Temptations as Impulsivity: How far are Regret and the Allais Paradox from Shoplifting?

Economic Modelling 51 (2015) 551–559

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Temptations as Impulsivity: How far are Regret and the Allais Paradox from Shoplifting? Elias L. Khalil ⁎ Department of Economics, Monash University, Clayton, VIC 3800, Australia

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Article history: Accepted 10 September 2015 Available online 28 September 2015 Keywords: Over-confidence (impulsivity) Under-confidence (compulsivity) Weakness of Will First-Degree Regret-of-Decision Second-Degree Regret-of-Decision Regret-of-State Tragic Regret Present-biased Preferences Self-cheating Cheating of Others Self-Blame Self-Deception Self-Congratulation

a b s t r a c t This paper uses shoplifting as an iconic example of succumbing to temptation, or weakness of will. It proposes that temptation is the outcome of impulsivity—i.e., biased over-confident (suboptimal) belief in success. This proposal challenges the standard literature that portrays temptation as the outcome of present-biased preferences. The payoff of the proposed modeling is that it can easily explain, first, regret, and second, the Allais paradox. Concerning regret, it is nothing but impulsivity-in-reverse: Regretting a rational decision means changing your belief about that decision so that what appeared optimal at the time now appears suboptimal. Concerning the Allais paradox (the certainty effect), it is the outcome of people’s fear of regret. Fear of regret leads people to become over-cautious, using biased under-confident beliefs that lead them to compulsive behavior such as seeking zero-risk options. © 2015 Elsevier B.V. All rights reserved.

1. When the Rich and Famous Are Caught Shoplifting Many people are intrigued when they read news about the rich and famous getting caught shoplifting. Such people, for certain, are not professional thieves. And for certain, the monetary benefit is usually miniscule relative to the expected cost of infamy, shame, and maybe jail time. According to the non-profit National Association for Shoplifting Prevention (based in Melville, New York), most shoplifters act on impulse, i.e., without much planning. In particular:

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▪ ▪ “Shoplifting is often not a premeditated crime. 73 percent of adult and 72 percent of juvenile shoplifters don’t plan to steal in advance.” ▪ “Shoplifters say they are caught an average of only once in every 48 times they steal. They are turned over to the police 50 percent of the time.” ▪ “Approximately 3 percent of shoplifters are “professionals” who steal solely for resale or profit as a business. These include drugaddicts who steal to feed their habit, hardened professionals who steal as a life-style and international shoplifting gangs who steal

⁎ Tel.: +61 3 9905 2407; fax: +61 3 9905 5476. E-mail address: [email protected]. URL: http://www.eliaskhalil.com.

http://dx.doi.org/10.1016/j.econmod.2015.09.016 0264-9993/© 2015 Elsevier B.V. All rights reserved.

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for profit as a business. “Professional” shoplifters are responsible for 10 percent of the total dollar losses.” “The vast majority of shoplifters are “non-professionals” who steal, not out of criminal intent, financial need or greed but as a response to social and personal pressures in their life.” “The excitement generated from “getting away with it” produces a chemical reaction resulting in what shoplifters describe as an incredible “rush” or “high” feeling. Many shoplifters will tell you that this high is their “true reward,” rather than the merchandise itself.” “Most non-professional shoplifters don’t commit other types of crimes. They’ll never steal an ashtray from your house and will return to you a $20 bill you may have dropped. Their criminal activity is restricted to shoplifting and therefore, any rehabilitation program should be “offense-specific” for this crime.” “Habitual shoplifters steal an average of 1.6 times per week.”1

The core thesis of this paper, which aims to account for these observations, is that it is better to view temptations, weakness of will, or what economists call “dynamic inconsistency”, as the outcome of impulsivity. There is a huge empirical literature in psychology on impulsivity which 1

http://www.shopliftingprevention.org/ (checked last: 27 August 2015).

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cannot be reviewed here [DeYoung, 2010]. As defined here, impulsivity is the result of acting according to biased beliefs in the direction of optimism or inflated expectation of success. Shoplifters realize, at a deep level, that they are taking unjustified risks—and this may explain why they take them. It is not (or not only) the consumption, but mainly the thrill that they enjoy upon learning that they have won and beaten the odds. The enjoyment of this thrill, the force behind impulsivity, may also explain the occasional gambling at casinos, where people know that the expected value of a $1 bet is far below the $1 at hand. The view proposed here challenges the received literature, which regards temptations or dynamic inconsistency as the outcome of biased time preferences. Such bias is supposedly the outcome of a biological tendency to favor present consumption excessively, i.e., favoring in excess of what is permitted by the usual linear discounting of future rewards. Prior to detailing the core thesis, two clarifications are in order: 1. This paper defines the term “temptation” as the psychological state that prompts a person to succumb to temptation. Most people are not tempted, or at least not tempted on a daily basis, to shoplift. To be tempted to shoplift is already to be in a state that strongly predisposes one to shoplift. Since the phenomenon of resistance to temptation is not in focus here, for convenience, this paper uses the terms “temptation” and “succumbing to temptation” interchangeably. 2. This paper assumes that when one is tempted, one is choosing a suboptimal option. This does not mean that the action is sub-subrational in the sense that the underpinning preferences are inconsistent. On the contrary, when one is tempted, the preferences are consistent. They are consistent when one obeys the most essential axioms of rationality, viz., the transitivity axiom and the completeness axiom. One might also include local non-satiation if one demands unique optimum, rather than multiple optima. So, while preferences are consistent, one my still fail to execute, for whatever reason, the optimum choice. One may instead, that is, chose a suboptimal choice. One reason is temptation. When the actual action fails to obey the optimum, as in temptation, the action does not obey a non-essential axiom of rationality, viz., the weak axiom of revealed preference (WARP) [Samuelson, 1938]. For WARP, as long as one has chosen bundle A over bundle B, it means definitely that one prefers A over B. WARP does not allow for the possibility that one’s action may deviate from one’s true preference. If we want to identify temptation, we need to reject WARP, which this paper does. But how should we model temptations-as-impulsivity? This paper starts with shoplifting as the iconic example of impulsivity. Then it exhibits the payoff of the proposed model in explaining two other phenomena that, so far, have been viewed as having no connection to temptations or dynamic inconsistency: 1) regret; and 2) the Allais paradox. It will become clear that regret is impulsivity-in-reverse and the Allais paradox arises from the fear of regret, i.e., the fear of impulsivityin-reverse. But first, we need to examine the received literature. 2. Review of the Literature and the Proposed Approach 2.1. Review With some differences in emphasis, the economics literature has concluded that temptation or weakness of will is about hyperbolic discounting, and that such discounting is the outcome of “presentbiased preferences” [Laibson, 1997; O’Donoghue and Rabin, 1999, 2001; Gul and Pesendorfe, , 2001, 2004a,b] or the outcome of dual-selves in conflict [Thaler and Shefrin, 1981; Fudenberg and Levine, 2006].2 This view 2 The dual-self approach should not be confused with the multiple-self approach. The term “multiple-self” term is better reserved for the approach of Amartya Sen, George Akerlog, Rachel Kranton, Roland Bénabou and Jean Tirole. This approach stresses that agents are motivated by a sense of identity, self-image, or moral compass that transcend utilitarian calculation [Elster, 1986].

can be traced back to the pioneering work of the psychologist Ainslie, 1975, 1992, 2001, 2005. Ainslie generalized Herrnstein’s matching law to model inconsistent bias as the outcome of hyperbolic discounting. Ainslie and the economists generally treat preferences over consumption goods (tastes) as if they are the reason for temptation. These approaches usually, but not universally, justify such a view on the assumption that humans are programmed by an emotional-biological system that favors—beyond the linear discounting factor—present consumption over future consumption. Other present-biased preference and dual-self approaches do not appeal to biology or visceral explanations [Benhabib and Bisin, 2004; Brocas and Carrillo, 2008; Köszegi and Rabin, 2009; Fudenberg and Levine, 2006; O’Donoghue and Rabin, 1999, 2001]. Nonetheless, insofar as they start with the set of tastes, they offer, first, an ad hoc and, second, narrow view of temptations. First, the received literature, and its emphasis on taste, is ad hoc because it presumes that the phenomenon is the outcome of tastes. Then, one may ask, why do some people have present-biased tastes with respect to some goods—but not other goods? To start with tastes raises more question than it answers. Second, the received literature is narrow because it misses the connection between temptation and impulsive behavior in general. Such impulsive behavior is not only about temptations that directly undermine the future self, as in self-cheating behavior ranging from overeating to under-saving and slackening. It is also about temptations that indirectly undermine the future self, as in cheating of others ranging from shirking to shoplifting. If one starts with tastes, in particular present-biased tastes, one can only see cases that directly undermine the future self—overlooking the important cases of cheating others as belonging to the same class of phenomenon. 2.2. The Proposed Approach Instead of starting with biased time preferences, this paper commences with biased beliefs and explores their implications. In particular, the proposed approach explains succumbing to temptation in terms of beliefs biased in the direction of optimism, i.e., suboptimal overconfidence: the present self systematically over-estimates his or her probability of success in undertaking a risky action. Interestingly, Ainslie also recognized the role of over-confidence, but only as a way to explain why people impose on themselves what can be called “internal constraints,” i.e., rules or devices that prevent them from even being exposed to temptations. According to Ainslie, people impose internal constraints on themselves because they are aware of their overconfidence and do not believe that they will succumb to temptation on only one occasion. They are ever afraid that a single deviation from the internal constraint would place them on a slippery slope leading to further suboptimal choices. This paper takes Ainslie, 1992 insight a bit further and argues that temptations, and not only internal constraints, can be traced to over-confidence. The proposed biased beliefs approach in explaining temptations has many payoffs. Aside from offering a unified framework for the analysis of cheating others (such as in shoplifting) and shirking [see Khalil, 2016 a, b], it can explain, first, regret, and, second, the Allais paradox. Regret, as defined here, is not about self-blame that prompts one to learn from experience about the probability distribution of the states of nature. Some researchers confuse the two beyond the issue of terminology. For instance, Bourgeois-Gironde, 2010 discusses regret in the sense of how economists studied it in the 1980s, i.e., as an explanation of the certainty effect [see Loomes and Sugden, 1982]. But Bourgeois-Gironde sets up an experiment that really concerns self-blame, i.e., how the emotion of blame (which calls “regret”) is rational since it teaches people not to ignore relevant signals. In this paper, regret is an emotion that arises from changing one’s beliefs of what was known in the past, so that an act (the focus of regret) that appeared optimal at the time of decision, now appears as suboptimal, i.e., the person should not have taken it. This change in beliefs about one’s past acts amounts to tipping

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the probability of success in a biased way in the direction of overconfidence. As detailed below, regret is nothing but impulsivity-inreverse. Also, as discussed below, such a definition of regret differs from regretting one’s state of being, such as being sick or healthy. Further, as clarified below, such a definition differs from tragedy, where one’s regret did not actually involve any choice. Concerning the Allais paradox, discussed below, it is the outcome of the fear of regret. People who anticipate regret become overcautious and compulsive, i.e., biasing their beliefs in the direction of under-confidence. Such over-cautious behavior prompts people to choose suboptimal options as long as they involve zero-risk, what is known as the “certainty effect” or the Allais Paradox [Machina, 1987; Quiggin, 1993; Oliver, 2003; Kahneman and Tversky, 1979; Shafir et al., 2008]. This over-cautious behavior is the mirror image of impulsivity. The proposed modeling of temptation as impulsivity, and hence as arising from biased beliefs rather than from biased time preferences, can be falsified empirically in three different ways. First, it can be falsified if one can show that shoplifting is not the result of biased beliefs, but rather the outcome of biased time preferences. Second, it can be falsified if one can show that regret is not impulsivity-in-reverse, but rather the outcome of some kind of strange preferences. Third, it can be falsified if one can show that the Allais paradox is not the mirror image of impulsivity, arising from fear of regret. But how could rational agents act impulsively, i.e., according to suboptimal, biased beliefs? This paper proposes a principal-agent approach that is somewhat different from the one used in the literature to discuss weakness of will [e.g., Thaler and Shefrin, 1981; Fudenberg and Levine, 2006]. In the approach proposed here, the principal does not stand for a future self that is in conflict with a present self (agent). Rather, the principal (calm self) is rational; it is in constant struggle with the agent (impulsive self). Each self—the principal and the agent—tries to take over what is called in this paper the “individual.” While both try to advance the interest of the individual, each self operates according to different probabilities concerning risk. If we put this conflict in terms of preferences, the principal takes care of the interest of the present and future selves, the agent takes care also of the interest of both, but the present self acts impetuously to the point of endangering the interest of the future self. So the principal can be better seen as the calm “parent” or “guardian” that tries to tame the impetuous child (the agent). Such a view is called here the “nested principalagent framework.” It is “nested” because what sets them apart are not the objective function, but rather the fact the parent’s (principal) view already includes the agent’s view, but tempers it with non-myopic assessment. In this nested principal-agent framework, the agent and principal are in conflict of who will be in control, i.e., send decisions to the organism, called here the "individual." The term "individual" stands for the actual choices taken. Such choices can be controlled by the calm self or by the impulsive self. The "calm self" or the "impulsive self" acts as a genetic code, and for the gene to express "itself," it needs the organic machinery of muscles, locomotion, etc., to undertake action–i.e., it needs the individual. When the individual is under the control of the impulsive self, the individual would experience the consequent emotions of self-blame, regret, and other emotions discussed below. Likewise, if the individual is under the command of the calm self, the individual would avoid such emotions. But what sets the principal apart from the agent? The principal here is the calm (non-myopic) decider that chooses according to unbiased beliefs in the sense that they are optimal given the information. The unbiased (impartial) beliefs can be mistaken—but only can be known through leaning through Bayesian updating. In contrast to the principal, the agent is the impulsive (myopic) decider that chooses according to biased beliefs in the sense that such beliefs cannot be justified given

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the information. For example, the shoplifter-as-agent has an unjustified belief that he or she is unlikely to be caught, whereas the shoplifter-asprincipal has a justified belief that there is a high likelihood of being caught. Both the calm decider and the impulsive decider (the principal and the agent) have the same objective function or preference set— i.e., the agent does not suffer from biased time preferences. If the (impulsive) agent is unrestrained by external or internal constraints or rules, the individual would operate according to the choices of the impulsive agent. That is, the individual would act according to the impulsive choices of the agent, ignoring the choices recommended by the calm self (principal). It is assumed here, though, that there are no naïve individuals. Even when the impulsive self dominates individuals, they “deeply” know that the calm self (principal) has been suppressed. But without restraints, the principal has no power to nullify or negate the domination of the impulsive self. So, we can define a myopic action, amounting to succumbing to temptation, as the action undertaken by the impulsive decider (agent). Again, the calm decider (principal) is aware of the agent’s suboptimal act, which differs from the standard principal-agent problem [Holmström, 1982]. To note, the received models of intra-individual conflict also make the action non-hidden [Thaler and Shefrin, 1981; Fudenberg and Levine, 2006]. However, the proposed theory, again, does not trace the intraindividual conflict to differences in the objective function. The proposed theory traces the intra-individual conflict—i.e., the conflict between the impulsive agent and the calm principal—to beliefs about risk assessment. 3. The Nested Principal-Agent Framework 3.1. Primitives Let us designate C as the set of consumption options, S the set of states of the world, P the set of beliefs concerning the probability distribution on S, and F the set of actions. F = CS á la Leonard Savage, 1954, i.e., it is the set of actions concerning consumption options in different states. In any state Si, an act f gives the consumption outcome f(Si). The choice of act f is based on two facts: the C set (consumption options or tastes) and the P set (beliefs about probability distributions). The individual is composed of two deciders, a principal with rankorder pp over F and an agent with rank-order pa over F. The difference in their rank order does not arise from differences in C, but from differences in P. That is, while both deciders have identical consumption indices over C, they choose different actions because they have different probability beliefs, pp and pa, over S respectively. These two deciders suggest different actions that can be represented by subjective expected utility. The principal’s belief (pp) concerning how likely action f over C will succeed is optimal, i.e., fully based on available information prior to action. That is, the principal’s belief is identical to the Bayesian belief, pp τ ¼ pb τ where pbτ is Bayesian-based probability at time τ. In contrast, the agent’s belief (pa) concerning the success of action f over same C is ex ante suboptimal in the sense of being flawed or impulsive, of which the principal is aware. That is, by definition, pa τ N pp τ While the principal tries to persuade the individual not to listen to the agent, usually via reflection and internal rules, it is supposed here that, in the act of temptation, the individual becomes controlled by the agent and acts according to the agent’s paτ rather than according to the principal’s ppτ.

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Now, we are ready to define temptations: Temptations: A temptation arises when the individual suffers from a conflict between the principal’s and the agent’s decision over F: An act gτ is tempting when compared to act fτ if f τ N p g τ and g τ N a f τ where N p and N a are the expected utility representation of the action dominated by either the agent or the principal. When we have no restraints, the agent’s choice rather than the principal’s choice dominates the individual’s action. The principal can punish the individual with selfblame, the ultimate weapon of the principal.

ramifications, this paper proposes a series of models that share these common assumptions: a. the principal and the agent have time-consistent tastes, i.e., neither of them experience quasi-hyperbolic discounting; b. the principal and the agent are risk-neutral; c. the principal and the agent have perfect and common information about all costs and benefits; d. the model consists of two periods–so, when the injured party retaliates against the agent’s transgression, the agent cannot retaliate in return. The retaliation of the injured party can be interpreted as punishment meted out by a third party, such as the criminal justice system, against which the agent cannot retaliate in return.

3.2. Discussion While the principal’s choice can be called the “first moment” of decision, the agent’s choice can be named the “second moment.” Both moments have identical arrangements over C, i.e., but have different choices over F because they have different assessments over P. This difference arises from the myopic nature of the second moment of the impulsive decider, in contrast to the non-myopic nature of the first moment of the calm decider. For instance, with regard to the probability of success of shoplifting, the agent (impulsive decider) operates according to a higher probability than the probability of the principal (calm decider). It is possible that the agent’s probability, in in some cases, is lower than the principal’s probability. Such cases generate excessively cautious behavior, which is suboptimal. Such behavior does not amount to temptation. It rather amounts to the opposite, the Allais paradox, as shown below. The (upward) bias of the agent’s belief makes the second moment decision “appears as if” it is tilted in favor of the wellbeing of the present self at the expense of the future self—which explains why the standard approaches model the conflict between the two deciders as originating from a supposed difference in the objective functions of the present and future selves. But why does the agent over-estimate the probability of success of cheating? One possible reason is that the agent is blinded by overconfidence. Neuroscientists have confirmed that neural processes in the brain, for most people, are biased towards beliefs of their own success, i.e., over-estimating the probability of success concerning their own situation compared to what is warranted by their experience [e.g., Sharot, 2011]. Psychologists have long noted the phenomenon of over-confidence [Moore and Healy, 2008]. They have actually identified different variations and deviations from over-confidence, calling them “selectivity in memory,” “confirmation bias,” “positive outcome bias,” “valence effect,” “wishful thinking,” “attributional bias,” “positive selfimage,” and “self-serving bias” [Matlin and Stang, 1978; Nickerson, 1998; Babcock and Loewenstein, 1997; Santos-Pinto and Sobel, 2005]. This paper takes over-confidence as a fact and, hence, does not go into analyzing its origins [see Khalil, 2016b]. It suffices to state briefly that over-confidence seems to stem from a simple asymmetry, on which Adam Smith long ago dedicated three chapters in The Theory of Moral Sentiments [Smith, 1976, pp. 92-108]: While agents tend to attribute success more to ability than to luck, they tend to attribute failure more to luck than to ability. This asymmetry, the origin of over-confidence, does not escape the principal—which explains the rift between the principal and the agent. The principal seeks to resolve the problem of overconfidence, i.e., the inner conflict between the principal and the agent, by erecting internal, ethical rules. Such a strategy, although of great importance, falls also outside the scope of this paper [Khalil, 2016b].

4. Cheating Others: To Shoplift or to Desist? The proposed model of shoplifting can be seen as representative of other phenomena of cheating others such as bribe taking, reneging on contracts, misrepresentation of facts (dishonesty), or, in short, social dilemmas in general [see Khalil, 2016 a, 2016b]. The contracts can be commercial agreements between individuals and firms, where opportunism and defection are well defined and punished. They can also be international treaties among countries on trade policies, carbon emissions, use of the oceans, to nuclear proliferation, and the treatment of prisoners of war. The decision making under focus involves two moments. The first moment is undertaken by the principal (calm decider) to assess what is the commitment as expressed in the implicit/explicit contract or treaty. Such a commitment is assumed in this paper to define what is the best (optimal) choice or action. The agent, in the role of the impulsive decider, makes decisions with regard to the second moment. The impulsive decider is also the one who actually carries out the action. The principal decides on whether to shoplift, given the benefit gained from the stolen good and the cost of punishment, given the probability of getting caught/punished. If the shopkeeper catches the shoplifter, the individual’s present self would be denied the stolen good and, further, the individual’s future self would incur a penalty in the form of imprisonment or stigma. The individual has to make sure that, before shoplifting or violating the commitment to observe the rights of others,3 the expected cost incurred by the future self does not exceed, after allowing for intertemporal discounting, the expected benefit enjoyed by the present self. The agent maximizes, over two periods, expected utility subject to a probability distribution p(s) of the states of the world s ∈ S. For simplicity, we assume s = {0,1} where p(0) or, in short, p is the probability of getting away with the consumption—whether it is the shoplifted good or the bribe, and p(1) or (1-p) is the probability of getting caught. In the first period, the present self enjoys the shoplifted item, if the agent shoplifts or undertakes the consumption in general. In the second period, the future self bears the consequences of getting caught, if the agent shoplifted or undertook the consumption in the first period. So, the principal, whose identity is suppressed, chooses from a binary decision (D), shoplifting or no-shoplifting, in order to maximize the objective function: Max UðDÞ ¼ ppτ fUðx1τ jDÞg – δð1 ‐ppτ ÞfUðx2τþ1 jDÞg – Uðx3τ jDÞ –appτ fUðx1τ jDÞg where D ¼ 0; 1

3.3. Assumptions

where D = 1 denotes the choice of avoidance of shoplifting; D = 0 denotes shoplifting; U(.) is the utility function, which takes the usual shape: τ is time; pp is the principal’s assessment of the probability of getting away with the shoplifted item; x1 is the shoplifted item; x2 is the penalty inflicted on the future self, which includes imprisonment,

To distinguish it from the standard approach, the proposed theory is expressed in a “nested principal-agent” framework. To explore its

3 Actually, in the proposed model, it does not matter if there are recognized rights. The proposed model can be seen as a theory of rights or commitment to such rights.

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ostracism, and restitution (x1); δ is the intertemporal discount factor (which can be ignored); x3 is transaction cost of theft; and a denotes the altruistic bond (usually 0 ≤ a b 1) between the principal and the injured party. To note, the altruistic bond and transaction cost simply raise the cost of shoplifting without influencing the analysis. Nonetheless, stated briefly, they are included to highlight two points. First, the altruistic bond is analytically identical to transaction cost. Second, the altruistic bond is analytically distinct from one’s commitment to observe the rights of others (justice), which basically stems from self-interest considerations. To simplify the manipulation, let us use the following notation:

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how temptations can become actual behavior. The individual may succeed, without the help of precommitments, in resisting the temptation. This possible success seems to depend on two critical parameters: First, the temptation intensity parameter (σ) measures how seductive power of the temptation, σ ¼ ðpa τ –wÞ=ðw−pp τ Þ

Bτ ðDÞ ≡ Uðx1τ jDÞ Cτþ1 ðDÞ ≡ Uðx2τþ1 jDÞ TCτ ðDÞ ≡ Uðx3τ jDÞ

So, the seductive power is greater the greater is the gap between the two probabilities. In order to determine whether an individual would succumb to temptations, we would need greater specifications of social factors, such as peer group pressure, as well as personal factors such as personality type (θ). Although such specification is outside the aim of this paper, one may hypothesize that, if one takes social factors as given, an individual would succumb to temptation when,

B stands for benefit, C for cost, TC for transaction cost of theft. Then, the maximization problem can be expressed as,

σ≥θ 17

Max UðDÞ ¼ pp τ Bτ ðDÞ–δð1 ‐pp τ ÞCτþ1 ðDÞ– TCτ ðDÞ–app τ Bτ ðDÞ where D ¼ 0; 1

Otherwise, the individual resists the temptation. 5. Cheating Oneself

Statement 1. The principal chooses D = 0 (shoplifting) if and only if ppτ ≥ w (where w is a critical parameter). Otherwise, the principal chooses D = 1 (avoidance of shoplifting). Proof. From the above objective function, the principal chooses D = 0 (shoplifting) if U(0) ≥ U(1), i.e., ð1‐aÞpp τ Bτ ð0Þ– δð1 ‐pp τ ÞCτþ1 ð0Þ– TCτ ð0Þ ≥ ð1‐aÞpp τ Bτ ð1Þ– δð1 ‐pp τ ÞCτþ1 ð1Þ– TCτ ð1Þ pp τ ≥ w ≡ δ½Cτþ1 ð0Þ‐Cτþ1 ð1Þ þ TCτ ð0Þ–TCτ ð1Þ δ½Cτþ1 ð0Þ−Cτþ1 ð1Þ þ ð1−aÞ½Bτ ð0Þ−Bτ ð1Þ

We can define the necessary condition for temptation-as-impulsivity as the principal’s decision to desist from shoplifting, i.e., when pp τ b w: Otherwise, the principal recommends shoplifting— as in the case of professional thieves—and hence there is no raison d'être for impulsivity to steal to arise. But under the necessary condition, the principal recommends against shoplifting or bribe taking. In this case, there is a possibility that the agent (impulsive self) might be tempted to steal, going against the decision of the principal (the calm self). This possibility arises because the agent maximizes a slightly different function: Max UðDÞ ¼ paτ Bτ ðDÞ– δð1 ‐paτ ÞCτþ1 ðDÞ– TCτ ðDÞ–apaτ Bτ ðDÞ where D ¼ 0; 1 pa is the agent’s assessed probability (prior) of success of avoiding detection if he or she shoplifts. Statement 2. The agent chooses D = 0 (shoplifting) if and only if paτ ≥ w. Otherwise, the agent chooses D = 1 (avoidance of shoplifting). Proof. see proof of Statement 1 Statement 2 provides another necessary condition for the emergence of the temptation to shoplift. Now, we can define temptation to shoplift as the combination of both necessary conditions, i.e., pp τ b w pa τ ≥ w This paper uses temptations and succumbing to temptations interchangeably. A brief word, though, can be said about the conditions of

5.1. To Regret or Not to Regret? 5.1.1. Why Regret? A few economists have started recently to analyze the emotions of anxiety or thrill that arise from the anticipation of an uncertain event. For example, Caplin and Leahy, 2001 try to incorporate such emotions within the standard expected utility framework. They probably could extend their revised “psychological” model to explain the emotion of either regret or elation that emerges upon revelation of the uncertain event. These pre- and post-event emotions are disregarded by standard expected utility theory. Psychologists [e.g., Kahneman, 1994; Kahneman et al., 1997] accord such emotions an equal place to the primary emotions that the agent captures. To be clear, for standard expected utility theory, one’s utility depends on the expected or the average outcome—i.e., one’s utility is independent of the length of time prior to the uncertain event as well as independent of the regret/elation that one may experience once the uncertainty is resolved [Pope, 1985]. Let us focus here only on regret—the analysis offered here can be extended, mutatis mutandis, to the question of elation. The emotion of regret, by definition, arises once the uncertainty about the state of the world is resolved. Loomes and Sugden, 1982 are the first to bring regret to the front of economic theory. However, they do not explain regret. They rather take it as a datum and proceed to use it in order to account for the certainty effect (Allais paradox), as discussed below. Although Sugden [Starmer and Sugden, 1993] later retracted his theory of regret, this paper accepts the basic thesis of Loomes and Sugden, 1982. Namely, agents who anticipate regret may try to avoid it, and such avoidance engenders the Allais paradox. This paper, however, does not take regret as datum. Regret is, rather, analyzed as impulsivity-in-reverse. That is, regret is not an inevitable emotion that arises whenever the ex post outcome of action is disappointing—irrespective of whether the ex ante action was optimal or not. As defined here, regret is rather a suboptimal emotion arising only when the ex ante action was rational, but was frustrated by an unfortunate state of nature. As such, regret amounts to succumbing to impulsivity, similar to the impulsivity of shoplifting discussed above. The only difference is that with regret, the impulsivity is retroactive or in reverse. To be clear, the proposed view of regret is limited to one kind of regret, what is called here “regret-of-decision.” Regret-of-decision, it is proposed here, should be delineated from “regret-of-state”: Regret-of-Decision:The emotional pain that arises when one compares the outcome of action f in a state of the world S1 with an

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outcome of a different action, g, but under the same state of the world, S1.Regret-of-State:The emotion of “wishful thinking,” i.e., the pain that arises when one compares the outcome of action f in a state of the world S1 with an outcome of same action (f), but under a different state of the world, S2. Regret-of-state is probably the source of risk-aversion [see Bell, 1982; Quiggin and Bell, 1983; Bell, 1985]. If so, it is about preferences and falls outside the scope of this paper. Further, regret-of-state is about how one assesses one’s utility in comparison to another state of nature: One may contrast one’s health to the better health of a friend; one may contrast one’s wealth to the higher wealth of a cousin; or one may contrast one’s accomplishment to one’s own self-expections. Such comparison would give one some ache and even the feelings of envy. On the other hand, one may compare one’s condition to people with worse conditions or one’s accomplishments to a much lower expectation of one’s self. Such comparison would give one some feelings of comfort and even hope. This amounts to how one assesses one’s fortune relative to other imagined conditions–similar, to use the cliché, of whether one sees the glass as half-full or half-empty. Such comparisons are basically about the framing effect, which which occasions context-dependent utility. Thus, the framing effect, and hence regret-of-state, is totally unrelated to regret-of-decision, the subject matter that is related to temptations and impulsiveness. Besides regret-of-decision and regret-of-state, there is still another kind of regret, which we may call “tragic regret,” that is also outside the focus of this paper.4 Consider the situation of Sophie in William Styron, 1979 novel, Sophie's Choice. Captured by the Nazis and transported to a concentration camp, on arrival there Sophie is forced by a sadistic Nazi doctor to choose one of her two beloved children to be immediately put to death in the gas chambers, as the condition for saving the other. Sophie chooses her daughter, Eva, to die, thereby saving her son. She lives the rest of her life in an agony of “tragic regret.” But Sophie’s tragic regret is not that she wishes that she had chosen the boy to die instead of the girl. Rather, she regrets having made any choice at all—when in fact she did not have a chance to refuse to make a choice. Her lamentation over something that she did not even had a choice is indicative of a “collapse of will”, and it can be analysed as a failure of the completeness axiom, which ensures that our preferences form a partially ordered set. The failure of the completeness axiom entails that one cannot choose: the options cannot be meaningfully compared with each other. It follows that a decision under such circumstances cannot be assessed as either rational or irrational. Economic theory is ill-equipped to deal with such decisions.5 5.1.2. Self-Blame and Self-Congratulation Let us assume that an individual faces two alternative actions: taking the automobile (Aa) or taking the train (At) to visit an uncle. We have two states of the world: safe-weather conditions (Ss) and dangerousweather conditions (Sd), with corresponding probabilities, (ls) and (1-ls). Let us assume that there would be zero likelihood of automobile or train accidents under Ss, while there would be π a and π t probabilities for, respectively, automobile and train accidents under Sd. Let us suppose that π a N π t, i.e., train travel is safer on average than automobile travel. But people find automobile travel more convenient than train travel. Let us assume that the expected injury or illness (I) from accident is the same for both means of transportation. Further, let us suppose that 4

I owe Steven Gardner the term “tragic regret.” In regret-of-decision, the focus of this paper, we assume there is no collapse of will. We rather focus on the weakness of will or impulsiveness. While the collapse of will amounts to the negation of the completeness axiom [see Khalil, 1997], the weakness of will amounts to the negation of the weak axiom of revealed preference (WARP). WARP can be negated while the completeness axiom, and the whole consistent ordering of preferences, is kept intact. 5

the weather condition is revealed only after one takes the train or the automobile. The principal takes the binary decision (A) to maximize the following function, Max UðAÞ ¼

 p ls Ba ðAÞ – ð1 ‐ls Þ a CðAÞ ‐ fls Bt ðAÞ – ð1 ‐ls Þπp t CðAÞg A ¼ Aa ; At

where C is cost of the injury; π pa is the principal’s assessment of probability of automobile accident given the action is automobile driving; and π pt is the principal’s assessment of probability of train accident given the action is train riding. Statement 5. The principal chooses A = Aa (automobile) if and only if (π pa - π pt) ≤ v (where v is some arbitrary critical parameter). Otherwise, the principal chooses A = At (train). That is, the necessary condition for temptation-as-impulsivity is the principal’s decision to take the train, ðπp a ‐πp t Þ N v: As in the previous cases, to establish the second necessary condition for temptation-as-impulsivity, we need to find out the condition under which the agent would find it optimal to take the automobile instead of the train. The agent takes the binary decision (A) to maximize the following function, Max UðAÞ ¼ fls Ba ðAÞ – ð1 ‐ls Þπp a CðAÞg ‐ fls Bt ðAÞ – ð1 ‐ls Þπp t CðAÞg A ¼ Aa ; At where π aa is the agent’s assessment of probability of automobile accident given the action is automobile driving; and π at is the agent’s assessment of probability of train accident given the action is train riding. Statement 6. The agent chooses A = Aa (automobile) if and only if (π aa - π at) ≤ v (where v is the critical parameter). Otherwise, the principal chooses A = At (train). Statement 6 provides the second necessary condition for temptation, i.e., taking the automobile. So, the combination of the two necessary conditions of temptation-as-impulsivity (taking the automobile), ðπ p a −p t Þ Nv ðπ a a ‐πa t Þ v Let us assume that the individual is dominated by the agent and makes the impulsive choice (automobile), i.e., favor convenience and maybe thrill over safety. Whether an accident arises or not, the principal will ex ante punish the agent with self-blame. Such emotion is rational because it is one way through which the principal tries to restrain the impulsive self from dominating the individual [see Bourgeois-Gironde, 2010]. The self-blame will be more acute if the weather turns out to be bad and an accident takes place. But the fact that the self-blame becomes stronger after an actual accident should not obfuscate the matter and lead us to conflate self-blame with regret. Self-blame would still rise before the revelation of state of nature, and would still persist even if one was lucky and there was no bad weather and no accident. That is, Self-Blame: Self-blame is an emotion that arises after an impulsive act, but prior to the revelation of the state of nature and hence the discovery of whether one was lucky or unlucky. That is, self-blame is the ex ante recognition that the agent has, in the first period, controlled the individual’s action against the recommendation of the principal. Of course, the principal’s recommendation is based on the optimal estimate of probability. It is usually inaccurate. Nonetheless, it should be treated as the best ((π pa - π pt) b v).

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The other case is when the individual acts impulsively, but luckily escaped harm. Here, self-blame arises, but would usually appear as weak. Weak self-blame may give an opportunity for the agent, if the agent takes a full control of the individual, to invoke self-deception. The agent here would be involved in self-deception—which is made easier as a result of the accidental success. One may define “self-congratulation” as the emotion of self-deception arising to suppress self-blame: Self-Congratulation: Self-congratulation is the emotion that the agent invokes to suppress principal’s message of self-blame. The suppression is usually made easier if the impulsive act has luckily succeeded, i.e., the person escaped harm. In The Theory of Moral Sentiments, Adam Smith, 1976, pp. 92-108] dedicated three chapters to decrying the phenomenon of selfcongratulation. He emphatically called such sentiments, i.e., purely arising from what her calls “fortune,” “irregular.” He lamented the nature of human affairs such that humans so easily succumb to judging others on the basis of the “empire of fortune”—rather than judgments solely based on ex ante optimal decisions. For Smith, it is utterly dismaying that spectators are prone to applaud and cheer an action simply on the basis of its consequences, rather than on the basis of reasoning. 5.1.3. Regret-of-Decision Let us suppose the contrary: The principal takes command of the individual and, hence, the individual acts calmly, refusing to submit to the impulsivity of the impetuous agent. In this case, the individual takes the train because (πpa - πpt) N v. Here, there is no reason for self-blame to arise. The individual rather experiences self-respect for acting according to the decision of the principal. Let us suppose that, after taking the train, dangerous-weather conditions (Sd) is revealed. Further, let us suppose that the train encounters an accident as a result of the weather and the person on the train gets hurt. Let us suppose that, for purely random shock, none of the people who took the automobile were hurt. Here, the individual, comparing oneself to the ones who took the automobile and escaped injury, may regret the decision of taking the train. We can define such regret-ofdecision as the emotion that arises as the outcome of the revelation of the state of nature. In such revelation, as epitomized in the case of dice tossing or coin flipping, there is no learning about probabilities of the state of nature. Such probabilities are known a priori, i.e., without the appeal to experience. But the person still regrets the decision. It could happen that the person learns something new about the probabilities in hindsight. Still such learning, if used incorrectly, would lead to regret-of-decision. In both cases, i.e., whether learning is relevant or not, regret-ofdecision amounts to the belief that the principal was not rational after all.6 The principal must have used, as he or she tries to be careful in excess, inaccurate probabilities, i.e.,   p‐expost πp‐expost a −π t ≤ v If the principal had used the supposedly the more accurate probabilities, the principal would have recommended taking the automobile and, hence, save the individual from the accident. This allows us to distinguish first-degree from second-degree regretof-decision. In first-degree, there are no new probabilities to be learned in hindsight—as in the case of coin tossing or dice throwing. So, we have here three wrongs in this case. First, the person experiencing the regretof-decision supposes that he or she has learned from the experience, which is impossible. Second, the person, therefore, manufactures a 6 Regret, in this light, seems contrary to self-deception—although both involves the rewriting of facts. In self-deception, the person tries to cover up wrong decisions in order to make them appear as correct [Khalil, 2015]. In regret-of-decision, the person re-represent correct decisions in order to make them appear as incorrect.

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new set of probabilities. Third, the person inserts such set retroactively into the ex ante decision process, which makes the rational decision of the individual look as if it was suboptimal. In the second-degree regret-of-decision, it is possible for learning to arise in hindsight. That is, the person, as a result of the experience, upgrades his or her belief using Bayes’ rule. But such person, as in the first-degree, inserts such learning retroactively, which makes the rational decision of the individual look as if it was suboptimal. What is common to both degrees of regret-of-decision is the insertion of new probabilities as if they should have been known ex ante, which cannot be the case. That is, the individual who, in general, surrenders to regret-of-decision deposits what arises ex post, irrespective of whether it is substantiated, “as if” it was available ex ante, but ignored. In this manner, the individual who surrenders to regret-of-decision thinks that it is (legitimate) to indulge in self-blame, when it cannot be the case. In effect, the person involved in regret-of-decision, irrespective of the degree, uses upgraded probabilities and insert them retroactively. This is similar to impulsivity, but in reverse: In impulsivity proper, as in shoplifting, the individual uses the upgraded probabilities of the impulsive agent before the action/event. In impulsivity-in-reverse, i.e., regret-of-decision, the individual also uses the upgraded probabilities, irrespective of whether they turned out to be correct, but after the action/event. 5.2. To Cling to Certainty/Security or to Take Risks? In the above analysis, regret-of-decision amounts to impulsivityin-reverse. We can take this analysis further by noticing that people who anticipate regret-of-decision, can become fearful of ever taking risks. Such people prefer, ceteris paribus, activities with zero risk, where there is no chance for regret to arise, even if it entails violating some logical principles in reasoning. Such a violation of the principles of reasoning, entailed by zero-risk choices, amounts to compulsive behavior that is the mirror-image of impulsive behavior. The principle of logical reasoning that is being violated here is called the independence axiom (or the “sure thing principle”). The possibility of such a violation was first suggested, in a hypothetical manner, by Maurice Allais in a 1953 paper, and hence became known as the “Allais paradox.” It was later confirmed in laboratory experiments [Kahneman and Tversky, 1979; Tversky and Kahneman, 1981; Machina, 1987]. The Allais paradox arises when agents choose an option that with lower expected utility than another option if that option is offered with zero risk. For instance, if agents are offered two risky options, $3 with 25% probability and $4 with 20% probability, they choose the riskier option, viz., the $4 option over the $3 option, because this maximizes their payoff. But if they are offered $3 with 100% probability and $4 with 80% probability, they reverse themselves and choose the zero-risk option, viz., the $3 option over the $4 option. You can Such a violation of logical reasoning, where one should not cling to choices only because they involve zero-risk, undermines expected utility theory as formulated by Savage, 1954]: The relative attractiveness of the $4 to the $3 is the same in both situations. The only difference is that one option avoids any risk of loss.7 To be clear, while some experiments confirm the Allais paradox, many others do not. For instance, Adam Oliver, 2003] shows that 14 out of 38 subjects in an experiment concerning health outcomes, rather than monetary outcomes, violate the independence axiom as predicted 7 This highlights a similarity between ambiguity aversion (Ellsberg paradox) and the certainty effect (Allais paradox). According to the rational principle of insufficient reason, choices should not be determined solely on whether the probabilities are ambiguous rather than definite. In ex ante reasoning, one should be indifferent between ambiguous and non-ambiguous risks. But agents, who are afraid of regret-of-decision, choose and ready to pay extra for non-ambiguous risk, which is analogous to choosing suboptimal no-risk choices. So, the ambiguity effect, which violates the independence axiom, is very close to the Allais paradox.

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by the Allais paradox. However, once asked to explain their choices, the offered explanations were reasonable in the sense that they did not assert that they were after zero-risk. But, to be clear, the offered explanations could be anything. The fact is that they violated the independence principle. Sharoni Shafir et al., 2008] show more clearly why the Allais paradox is not so robust. They show that subjects exhibit the “reverse certainty effect” when the subjects are given more accuracy concerning the outcomes. In situations when outcomes are subject to noise and vagueness, the same agents are more likely to be subject to the certainty effect. This finding confirms that people resort to certitude, i.e., avoid recklessness and act with compulsivity, when the outcomes are vague. The vagueness apparently enhances the specter of regret-of-decision. That is, there seems to be an intricate link between regret-of-decision and the Allais paradox. The Allais paradox expresses fear of regret-of-decision, as if the agent that takes control of the individual is under-confident. This can be expressed in terms of under-estimating the likelihood of success, or in our case of accidents, over-estimating the risk of automobile traveling. Expressed formally, the Allais paradox arises under the combination of two necessary conditions, ðπp a ‐πp t Þ b v ðπa a ‐πa t Þ ≥ v Here, the calm self (principal) decides that automobile travel is safe, while the compulsive self (agent) determines, opposite of the impulsive, that automobile travel is too risky. The compulsive agent may also determine that train travel, relative to staying home, is also too risky, and opts for zero-risk options such as staying home. The fear of regret-of-decision usually involves mild compulsivity such as checking four or five times if the door is locked, the stove is turned off, and the hands are clean. Such behavior can become pathological, what is known as the obsessive-compulsive disorder (OCD). But mild cases of compulsivity, the focus here, can still be of interest as examples of the anti-thesis of impulsivity-in-reverse (regret-ofdecision). So, the Allais paradox can be modeled as mild compulsivity that is based on under-confidence-biased beliefs. This would be symmetrical to the above model of shoplifting, which is based on overconfidence-biased beliefs. 6. Conclusion This paper proposes that temptations are best understood as arising from biased beliefs, and biased in the direction of inflated likelihood of success. This challenges the standard approach that temptations are the result of biased time preferences. To understand biased beliefs, this paper uses a nested principal-agent framework. The principal and the agent have identical preferences. They differ only with respect to their beliefs. The principal’s beliefs are optimal in the sense of being the best given the information. The agent’s beliefs are suboptimal; they are based on over-estimation of the likelihood of success. Consequently, the agent recommends to the individual impulsive (suboptimal) actions, while the principal recommends to the individual optimal decisions. It is outside the scope of this paper to lay the conditions that determine whether the individual is commanded by its principal or its agent. It rather lays out the conditions under which impulsive behavior arises. The payoff of the biased belief approach resides in shedding light on three apparently unrelated phenomena: shoplifting, regret-of-decision, and the Allais paradox. In the case of shoplifting, the paper shows that shoplifting is the iconic example of impulsivity. Here the impulsive agent takes over the individual and prompts him or her to act according to ex anger suboptimal probability. In the case of regret-of-decision, the paper demonstrates that regret-of-decision is impulsivity-in-reverse. Here the impulsive agent takes over the individual and prompts him

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