION certainty

probability

8

subjective certainty

3. Results

0.0 55 60 65 70 75 80 85 90 95

1.0 0.8

6

0.6 4 0.4 2

0.2 0.0

0 55 60 65 70 75 80 85 90 95 speed in km/h

(c)

IMPACT SPEED expected value

observed value

60

impact speed in km/h

was determined instead of the number of responses. This allows a finely graduated assessment of activity even within the short time window of the trial runs. The pulse volume was recorded with a photoelectric plethysmograph sensor placed on the last section of the left index finger. Because the acquired signal lends itself to indicate changes rather than absolute values, the mean of the pulse volume amplitude within each assessment phase was computed in arbitrary units. A more detailed description of the assessment and analysis of the physiological signals can be found in previous publications (Schmidt-Daffy, 2013; Schmidt-Daffy et al., 2013).

objective probability

maximum payout

1.0

objective probability

1.2

57

50 40 30 20 10 0 55 60 65 70 75 80 85 90 95 speed in km/h

Fig. 7. Subjective certainties and objective probabilities related to the passing of the finish line if no deer appears (a), to the avoidance of a collision if a deer appears (b), and to the expected and actual impact speed in the case of a deer encounter (c).

significantly lower than the objective probability. Both values converged at speeds beyond 90 km/h at which collision avoidance became unlikely. While driving at moderate speeds, participants expected a higher impact speed in case of a deer encounter compared to the actual impact speed observed in the task of quickly responding to

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M. Schmidt-Daffy / Accident Analysis and Prevention 63 (2014) 49–64

Table 1 One sample t-test results comparing participants’ subjective estimates with respective objective probabilities and values at prescribed speed ranges. Speed range (km/h)

50–55 55–60 60–65 65–70 70–75 75–80 80–85 85–90 90–95 95–100

Passing the finish line if no deer appears

Avoiding a collision if a deer appears

Impact speed

t-Value

p

t-Value

p

t-Value

p

3.29 2.68 6.04 8.39 4.40 2.71 0.20 −4.67 −3.19 −2.56

0.003* 0.013 <0.001* <0.001* <0.001* 0.013 0.985 <0.001* 0.004* 0.017

−2.29 −3.41 −4.63 −6.72 −9.76 −5.24 −9.31 −2.40 0.41 2.01

0.032 0.002* <0.001* <0.001* <0.001* <0.001* <0.001* 0.025 0.684 0.057

1.45 2.01 3.41 3.51 4.68 3.90 4.68 2.56 1.30 −0.90

0.162 0.057 0.002* 0.002* <0.001* 0.001* <0.001* 0.017 0.205 0.380

Note: df = 23. * p < 0.05 with Holm-correction.

a traffic hazard (Fig. 7c). Only at very low and very high speeds did the subjective and objective values not differ significantly. Participants gave their subjective certainty of a deer encounter an average rating of 3.82 on a 9-point rating scale. Converted to the probability scale this resembled a mean value of 0.48 (SD = 0.16). The objective probability was 0.25. Although this probability was repeatedly announced at the beginning of the task a one-sample ttest showed that the subjective certainty was significantly higher, t(23) = 7.06, p < 0.001. To sum up, participants’ self-report data were in line with predictions. Findings indicate that the subjective certainties related to the achievement of a gain and the avoidance of a loss deviated from the objective conditions. In particular they accord with the expected tendency to overweight losses and small risks which is well known from general research into decision-making. Thus, the self-report data proved to be suitable for estimating the central variables of prospect balancing theory: the subjective efficacies and the total values. 3.3. Subjective efficacies and total values within prescribed speed ranges Fig. 8a illustrates the relationship between the estimated subjective efficacies and the velocity. The curve progressions obtained accord with general characteristics proposed for the relationship between efficacy and speed. In the present study, the curve progression indicates that the subjective efficacy of deceleration approaches zero at speeds below 60 km/h. In contrast, the estimated subjective efficacy of acceleration approaches zero above 95 km/h. At the other side of the velocity continuum the curves approximate maximum values. Deceleration is attributed the highest efficacy at high speeds whereas acceleration is attributed the highest efficacy at low speeds. The respective maximum

values depended on the subjective certainty of a deer encounter or conversely the certainty of not encountering a deer on the journey. Because participants overestimated the probability of a deer encounter, the maximum deceleration efficacy was higher than the base rate of journeys with a deer encounter and the maximum efficacy of acceleration was lower than the base rate of journeys on which the finish line was passed. This illustrates how, according to prospect balancing theory, a biased evaluation of probabilities might contribute to a preference for low driving speeds. Fig. 8b illustrates the speed-dependent progressions of the subjective total values. These values combine the subjective efficacies with estimates of the respectively associated subjective values. Because the total values of the deceleration option incorporate the increase in expected loss at higher speeds, the curve progression of these values deviates considerably from the respective progression of the efficacy values. Combined with the assumption that losses are weighted more heavily, this causes the curves of the total values to cross each other at a lower speed than the curves of the subjective efficacies. Thus, comparing the intersection points in Fig. 8a and b shows how, according to prospect balancing theory, a bias in the evaluation of gains and losses contributes to a cautious speed choice in addition to biased evaluation of the respective probabilities. According to the estimated speed functions, the subjective total value of acceleration balanced with the subjective total value of deceleration at 73.54 km/h (the intersection point of both curves). Thus, the estimated total values suggest that beneath that value, participants’ motivation to accelerate prevailed whereas above that speed their choice was dominated by the motivation to decelerate. This conclusion was in line with participants’ speed choice in the trips with prescribed speed ranges (Fig. 9). Beneath 75 km/h, participants chose speeds in the upper half of the permitted range. Above 75 km/h, they preferred speeds in the lower half. However, the curve that was fitted to these speed values suggests that the

SUBJECTIVE EFFICACY

subjective efficacy

1.0 0.8 0.6 0.4 0.2 0.0

a)

1.2

deceleration subjective total value

acceleration

SUBJECTIVE TOTAL VALUE

1.0 0.8 0.6 0.4 0.2 0.0

55 60 65 70 75 80 85 90 95 speed in km/h

b)

55 60 65 70 75 80 85 90 95 speed in km/h

Fig. 8. Estimated subjective efficacy (a) and subjective total values (b) of accelerating and decelerating.

M. Schmidt-Daffy / Accident Analysis and Prevention 63 (2014) 49–64

speed range in km/h

SPEED CHOICE chosen speed relative to prescribed speed range limits

5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0

59

choice. As predicted, participants tended to drive more slowly than would be required to maximize their pay-out. The self-report data show that this tendency corresponds with biased evaluations regarding the chance of achieving a gain and avoiding a loss. Thus, results support the new concept of subjective efficacy, introduced by prospect balancing theory to describe how drivers’ speed change motivations vary with velocity. The following sections discuss in more detail how these interpretations are supported by the behavioural, self-report, and physiological data. 4.1. Speed selection under motivational conflict

55 60 65 70 75 80 85 90 95 speed in km/h

Fig. 9. Chosen speed within the 5 km/h wide speed ranges.

preference for high speeds switched to a preference for low speeds at a value that was higher than the balance point of the estimated total values. Likewise, the speed chosen in the task with free choice of speed was significantly higher than the predicted balance point (M = 78.40 km/h vs. 73.54 km/h), t(23) = 6.28, p < 0.001. 3.4. Physiological responses at prescribed speed ranges The skin conductance level and the pulse volume amplitude while driving with prescribed speed ranges was analyzed to explore whether physiological variables provide additional information about the internal determinants of drivers’ speed choice. For each dependent measure a 2 × 10 analysis of variance for repeated measures tested the effects of run type (main run vs. trial run) and speed range. A violation of the sphericity assumption for the effects of speed range was corrected using the Greenhouse–Geisser correction. The run type significantly influenced the electrodermal activity, F(1,23) = 5.41, p = 0.029, f = 0.48. Compared to the trial runs, the skin conductance level increased in the main runs in which participants anticipated a gain or loss while driving within the same speed range. A marginally significant interaction suggests that this effect depended on the driving speed; F(9,89.99) = 2.28, p = 0.068, f = 0.32. An increase in skin conductance was found particularly if participants had to drive at high speeds. Fig. 10 illustrates how the difference between main runs and trial runs increased with velocity. A significant main effect of speed range was not observed F(9,49.99) = 1.17, p = 0.320, f = 0.23. The pulse volume amplitude decreased in the main runs compared to the trial runs; F(1,23) = 29.43, p < 0.001, f = 1.13. Like the increase in skin conductance, this main effect of trip type suggests that if money was at stake, a higher activation of the sympathetic part of the autonomous nervous system resulted. Additionally, there was a significant interaction of run type and speed range; F(9,107.19) = 3.55, p = 0.006, f = 0.39. The higher the prescribed speeds, the more the pulse volume amplitude in the main runs deviated from the trial runs (Fig. 10). The main effect of speed range was not significant; F(9,115.90) = 1.44, p = 0.213, f = 0.25. 4. Discussion Participants’ speed selection results are consistent with the assumption that bounded rationality accounts for drivers’ speed

The present study is the first that provides direct evidence that, in a conflict between velocity and safety, drivers have a higher preference for the option of decelerating compared to the option of accelerating. Previous findings (Schmidt-Daffy, 2012, 2013; Schmidt-Daffy et al., 2013) did not eliminate the alternative interpretation that drivers have a default preference for accelerating which is attenuated upon the onset of a motivational conflict. This interpretation would imply that the rationality of drivers’ speed choice is bounded mainly due to a gain orientation or the underweighting of risks. However, the present findings point to the opposite. Because participants chose a speed that was lower than required for the maximum pay-out, findings rather suggest a tendency to overweight the amount of loss or the accident risk. Thus, the speed choice was in line with findings from general decision-making research indicating that choices under risk are often characterized by loss aversion (e.g., Abdellaoui et al., 2007) and a tendency to avoid risks (Rabin and Thaler, 2001). Interpreting the speed choice results as evidence for bounded rationality assumes that the task of reaching the finish line in time and the task of responding quickly to a traffic hazard provided an adequate basis for estimating the optimal speed for maximum payout. Admittedly, if participants’ capability to avoid a collision with a deer was reduced when they had a free choice of speed, it was reasonable that they drove more slowly than suggested by their performance in the previous task. However, it is rather unlikely that this was the reason for participants’ preference for cautious speeds, given the low number of deer encounters in the task with free speed choice. In contrast, participants had extensive opportunities to evaluate their capabilities during the tasks that were used concurrently to calculate the utilities and disutilities. Because of this congruence, the speed choice results support the assumption that participants did not evaluate the available information in a purely rational way. Results suggest that participants would have achieved higher pay-outs if they had driven faster. Thus, from a financial point of view, it seems that the preference for cautious speeds was disadvantageous for the participants. However, this conclusion does not necessarily apply to other evaluation criteria, for instance the emotional stress during driving and the impact of the trip’s outcome on drivers’ self-esteem and contentment. This has to be considered if one wants to draw conclusions for real driving. The potential loss that is associated with a real accident should not be quantified solely in terms of money. Accidents can involve serious social and psychological consequences for the driver (e.g., Mayou et al., 1993; Bennun and Bell, 1999) including depression, travel anxiety, or a post-traumatic stress disorder. If such non-material consequences are taken into account, choosing a cautious driving speed cannot be considered irrational. Instead, it is probably the best choice most of the time even if the occurrence of a traffic hazard is unlikely and the vehicle insurance would minimize the financial loss. However, what is in doubt here is that such advantageous behaviour is based on a rational choice in the sense that all the potential material, social and psychological consequences are taken into account by the drivers. On the contrary, prospect balancing theory proposes

ELECTRO-

baseline-corrected biosignal

PULSE

DERMAL

conditional probability of passing the finish line

VOLUME

ACTIVITY

conditional probability of a deer collision

AMPLITUDE

-0.6

1.0

0.5

0.8

-0.5

0.8

0.4

0.6

0.3 0.4

0.2

0.2

0.1 0.0

(a)

probability

1.0

0.0 55 60 65 70 75 80 85 90 95 speed in km/h

PVA in arbitrary units

0.6

-0.4

0.6

-0.3 0.4

-0.2

0.2

-0.1 0.0

(b)

probability

M. Schmidt-Daffy / Accident Analysis and Prevention 63 (2014) 49–64

EDL in µS

60

0.0 55 60 65 70 75 80 85 90 95 speed in km/h

Fig. 10. Baseline-corrected changes of the level of electrodermal activity (a) and of the pulse volume amplitude (b). Conditional probabilities for passing the finish line and for colliding with a deer are depicted as a reference.

that drivers include only those outcomes that relate to their currently predominant action goals. It is assumed that the pursuit of these goals is guided by intuition which involves a tendency to avoid losses and a tendency to overweight small risks. The universal validity of these tendencies might explain why loss aversion also occurred in the present study although the consequences of speeding were far less severe than they would have been outside the laboratory. The present study suggests that an intuitive speed selection favours traffic safety. This is consistent with findings from general research into decision-making indicating that intuition often enables highly adaptive behaviour (Gigerenzer, 2007). However, this requires a more precise definition of bounded rationality. According to prospect balancing theory the rationality of drivers’ speed choice is bounded because decision-making is biased by emotional evaluations. However, applying the concept to the resulting decision requires that the evaluation criterion for a rational choice is restricted to a numeric analysis of the material consequences. In the present study this criterion has been applied because it is the most common way to prove loss aversion in decision-making research (e.g., Schmidt and Traub, 2002). However, if one defines a rational choice by its comprehensive benefit within a given environment (ecological rationality, Goldstein and Gigerenzer, 2002), the term bounded rationality is inappropriate to characterize the speed choice predicted by prospect balancing theory. Instead, it would be more appropriate to state that the theory proposes an emotionally adjusted rationality. According to Gigerenzer (2007) the wisdom of intuition is based – at least partially – on the exploitation of brain functions that proved of value throughout the evolutionary history of mankind. A universal selection pressure, that could have shaped such a brain function, is the fact that in conflict situations harm avoidance (e.g. responding to cues indicating a predator) is usually more important for survival than the immediate fulfilment of hedonic needs (e.g. eating or drinking). Gray and McNaughton (2000) proposed a neuronal based emotion system, called the behavioural inhibition system, which detects goal conflicts and contributes to their dissolution by favouring the pursuit of the safe goals. The goal conflict model (Schmidt-Daffy, 2012) transferred this theory to the field of driving behaviour. It predicts that drivers in a velocity-safety conflict tend to prefer lower driving speeds due to the activation of their behavioural inhibition system. This activation might represent the evolved brain function that underlies the bounded rationality of drivers’ speed choice. Whilst prospect balancing theory provides a comprehensive psychological description of decision-making, the

goal conflict model amends a neurobiological explanation of why safe driving speeds are preferred. These psychological and neurobiological levels of explanation are connected by the assumption that goal conflicts cause an increase in the valence of affectively negative stimuli and associations. In previous studies, this negative bias has been concluded from symptoms of anxiety experienced while driving under a velocity-safety conflict (Schmidt-Daffy, 2012, 2013; Schmidt-Daffy et al., 2013). The present study assessed this bias more explicitly by asking participants to evaluate the driving situation with respect to the achievement of their action goals. The results of these assessments are discussed in the following section.

4.2. Negative bias in the evaluation of the speed options The self-report data support the new construct introduced by prospect balancing theory: the subjective efficacy. The subjective efficacy was deduced from participants’ self-reported certainty of achieving travel-related action goals. In line with predictions, these ratings varied in a non-linear fashion with driving speed and by doing so deviated systematically from the corresponding objective probabilities. The observed deviations between subjective certainty and objective probability resemble findings from general research into decision-making indicating that low probabilities are given too much weight whereas high probabilities tend to be incorporated with insufficient weight (Tversky and Kahneman, 1992). In particular, the overweighting of low probabilities manifested itself in the subjective certainty of reaching the finish line. In contrast, the bias of underweighting high probabilities occurred in the subjective certainty of avoiding a collision with a deer. Transferred to the construct of subjective efficacy, these deviations suggest that participants underestimated the efficacy of the acceleration option and overestimated the efficacy of the deceleration option. Both biases are in line with the observed preference for low driving speeds. The certainty ratings also match previous findings from the field of traffic psychology. Results regarding the certainty of reaching the finish line are consistent with time-saving bias (Svenson, 2008, 2009; Peer, 2010). This bias describes the observation that drivers tend to underestimate the gain of time they would achieve by accelerating at low speeds and overestimate the benefit of acceleration at high speeds. Accordingly, participants’ certainty of reaching the finish line increased in a less pronounced manner than the actual probability across low to intermediate driving speeds. At high speeds they were not sure if the speed would be sufficient to

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pass the finish line although the actual probability approximated certainty. Results regarding the subjective certainty of avoiding a collision with a deer are consistent with findings from Fuller et al. (2008b) (see also Lewis-Evans and Rothengatter, 2009). In their study participants reported experiencing risk while judging low driving speeds despite estimating the accident frequency to be zero. Likewise, participants from the current study reported to be uncertain about being able to avoid a deer collision at speeds at which driving was actually safe. The findings of Fuller et al. (2008b) suggest that the deviation that was observed in the present study, indicate a subjective/emotional weighting rather than a misjudgement of probabilities. The certainty ratings indicate that biased evaluations of both positive and negative outcomes might have contributed to the choice of cautious driving speeds. This interpretation is in line with the widely accepted notion that speed choice depends on a trade-off between goals related to velocity and safety (SchmidtDaffy et al., 2013). However, consistent with Rothengatter (1988) and Summala (2007), it can be concluded that models of driving behaviour should be less focused on accident risk (Näätänen and Summala, 1974; Wilde, 1982; Zuckerman, 2007; Koornstra, 2009; Fuller, 2011). The certainty ratings suggest that participants anticipated a deer encounter with a rate of almost 50%. This is in line with the well-known tendency to neglect unbalanced base rates in the evaluation of decision options (Kahneman and Tversky, 1973). In the present study this tendency involved an overestimation of the risk of encountering a hazardous driving situation. Applied to real driving this bias could constitute an additional factor that favours traffic safety. Interestingly, participants of the current study overestimated the probability of a deer encounter although the actual base rate was repeatedly announced at the beginning of the task. This provides further support for the assumption that the certainty ratings incorporated an emotional weighting that goes beyond a mere internal representation of the probability. Finally participants tended to overestimate the impact speed in case of a collision with a deer. This indicates that not only subjective weightings of outcome probabilities but also biased evaluation of the outcome severity might have contributed to the preference for lower driving speeds. Results are consistent with previous findings from traffic psychology indicating that the expected impact speed increases less sharply with increased driving speed than the actual impact speed (Svenson, 2009; Svenson et al., 2012a,b). However, in contrast to these pencil and paper studies, the present driving simulation suggests that this smaller increase is caused by an overestimation of the impact speed at moderate speeds rather than by an underestimation at high speeds. The expected impact speed shows that in both conflict tasks, participants preferred speeds at which they already expected a collision in case of a deer encounter. This contradicts the assumption that drivers seeks to keep the risk beneath the perceptual threshold (the zero risk model, Näätänen and Summala, 1974). The subjective total values combined the estimated subjective efficacies and subjective values to predict drivers’ choice of speed. The total values predicted a speed choice that is significantly lower than required for a maximum pay-out. In line with this prediction participants preferred a lower driving speed in the conflict task with free choice of speed. Thus, results support prospect balancing theory and suggest that the estimated total values were suitable indicators of participants’ decision-making. However, the predicted speed was considerably lower than the actual speed choice. This suggests that the assessment and calculation of the total values overestimated participants’ preference for low driving speeds. On the one hand, this might be explained by the assumption that participants did not rely totally on their intuition but incorporated to

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some extent also objective probabilities and rational considerations into their speed choice (the reasoning decision system, Kahneman, 2003). On the other hand, typical errors of rating scale judgements (e.g. error of central tendency) and the wording of the question (e.g., avoiding a collision vs. causing a collision) might have influenced the accuracy of the estimated total values. In future research this accuracy might be improved by modifying the assessment of the self-report data and adjusting the computation of total values to the observed speed choice. However, the gap between the proposed internal constructs on the one hand and the assessed indicators on the other hand may not be able to be bridged completely. The benefit of prospect balancing theory might be less that of allowing precise predictions about the exact speed that drivers will chose in a particular situation. More importantly, the theory claims to enable accurate predictions about how the interplay of motivational incentives and task demands influence drivers’ speed choice. Thus, the paramount challenge for future studies is to show that prospect balancing theory models these relations more adequately than other theoretical approaches. In addition to the self-report data, physiological measures might help to substantiate the internal variables and processes that are proposed to mediate these relationships.

4.3. Physiological concomitances of drivers’ speed change motivations In the conflict task with prescribed speed ranges, the physiological measures indicated a higher activation of the sympathetic part of the autonomous nervous system on the main runs compared to the trial runs. The key difference between both runs was that only in the main runs could participants win or lose money. Therefore the physiological measures confirm the effectiveness of the motivational condition established to investigate drivers speed choice. An interaction of speed range and run type suggests that bodily arousal increased with velocity while driving under a goal conflict. Because the main effects of speed range were not significant this was probably not a mere velocity effect induced for instance by a more frequent visual stimulation or the increasing pitch of the engine noise. Instead, it might indicate the evaluation of the speed against the background of the current motivational condition. This could provide additional information about the internal processes that guide drivers’ speed-related decision-making. However, further research should seek to experimentally vary the motivational incentives and task demands in order to explore the relations between different components of prospect balancing theory and particular physiological parameters.

5. Conclusion and outlook The present study provides the first clues that prospect balancing theory lends itself to describe drivers’ speed choice. In addition, results confirm that the applied driving tasks were suitable to test the theory within a highly standardized laboratory setting. In future studies, different aspects of the driving task can be experimentally varied in order to examine the interplay of external and internal determinants of speed choice, e.g. trip time, visibility of the road, magnitude of gains and losses, likelihood of a traffic hazard, and the vehicle’s braking performance. In the current study these variables were kept constant in order to initially focus on the relationship between the subjective efficacy and the driving speed. However, future studies should test whether prospect balancing theory allows better predictions of the interplay of these variables than existing models.

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With respect to road safety, it is important to note that in the present study, the participants’ task was restricted to collision avoidance. The potential deer encounter can be considered to be an example of a driving situation in which a driver judges a possible obstacle on the road to be the key threat to the achievement of the safety-related action goal. Other examples of anticipated obstacles might include a child that appears from behind a parked car or a slow vehicle on a rural road just behind a blind summit. In real life, after leaving such a potentially hazardous situation behind, another safety-relevant task demand usually comes to the fore. For instance the driver might approach a curve in which keeping the vehicle on track becomes the key requirement for achieving his goal of accident avoidance. Since steering was not included in the simulation, however, it is more appropriate to consider the study’s results as a selective snapshot of a motivational condition that might occur while driving. In order to study the basic principles of speed choice, restricting the focus to collision avoidance on a straight road has a considerable advantage: It allows the assessment of subjective and physiological indicators for drivers’ speed evaluation with respect to a constant motivational condition. Nevertheless, prospect balancing theory applies to decision making under other driving conditions as well. For instance, while approaching a curve, the theory would predict that the subjective efficacy of deceleration is higher the faster the speed and the smaller the perceived curve radius. On a winding road the subjective efficacy of deceleration might therefore vary constantly depending on the perceived course of the road. It might be challenging to find indicators that allow us to study this continuous adjustment of subjective efficacy. Nevertheless, future studies should confirm the assumption that prospect balancing theory also applies to drivers’ behaviour during more complex and fluctuating task demands. Prospect balancing theory aligns assumptions about drivers’ speed choice with knowledge about risk-related judgments and choice in general. The present study suggests that this approach provides a framework for explaining established biases in drivers’ judgments (Svenson, 2008, 2009; Peer, 2010; Svenson et al., 2012a) and behaviour (Schmidt-Daffy, 2012, 2013; Schmidt-Daffy et al., 2013). Moreover, this approach might contribute to the understanding of inter-individual differences in accident risk. Young drivers more often engage in risky driving activities and have an elevated risk of being involved in speed-related crashes (e.g., Fuller et al., 2008a). Among various factors (Deery, 1999; Ferguson, 2003) this has been ascribed to novice drivers’ deficit in perceiving traffic hazards (Finn and Bragg, 1986). In line with this explanation, prospect balancing theory predicts that bounded rationality cannot favour cautious driving if a risk is not noticed in the first place (at the very least on a non-conscious level of information processing). However, the theory allows for the impact of other factors as well. It can be assumed that young drivers’ action goals tend to differ from those of older drivers. For instance, it is more important for young drivers to conform to the driving style of their peer group (Clark, 1976). If they believe fast and risky driving to be the group’s standard driving style, their action goal related to acceleration might be motivated by the aim of avoiding a loss (e.g. loss of reputation) rather than by the aim of achieving a gain (e.g. gaining admiration). Under this condition loss aversion cannot favour the deceleration option. In the present simulator study mainly young drivers were examined. However, they were given extensive opportunities to become acquainted with the collision risk beforehand. Moreover definite action gaols were induced by financial gains and losses. Thus, it remains an open question whether the present results also apply to less experienced participants and motivational conditions that are more characteristic of young drivers.

Prospect balancing theory, however, also suggests a third explanation for young drivers’ increased crash risk. They might have a deficit in the subjective weighting of probabilities and losses (Deery, 1999; Clarke et al., 2005) as opposed to the assessment of objective risks. This is supported by studies indicating that, in financial choices with a specified amount of risk or known objective values, risk and loss aversion increases with the age of the decision maker (e.g., Johnson et al., 2006; Yao et al., 2011). On average, however, these typical biases are already evident in the decisions of young adults (e.g., Rieger et al., 2011). Concurrently, results of the present study suggest that bounded rationality favours the choice of more cautious speeds also in young drivers—at least if they are adept in the driving task and motivated by financial gains and losses. Future studies might shed light on the factors that affect this decision bias, e.g., by varying participants’ age and previous task experience and investigating the effect of a passenger. Another example of how prospect balancing theory might enhance the understanding of variation in drivers’ accident risk refers to the highly differing number of road fatalities between countries (W.H.O, 2013). Of course, this number significantly depends on factors like population, motorization and economic wealth (Kopits and Cropper, 2005; Elvik et al., 2009). However, if such factors are controlled for, cultural differences regarding the subjective weighting of risks might account for a considerable part of the remaining variance. For instance, there are indications that members of more collectivistic societies are less risk-averse and less sensitive to impending losses (Rieger et al., 2011), probably because in the case of misfortune, they can rely on the help of their social network more than members of individualistic societies (Hsee and Weber, 1999). Thus, during driving their behaviour might be less influenced by the decision biases that are proposed to favour road safety. It is important to note, though, that such cultural differences can influence road safety also on the political level, e.g. via legislation and national investments in road safety. Ultimately, the benefit of a theory of driving behaviour depends on its potential contribution to the improvement of road safety. The present study suggests that the tendency to avoid losses and risks which is well-known from general research into decision-making also applies to the choice of driving speed. Thus, more in-depth knowledge about the factors that influence this tendency could help to evaluate existing safety measures and develop new approaches. With the current state of theory formation the following implications have become apparent: • The concept of subjective efficacy suggests exploring how perceptual features of the road, the environment, and the vehicle influence drivers’ subjective certainty of achieving their dominant action goals. Already a lot of features have been identified that induce drivers to choose a lower driving speed (Martens et al., 1997; Edquist et al., 2009). Their effectiveness was explained as having an influence on drivers’ perception of the current speed and on the perceived accident risks (e.g., Edquist et al., 2009). Prospect balancing theory extends this explanation by proposing that their effect on speed choice is modulated by their perceived relevance for goal achievement. Thus, the safety effect of a particular design might be enhanced by inducing an adequate goal (e.g. a road design that increases the perceived accident risk may be more effective after an accident warning sign compared to a sign warning of a radar speed check). Aside from features that decrease drivers’ certainty of achieving the decelerationrelated action goal (i.e. which increase the perceived accident risk), prospect balancing theory suggests searching for features that enhance the certainty of reaching the acceleration-related action goal (e.g. reduction of the perceived distance to the destination).

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• There are many road safety measures that directly decrease the accident risk (Elvik et al., 2009). Prospect balancing theory gives a more optimistic view of the effectiveness of these measures than many other motivational models of driving behaviour. Since the theory does not assume that drivers align their speed unilaterally to a threshold, target level, or range of subjective risk (e.g., Näätänen and Summala, 1974; Wilde, 1982; Koornstra, 2009), it does not predict that a perceived safety gain is inevitably compensated by more risky behaviour. Instead, compensation does not appear if accident avoidance is currently not the predominant action goal or if the safety measure simultaneously increases drivers’ certainty of achieving velocity-related action goals (for example by providing more opportunities to overtake). • With respect to speed limit enforcement and sanctions (Elvik et al., 2009), prospect balancing theory strongly recommends the consideration of subjective base rates. For instance, increasing the size of speeding fines is predicted to only have a minimal effect if the subjective certainty of a radar control is low. Acknowledgements I would like to thank Klaus Gramann, Manfred Thüring, and Helmut Jungermann for their encouragement and two anonymous reviewers for their useful comments on this paper. Furthermore I would like to acknowledge Hamilton Gross for proof reading the article. References Aarts, L., Van Schagen, I., 2006. Driving speed and the risk of road crashes: a review. Accident Analysis and Prevention 38, 215–224. Abdellaoui, M., Bleichrodt, H., Paraschiv, C., 2007. Loss aversion under prospect theory: a parameter-free measurement. Management Science 53, 1659–1674. Bennun, I.S., Bell, P., 1999. Psychological consequences of road traffic accidents. Medicine, Science, and the Law 39, 167–172. Clark, A.W., 1976. A social role approach to driver behaviour. Perceptual and Motor Skills 42 (1), 325–326. Clarke, D.D., Ward, P., Truman, W., 2005. Voluntary risk taking and skill deficits in young driver accidents in the UK. Accident Analysis and Prevention 37 (3), 523–529. Damasio, A.R., 1994. Descartes’ Error: Emotion, Reason and Human Brain. G.P. Putnam’s and Sons, New York. Deery, H.A., 1999. Hazard and risk perception among young novice drivers. Journal of Safety Research 30 (4), 225–236. Edquist, J., Rudin-Brown, C.M., Lenne, M., 2009. Road Design Factors and Their Interactions With Speed and Speed Limits. Monash University Accident Research Centre, Melbourne, Australia. Elvik, R., Høye, A., Vaa, T., Sørensen, M., 2009. The Handbook of Road Safety Measures, 2nd ed. Elsevier, Amsterdam. Ferguson, S.A., 2003. Other high-risk factors for young drivers—how graduated licensing does, doesn’t, or could address them. Journal of Safety Research 34 (1), 71–77. Finn, P., Bragg, B.W.E., 1986. Perception of the risk of an accident by young and older drivers. Accident Analysis and Prevention 18 (4), 289–298. Fuller, R., 2005. Towards a general theory of driver behaviour. Accident Analysis and Prevention 37 (3), 461–472. Fuller, R., 2011. Chapter 2—driver control theory: from task difficulty homeostasis to risk allostasis. In: Porter, B.E. (Ed.), Handbook of Traffic Psychology. Academic Press, San Diego, pp. 13–26. Fuller, R., Bates, H., Gormley, H., Hannigan, B., Stradling, S., Broughton, P., Kinnear, N., O’Dolan, C., 2008a. The conditions for inappropriate high speed: A review of the research literature from 1995 to 2006. In: Road Safety Research Report 92. Department for Transport, London. Fuller, R., McHugh, C., Pender, S., 2008b. Task difficulty and risk in the determination of driver behaviour. European Review of. Applied Psychology 58, 13–21. Gibson, J.J., Crooks, L.E., 1938. A theoretical field-analysis of automobile driving. American Journal of Psychology 51, 453–471. Gigerenzer, G., 2007. Gut Feelings: the Intelligence of Unconscious. Viking Press, New York. Goldstein, D.G., Gigerenzer, G., 2002. Models of ecological rationality: the recognition heuristic. Psychological Review 109, 75–90. Gray, J.A., McNaughton, N., 2000. The Neuropsychology of Anxiety. Oxford University Press, New York. Harinck, F., Dijk, E.V., Beest, I.V., Mersmann, P., 2007. When gains loom larger than losses: reversed loss aversion for small amounts of money. Psychological Science 18, 1099–1105.

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