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Social discounting: The effect of outcome uncertainty
Behavioural Processes 85 (2010) 24–27
Contents lists available at ScienceDirect
Behavioural Processes journal homepage: www.elsevier.com/locate/behavproc
Social discounting: The effect of outcome uncertainty ´ Jerzy Osinski University of Warsaw, Faculty of Psychology, Stawki 5/7, 00-183 Warsaw, Poland
a r t i c l e
i n f o
Article history: Received 19 May 2009 Received in revised form 12 May 2010 Accepted 24 May 2010 Keywords: Amount effect Emotional closeness Reciprocity Sharing Social discounting Trust
a b s t r a c t The purpose of the study was to determine the lowest hypothetical amount a participant would keep for himself/herself, preferring it over a reward that he/she would have shared with another individual representing various levels of past reciprocation. Other manipulated aspects were: emotional closeness of the receiver (close vs. distant person), procedure for deciding on how to share the reward (mutual decision vs. decision made by partner) and amount of reward to be shared (PLN 494 vs. PLN 49,400). It was found that preference for the reward to be shared increased as a function of reciprocity, and that it is higher when sharing with an emotionally close person, when the decision does not depend entirely on the partner, and when sharing a small reward. The effect of the level of reciprocity was the smallest when the reward was shared with an emotionally close person and the decision was mutual. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Rachlin and Raineri (1992) proposed to relate the idea of discounted value to a reward divided among a group of people. For example, a reward of $100 shared with nine other people after being averaged relative to the number of people has an “objective” value of $10 (Rachlin and Raineri, 1992). However, subjective value of a reward may differ depending on the degree to which an individual perceives himself to be separate from the group, e.g. it may be higher when sharing with family members. Social discounting as a function of social distance’s effect on value of a reward was investigated in a series of studies conducted by Rachlin and Jones. Participants were asked to choose between a changing amount of reward for themselves only and an equal fixed-amount reward for themselves and another person (Jones and Rachlin, 2006) or a fixed reward for another person only (Rachlin and Jones, 2008a,b). The purpose of that procedure was to identify the amount of reward only for themselves that participants would be willing to forgo another person could benefit. As expected, selfishness of choices made by participants increased as a function of social distance. Rachlin and Raineri (1992) originally assumed that the very act of sharing may alter the reward’s subjective value. In the present study their method was therefore used to assess the subjective value of a reward shared with another person when the amount of that reward to be assigned to the participant is not predetermined. Choosing a reward to be shared in such circumstances is associated with uncertainty (the result may be either worse or better than choosing a reward for oneself only). The purpose of the study
E-mail address: [email protected]. 0376-6357/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.beproc.2010.05.010
was to answer the following questions: (1) whether the subjective value of a reward which must be shared is affected by the receiver’s level of reciprocity (defined as the participant’s previous experience from interactions with that receiver), social distance between participant and receiver (defined in terms of emotional closeness), method of dividing the reward between participant and receiver (mutual decision vs. decision made by partner) and amount of the reward; (2) whether the effect of the receiver’s level of reciprocity on the subjective value of a shared reward depends on social distance, how the reward is shared and its amount. 2. Materials and methods The study employed a mixed, between- and within-subject design. The amount of the reward was taken into account as a between-subjects factor, and the other independent variables as within-subject factors. 2.1. Participants Participants were 102 full-time and extramural students of Warsaw’s colleges (mean age = 24.38 years, SD = 7.06 years), 50 females and 52 males. 2.2. Materials The rate of social discounting was measured using a set of questionnaires. Each participant received a set of four questionnaires covering all combinations of independent variables: (1) close person/partner decides, (2) close person/mutual decision, (3) distant person/partner decides, and (4) distant person/mutual decision.
J. Osi´ nski / Behavioural Processes 85 (2010) 24–27
The sequence of questionnaires varied between sets. Instructions in combinations (1) and (4) were as follows (the other two combinations are derived from these two): (1) Imagine you have created a list of ten people who are emotionally close to you (e.g. members of your immediate family), whom you have helped in various ways over the past several years. People in this list are ordered by their willingness to return a favour. Person number 1 always reciprocated for your help, while person number 10 never did so. You do not need to write the list down, you only need to imagine it. On the following six pages you will be asked to make hypothetical choices between “option A” and “option B”. • Option A will always represent a certain amount of money for you exclusively. • Option B – a certain amount of money to be divided between you and a specific person on your list. Remember that the other person will decide how to use the money. (4) Imagine you have created a list of ten people who are not emotionally close to you (e.g. acquaintances, but not friends), whom you have helped in various ways over the past several years. People in this list are ordered by their willingness to return a favour. Person number 1 always reciprocated for your help, while person number 10 never did so. You do not need to write the list down, you only need to imagine it. On the following six pages you will be asked to make hypothetical choices between “option A” and “option B”. • Option A will always represent a certain amount of money for you exclusively. • Option B – a certain amount of money to be divided between you and a specific person on your list. Remember that you will decide together how to use the money. Each questionnaire contained six pages with thirty alternative choices arranged in the following manner: in the left hand column option A – reward for oneself only, and in the right hand column option B – reward shared with one person whose degree of reciprocity, i.e. the rank on the imaginary list, varied from sheet to sheet. On the successive pages of the questionnaire, it was the first-, second-, fourth-, sixth-, eighth- and tenth-ranked person, respectively. The values of the reward were expressed in Polish currency (PLN). At the time the study was conducted, the exchange rate of dollar to Polish zloty was 1:2.20. In the left hand column, the amounts were ordered from smallest to largest. The right hand column contained a constant value of the reward to be shared. In the small reward version, the following values of the reward were used for option A: PLN 0.49; 2.47; 4.94; 9.88; 19.76; 29.64; 39.52; 49.40; 74.10; 98.80; 123.50; 148.20; 172.90; 197.60; 222.30; 247.00; 271.70; 296.40; 321.10; 345.80; 370.50; 395.20; 419.90; 444.60; 454.48; 464.36; 474.24; 484.12; 489.06; 494.00. Option B was a fixed amount of PLN 494. In the large reward version, the following amounts were used for option A: PLN 49.50; 247; 494; 988; 1976; 2964; 3952; 4940; 7410; 9880; 12,350; 14,820; 17,290; 19,760; 22,230; 24,700; 27,170; 29,640; 32,110; 34,580; 37,050; 39,520; 41,990; 44,460; 45,448; 46,436; 47,424; 48,412; 48,906; 49,400, and PLN 49,400 for option B. Here are some sample choices from the first page of the small rewards version of the questionnaire: 1.
A:
PLN 0.49 for oneself
B:
2.
A:
PLN 2.47 for oneself
B:
29.
A:
PLN 489.06 for oneself
B:
30.
A:
PLN 494 for oneself
B:
PLN 494 to be shared with the first person from the list PLN 494 to be shared with the first person from the list PLN 494 to be shared with the first person from the list PLN 494 to be shared with the first person from the list
25
Table 1 Mean and standard error values for index of subjective value of a reward to be shared (the ratio of the lowest amount a participant would keep for themselves to the amount to be shared) depending on the reciprocity level. Reciprocity level
1 (highest) 2 4 6 8 10 (lowest)
Subjective value of a reward to be shared Mean
SE
0.728 0.664 0.588 0.495 0.415 0.338
0.021 0.020 0.020 0.021 0.022 0.022
Participants were asked to select one option for each pair. The aim of the procedure was to estimate the lowest amount that the participant would keep for himself/herself, preferring it over the reward that he/she would have shared with one other person. This amount (referred to as the indifference point) was considered the estimated, subjective value of the reward shared (small – PLN 494, large – PLN 49,400) with the person of a given rank in the reciprocation list (rank 1, 2, 4, 6, 8, 10) and for a given degree of emotional closeness (emotionally close or distant person) and conditions for making the decision about using the reward shared (decided by the other person or decision made together). 2.3. Procedure Participants received a booklet containing the questionnaires for measuring the rate of social discounting. The small and large amount versions of the questionnaires were assigned randomly. The questionnaires were completed in the presence of the investigator, who encouraged subjects to ask questions and provided explanations. There was no time limit for completing the questionnaires. 3. Results The index of the relative subjective value of a reward shared was computed for each reciprocity level (the ratio of the lowest amount a participant would keep for themselves, i.e. indifference point, to the amount to be shared). This ratio was then subjected to a MANOVA taking into account the reciprocity level as a withinsubjects factor. The analysis revealed a strong effect of the level of reciprocity (F(5,90) = 56.533, p < .001, partial eta squared = 0.758, see Table 1). Helmert contrast tests (comparing the mean from each measurement with the mean from subsequent measurement) yielded significant differences between all reciprocity levels. In order to test the effects of other variables, the rate of discounting was calculated using the method proposed by Myerson et al. (2001). This method involves computing the area under the curve obtained by connecting successive points representing the subjective values of the reward to be shared for successive values of the discounting factor (here: reciprocity level). The area under the curve (AUC) is inversely proportional to the rate of discounting. The AUC index was subjected to a 2(emotional closeness) × 2(decision-making conditions) × 2(amount of the reward) MANOVA. The analysis demonstrated a significant effect of all independent variables. The reward shared had a higher subjective value when sharing with an emotionally close person (F(1,95) = 147.629, p < .001, partial eta squared = 0.611) when the decision on how to use the reward was to be made together (F(1,95) = 71.392, p < .001, partial eta squared = 0.432) and for a small reward (F(1,95) = 3.281, p < .05, partial eta squared = 0.034). No interactions between variables were found. Mean values for individual levels of independent variables are shown in Fig. 1.
26
J. Osi´ nski / Behavioural Processes 85 (2010) 24–27
Fig. 2. Effect of interaction between the procedure for deciding on how to use the reward to be shared and emotional closeness on the steepness index. Fig. 1. Mean values of the area under the curve (AUC) for each combination of emotional closeness, procedure for deciding on how to use the reward to be shared and reward amount.
The AUC index reflects two types of effects: (1) decrease in the subjective value of a reward prompted by having to share it with another person and (2) decrease in the value of a reward relative to partner’s reciprocity level. In order to obtain a measure of the discount curve steepness (i.e. the effect associated only with reciprocity), the area under the curve was calculated by normalizing the value of reward shared for successive reciprocity levels relative not to the amount to be shared, but the subjective value of the reward for the first level of reciprocity. The steepness index was subjected to a 2(emotional closeness) × 2(decision-making conditions) × 2(amount of the reward) MANOVA. The effect of reward amount was not significant (F(1,95) = 0.773; n.s.). The analysis revealed an effect of interaction between emotional closeness and decision-making conditions (F(1,95) = 4.945, p < .05, partial eta squared = 0.049). The analysis of simple effects using t-test for dependent samples showed that when sharing with a close person, the procedure for making the decision affects curve steepness (t(100) = 6.364, p < .001; greater steepness when decision is made by partner), while in the situation of sharing with a distant person, the procedure for making the decision has no statistically significant effect (t(97) = 1.049, n.s.). Furthermore, the analysis demonstrated that when decision is mutual, emotional closeness affects the rate of discounting (t(99) = 4.635, p < .001; greater steepness when decision is made by a distant person), but has no statistical significance when it is the partner who decides how the reward is to be shared (t(97) = 0.717, n.s.). Fig. 2 presents the interaction effect. Goodness of fit of the hyperbolic model to medians of relative values of indifference points for the six levels of the reciprocity factor (i.e. disregarding the undiscounted value) varied from R2 = 0.500 to R2 = 0.959, depending on the level of the independent variable. As seen in Table 2, the linear function offered a better fit to empirical data.
ness index carries no information whether the subjective value of a reward is high or low) was relatively unaffected by the other variables (see Fig. 2). The receiver’s level of reciprocity had the smallest effect on the value of a reward shared with an emotionally close person when the decision how to share it was to be mutual, i.e. in the condition where the choice of a shared reward carried the lowest risk. Participants’ choices were to a large degree determined by other variables that may have affected the perception of the risk associated with choosing a shared reward: the procedure for making the decision and emotional closeness. Subjective value of reward measured by AUC index was higher when the decision how to share the reward was mutual and, similarly to the results obtained by Rachlin and Jones (2008a,b) in their research on social discounting, when sharing with a close person. Rachlin and Jones (2010) reported a parallel effect of social distance in the dictator and ultimatum games. The effect of reward amount proved to be weak, though statistically significant. The rate of discounting expressed by the AUC index was lower for small amounts, which indicates the presence of the reversed amount effect reported for discounting of uncertain rewards (Green et al., 1999). This result can also be explained in terms of risk associated with choosing a reward to be shared. In the case of large rewards, the risk may be perceived as greater, which in turn should reinforce the preference for individual reward at amounts proportionally lower than is the case for smaller rewards. A reversed amount effect was also found for choices made in the dictator and ultimatum games (Rachlin and Jones, 2010). The effect Table 2 Goodness of fit (R2 ) of the discounting function to medians of the relative values of indifference points (the ratio of the lowest amount a participant would keep for themselves, to the amount to be shared) for individual levels of independent variables. The regression model was fitted to the six discounted values (i.e. disregarding the undiscounted value = 1). Proportion of variance explained (R2 ) by the model
4. Discussion One of the important factors having an effect on the choice of shared reward in the present study was uncertainty of outcome. Consequently, the results can be interpreted in terms of trust. As expected, choices made by participants were determined by the receiver’s level of reciprocity. The effect of the level of reciprocity measured by the steepness index (showing how the perceived value of a reward to be shared with individuals representing successive levels of reciprocity changes relative to the reward shared with the person ranked first in the reciprocation ranking; the steep-
Emotional closeness Close person Distant person
Hyperbolic
Linear
0.948 0.500
0.953 0.993
Procedure of deciding how to use the reward to be shared Partner decides 0.951 0.984 Mutual decision 0.864 0.991 Reward amount Small – PLN 494 Large – PLN 49,400
0.959 0.772
0.997 0.992
J. Osi´ nski / Behavioural Processes 85 (2010) 24–27
was markedly stronger for the ultimatum game, which could be explained by the uncertainty of the game’s outcome. Participants may have assumed that receivers would accept offered amounts of high absolute value even if they represented a relatively small part of the initial endowment. The explanation in terms of perceived risk associated with choosing a shared reward is consistent with the interpretation proposed by Rachlin (2000), which refers to perceiving one’s interests as common with another person’s benefit. Both emotional closeness and reciprocation facilitate that process. It is possible that making a decision together has similar connotations, even though the results of the present study are inconclusive in that respect. It is worth mentioning in conclusion that the variables positively associated with seeing common interests may be predicted on the basis of evolutionary concepts, e.g. the inclusive fitness theory (Hamilton, 1964) and reciprocal altruism theory (Trivers, 1971). Acknowledgement The research was supported by a grant BST 134008 from the Faculty of Psychology, University of Warsaw.
27
References Green, L., Myerson, J., Ostaszewski, P., 1999. Amount of reward has opposite effects on the discounting of delayed and probabilistic outcomes. J. Exp. Psychol. Learn. 25, 418–427. Hamilton, W.D., 1964. The genetical evolution of social behaviour II. J. Theor. Biol. 7, 17–52. Jones, B.A., Rachlin, H., 2006. Social discounting. Psychol. Sci. 17, 283–286. Myerson, J., Green, L., Warusawitharana, M., 2001. Area under the curve as a measure of discounting. J. Exp. Anal. Behav. 76, 235–243. Rachlin, H., 2000. The Science of Self-Control. Harvard University Press, Cambridge, 220 pp. Rachlin, J., Jones, B.A., 2008a. Altruism among relatives and non-relatives. Behav. Process. 79, 120–123. Rachlin, J., Jones, B.A., 2008b. Social discounting and delay discounting. J. Behav. Decis. Making 21, 29–43. Rachlin, J., Jones, B.A., 2010. The extended self. In: Madden, G.J., Bickel, W.K. (Eds.), Impulsivity: The Behavioral and Neurological Science of Discounting. American Psychological Association, Washington DC, pp. 411–431. Rachlin, H., Raineri, A., 1992. Irrationality, impulsiveness, and selfishness as discount reversal effects. In: Loewenstein, G.F., Elster, J. (Eds.), Choice Over Time. Russell Sage Foundation, New York, pp. 93–118. Trivers, R.L., 1971. The evolution of reciprocal altruism. Q. Rev. Biol. 46, 35–57.
Contents lists available at ScienceDirect
Behavioural Processes journal homepage: www.elsevier.com/locate/behavproc
Social discounting: The effect of outcome uncertainty ´ Jerzy Osinski University of Warsaw, Faculty of Psychology, Stawki 5/7, 00-183 Warsaw, Poland
a r t i c l e
i n f o
Article history: Received 19 May 2009 Received in revised form 12 May 2010 Accepted 24 May 2010 Keywords: Amount effect Emotional closeness Reciprocity Sharing Social discounting Trust
a b s t r a c t The purpose of the study was to determine the lowest hypothetical amount a participant would keep for himself/herself, preferring it over a reward that he/she would have shared with another individual representing various levels of past reciprocation. Other manipulated aspects were: emotional closeness of the receiver (close vs. distant person), procedure for deciding on how to share the reward (mutual decision vs. decision made by partner) and amount of reward to be shared (PLN 494 vs. PLN 49,400). It was found that preference for the reward to be shared increased as a function of reciprocity, and that it is higher when sharing with an emotionally close person, when the decision does not depend entirely on the partner, and when sharing a small reward. The effect of the level of reciprocity was the smallest when the reward was shared with an emotionally close person and the decision was mutual. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Rachlin and Raineri (1992) proposed to relate the idea of discounted value to a reward divided among a group of people. For example, a reward of $100 shared with nine other people after being averaged relative to the number of people has an “objective” value of $10 (Rachlin and Raineri, 1992). However, subjective value of a reward may differ depending on the degree to which an individual perceives himself to be separate from the group, e.g. it may be higher when sharing with family members. Social discounting as a function of social distance’s effect on value of a reward was investigated in a series of studies conducted by Rachlin and Jones. Participants were asked to choose between a changing amount of reward for themselves only and an equal fixed-amount reward for themselves and another person (Jones and Rachlin, 2006) or a fixed reward for another person only (Rachlin and Jones, 2008a,b). The purpose of that procedure was to identify the amount of reward only for themselves that participants would be willing to forgo another person could benefit. As expected, selfishness of choices made by participants increased as a function of social distance. Rachlin and Raineri (1992) originally assumed that the very act of sharing may alter the reward’s subjective value. In the present study their method was therefore used to assess the subjective value of a reward shared with another person when the amount of that reward to be assigned to the participant is not predetermined. Choosing a reward to be shared in such circumstances is associated with uncertainty (the result may be either worse or better than choosing a reward for oneself only). The purpose of the study
E-mail address: [email protected]. 0376-6357/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.beproc.2010.05.010
was to answer the following questions: (1) whether the subjective value of a reward which must be shared is affected by the receiver’s level of reciprocity (defined as the participant’s previous experience from interactions with that receiver), social distance between participant and receiver (defined in terms of emotional closeness), method of dividing the reward between participant and receiver (mutual decision vs. decision made by partner) and amount of the reward; (2) whether the effect of the receiver’s level of reciprocity on the subjective value of a shared reward depends on social distance, how the reward is shared and its amount. 2. Materials and methods The study employed a mixed, between- and within-subject design. The amount of the reward was taken into account as a between-subjects factor, and the other independent variables as within-subject factors. 2.1. Participants Participants were 102 full-time and extramural students of Warsaw’s colleges (mean age = 24.38 years, SD = 7.06 years), 50 females and 52 males. 2.2. Materials The rate of social discounting was measured using a set of questionnaires. Each participant received a set of four questionnaires covering all combinations of independent variables: (1) close person/partner decides, (2) close person/mutual decision, (3) distant person/partner decides, and (4) distant person/mutual decision.
J. Osi´ nski / Behavioural Processes 85 (2010) 24–27
The sequence of questionnaires varied between sets. Instructions in combinations (1) and (4) were as follows (the other two combinations are derived from these two): (1) Imagine you have created a list of ten people who are emotionally close to you (e.g. members of your immediate family), whom you have helped in various ways over the past several years. People in this list are ordered by their willingness to return a favour. Person number 1 always reciprocated for your help, while person number 10 never did so. You do not need to write the list down, you only need to imagine it. On the following six pages you will be asked to make hypothetical choices between “option A” and “option B”. • Option A will always represent a certain amount of money for you exclusively. • Option B – a certain amount of money to be divided between you and a specific person on your list. Remember that the other person will decide how to use the money. (4) Imagine you have created a list of ten people who are not emotionally close to you (e.g. acquaintances, but not friends), whom you have helped in various ways over the past several years. People in this list are ordered by their willingness to return a favour. Person number 1 always reciprocated for your help, while person number 10 never did so. You do not need to write the list down, you only need to imagine it. On the following six pages you will be asked to make hypothetical choices between “option A” and “option B”. • Option A will always represent a certain amount of money for you exclusively. • Option B – a certain amount of money to be divided between you and a specific person on your list. Remember that you will decide together how to use the money. Each questionnaire contained six pages with thirty alternative choices arranged in the following manner: in the left hand column option A – reward for oneself only, and in the right hand column option B – reward shared with one person whose degree of reciprocity, i.e. the rank on the imaginary list, varied from sheet to sheet. On the successive pages of the questionnaire, it was the first-, second-, fourth-, sixth-, eighth- and tenth-ranked person, respectively. The values of the reward were expressed in Polish currency (PLN). At the time the study was conducted, the exchange rate of dollar to Polish zloty was 1:2.20. In the left hand column, the amounts were ordered from smallest to largest. The right hand column contained a constant value of the reward to be shared. In the small reward version, the following values of the reward were used for option A: PLN 0.49; 2.47; 4.94; 9.88; 19.76; 29.64; 39.52; 49.40; 74.10; 98.80; 123.50; 148.20; 172.90; 197.60; 222.30; 247.00; 271.70; 296.40; 321.10; 345.80; 370.50; 395.20; 419.90; 444.60; 454.48; 464.36; 474.24; 484.12; 489.06; 494.00. Option B was a fixed amount of PLN 494. In the large reward version, the following amounts were used for option A: PLN 49.50; 247; 494; 988; 1976; 2964; 3952; 4940; 7410; 9880; 12,350; 14,820; 17,290; 19,760; 22,230; 24,700; 27,170; 29,640; 32,110; 34,580; 37,050; 39,520; 41,990; 44,460; 45,448; 46,436; 47,424; 48,412; 48,906; 49,400, and PLN 49,400 for option B. Here are some sample choices from the first page of the small rewards version of the questionnaire: 1.
A:
PLN 0.49 for oneself
B:
2.
A:
PLN 2.47 for oneself
B:
29.
A:
PLN 489.06 for oneself
B:
30.
A:
PLN 494 for oneself
B:
PLN 494 to be shared with the first person from the list PLN 494 to be shared with the first person from the list PLN 494 to be shared with the first person from the list PLN 494 to be shared with the first person from the list
25
Table 1 Mean and standard error values for index of subjective value of a reward to be shared (the ratio of the lowest amount a participant would keep for themselves to the amount to be shared) depending on the reciprocity level. Reciprocity level
1 (highest) 2 4 6 8 10 (lowest)
Subjective value of a reward to be shared Mean
SE
0.728 0.664 0.588 0.495 0.415 0.338
0.021 0.020 0.020 0.021 0.022 0.022
Participants were asked to select one option for each pair. The aim of the procedure was to estimate the lowest amount that the participant would keep for himself/herself, preferring it over the reward that he/she would have shared with one other person. This amount (referred to as the indifference point) was considered the estimated, subjective value of the reward shared (small – PLN 494, large – PLN 49,400) with the person of a given rank in the reciprocation list (rank 1, 2, 4, 6, 8, 10) and for a given degree of emotional closeness (emotionally close or distant person) and conditions for making the decision about using the reward shared (decided by the other person or decision made together). 2.3. Procedure Participants received a booklet containing the questionnaires for measuring the rate of social discounting. The small and large amount versions of the questionnaires were assigned randomly. The questionnaires were completed in the presence of the investigator, who encouraged subjects to ask questions and provided explanations. There was no time limit for completing the questionnaires. 3. Results The index of the relative subjective value of a reward shared was computed for each reciprocity level (the ratio of the lowest amount a participant would keep for themselves, i.e. indifference point, to the amount to be shared). This ratio was then subjected to a MANOVA taking into account the reciprocity level as a withinsubjects factor. The analysis revealed a strong effect of the level of reciprocity (F(5,90) = 56.533, p < .001, partial eta squared = 0.758, see Table 1). Helmert contrast tests (comparing the mean from each measurement with the mean from subsequent measurement) yielded significant differences between all reciprocity levels. In order to test the effects of other variables, the rate of discounting was calculated using the method proposed by Myerson et al. (2001). This method involves computing the area under the curve obtained by connecting successive points representing the subjective values of the reward to be shared for successive values of the discounting factor (here: reciprocity level). The area under the curve (AUC) is inversely proportional to the rate of discounting. The AUC index was subjected to a 2(emotional closeness) × 2(decision-making conditions) × 2(amount of the reward) MANOVA. The analysis demonstrated a significant effect of all independent variables. The reward shared had a higher subjective value when sharing with an emotionally close person (F(1,95) = 147.629, p < .001, partial eta squared = 0.611) when the decision on how to use the reward was to be made together (F(1,95) = 71.392, p < .001, partial eta squared = 0.432) and for a small reward (F(1,95) = 3.281, p < .05, partial eta squared = 0.034). No interactions between variables were found. Mean values for individual levels of independent variables are shown in Fig. 1.
26
J. Osi´ nski / Behavioural Processes 85 (2010) 24–27
Fig. 2. Effect of interaction between the procedure for deciding on how to use the reward to be shared and emotional closeness on the steepness index. Fig. 1. Mean values of the area under the curve (AUC) for each combination of emotional closeness, procedure for deciding on how to use the reward to be shared and reward amount.
The AUC index reflects two types of effects: (1) decrease in the subjective value of a reward prompted by having to share it with another person and (2) decrease in the value of a reward relative to partner’s reciprocity level. In order to obtain a measure of the discount curve steepness (i.e. the effect associated only with reciprocity), the area under the curve was calculated by normalizing the value of reward shared for successive reciprocity levels relative not to the amount to be shared, but the subjective value of the reward for the first level of reciprocity. The steepness index was subjected to a 2(emotional closeness) × 2(decision-making conditions) × 2(amount of the reward) MANOVA. The effect of reward amount was not significant (F(1,95) = 0.773; n.s.). The analysis revealed an effect of interaction between emotional closeness and decision-making conditions (F(1,95) = 4.945, p < .05, partial eta squared = 0.049). The analysis of simple effects using t-test for dependent samples showed that when sharing with a close person, the procedure for making the decision affects curve steepness (t(100) = 6.364, p < .001; greater steepness when decision is made by partner), while in the situation of sharing with a distant person, the procedure for making the decision has no statistically significant effect (t(97) = 1.049, n.s.). Furthermore, the analysis demonstrated that when decision is mutual, emotional closeness affects the rate of discounting (t(99) = 4.635, p < .001; greater steepness when decision is made by a distant person), but has no statistical significance when it is the partner who decides how the reward is to be shared (t(97) = 0.717, n.s.). Fig. 2 presents the interaction effect. Goodness of fit of the hyperbolic model to medians of relative values of indifference points for the six levels of the reciprocity factor (i.e. disregarding the undiscounted value) varied from R2 = 0.500 to R2 = 0.959, depending on the level of the independent variable. As seen in Table 2, the linear function offered a better fit to empirical data.
ness index carries no information whether the subjective value of a reward is high or low) was relatively unaffected by the other variables (see Fig. 2). The receiver’s level of reciprocity had the smallest effect on the value of a reward shared with an emotionally close person when the decision how to share it was to be mutual, i.e. in the condition where the choice of a shared reward carried the lowest risk. Participants’ choices were to a large degree determined by other variables that may have affected the perception of the risk associated with choosing a shared reward: the procedure for making the decision and emotional closeness. Subjective value of reward measured by AUC index was higher when the decision how to share the reward was mutual and, similarly to the results obtained by Rachlin and Jones (2008a,b) in their research on social discounting, when sharing with a close person. Rachlin and Jones (2010) reported a parallel effect of social distance in the dictator and ultimatum games. The effect of reward amount proved to be weak, though statistically significant. The rate of discounting expressed by the AUC index was lower for small amounts, which indicates the presence of the reversed amount effect reported for discounting of uncertain rewards (Green et al., 1999). This result can also be explained in terms of risk associated with choosing a reward to be shared. In the case of large rewards, the risk may be perceived as greater, which in turn should reinforce the preference for individual reward at amounts proportionally lower than is the case for smaller rewards. A reversed amount effect was also found for choices made in the dictator and ultimatum games (Rachlin and Jones, 2010). The effect Table 2 Goodness of fit (R2 ) of the discounting function to medians of the relative values of indifference points (the ratio of the lowest amount a participant would keep for themselves, to the amount to be shared) for individual levels of independent variables. The regression model was fitted to the six discounted values (i.e. disregarding the undiscounted value = 1). Proportion of variance explained (R2 ) by the model
4. Discussion One of the important factors having an effect on the choice of shared reward in the present study was uncertainty of outcome. Consequently, the results can be interpreted in terms of trust. As expected, choices made by participants were determined by the receiver’s level of reciprocity. The effect of the level of reciprocity measured by the steepness index (showing how the perceived value of a reward to be shared with individuals representing successive levels of reciprocity changes relative to the reward shared with the person ranked first in the reciprocation ranking; the steep-
Emotional closeness Close person Distant person
Hyperbolic
Linear
0.948 0.500
0.953 0.993
Procedure of deciding how to use the reward to be shared Partner decides 0.951 0.984 Mutual decision 0.864 0.991 Reward amount Small – PLN 494 Large – PLN 49,400
0.959 0.772
0.997 0.992
J. Osi´ nski / Behavioural Processes 85 (2010) 24–27
was markedly stronger for the ultimatum game, which could be explained by the uncertainty of the game’s outcome. Participants may have assumed that receivers would accept offered amounts of high absolute value even if they represented a relatively small part of the initial endowment. The explanation in terms of perceived risk associated with choosing a shared reward is consistent with the interpretation proposed by Rachlin (2000), which refers to perceiving one’s interests as common with another person’s benefit. Both emotional closeness and reciprocation facilitate that process. It is possible that making a decision together has similar connotations, even though the results of the present study are inconclusive in that respect. It is worth mentioning in conclusion that the variables positively associated with seeing common interests may be predicted on the basis of evolutionary concepts, e.g. the inclusive fitness theory (Hamilton, 1964) and reciprocal altruism theory (Trivers, 1971). Acknowledgement The research was supported by a grant BST 134008 from the Faculty of Psychology, University of Warsaw.
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