Generosity subject to uncertainty:
Impact of stochastic income on sharing
Justyna Słonecka
11723238
14 August 2018
MSc Business Economics
Track: Managerial Economics and Strategy
Master’s thesis
15 ECTS points
Statement of Originality
This document is written by Student Justyna Słonecka who declares to take full responsibility for the contents of this document. I declare that the text and the work
presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of
Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Abstract
It has been established that uncertainty can play a significant role in influencing human decision-making. It is still being examined however how this uncertainty can be a factor when it comes to decisions invoking other-regarding preferences. In this study we check, by means of a dictator game experiment, how people react to endowment uncertainty and depending on conditions whether it results in different sharing patterns compared to certainty. We do this in two ways. First, we check whether conditional donations due to social/self-signalling can result in larger numbers shared than choices with endowment certainty. Secondly, we compare conditional and certain choices to probabilistic ones, where initial endowment is uncertain to see whether risk can diminish amounts shared. The results show that choices with endowment certainty result in slightly higher levels of sharing compared to conditional treatments, whereas probabilistic choices do not result in different sharing patterns.
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1. Introduction
There have been many studies investigating other-regarding preferences, mostly in environments involving no risk. As far as they brought numerous interesting insights they lacked applicability to situations with uncertainty, which are often present in our lives and should be part of analysis. This study examines if income uncertainty and conditionality of choices can constitute an important factor in determining the extent of other-regarding behaviour. This is particularly interesting because of the possible implications of assessing such impact, e.g. uncertainty might be limiting generosity, but an opportunity to condition your choices on the possible outcomes might be encouraging to share more. Generally, the act of committing in a situation with uncertainty might be of key importance, because people tend to make unrealistic assumptions about the future (e.g. Malmandier and Della Vigna, 2006). Following the principle of expected utility maximization, time when the decision is made should not influence the decision itself if final outcomes remain the same. Yet, behavioural research has shown that this might not be a true depiction of reality.1 Trying to
understand human behaviour in this domain can help in designing right approaches to boost people’s willingness to help others financially, given factual or possible benefits. This study makes use of the dictator game setting that, with more than 200 publications, has been a well-established way of testing other-regarding preferences (Engel, 2010). The adjusted version of the game tries to point at the way sharing patterns are influenced by income uncertainty. Subjects are faced with three types of choices: certain, conditional and probabilistic. Given the current state of knowledge, we know that people might be responsive to conditionality of donations, that is, they commit to donate more in the case of winning a lottery, than they do after they win one (Kellner, Reinstein and Riener, 2015). However, we know little about how robust these findings are and how we can extend this knowledge to environments with larger uncertainty. This has led to the research question, formulated as follows: Can conditionality and uncertainty of income result in different sharing patterns given the level of contributions with income certainty?
1 Kellner et al. (2015) shows that men donate more when they commit before winning the lottery than
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This matter is investigated by introducing conditional treatments where subjects decide how much to share in the case of winning and losing in the lottery, and by adding probabilistic treatments where choices in the lottery cannot be made accordingly to each outcome. The results show that subjects in fact give less in the conditional treatments than in certain ones, which is mostly driven by female respondents. There is no significant difference between conditional and probabilistic (riskier) choices. This thesis paper is organised in the following order. The first part constitutes an overview of related literature. Following this, methodology and proposed hypotheses are presented. Further section includes the analysis of results, which is followed by discussion and concluding remarks.
2. Related literature
On the rise of discovering prevalence of other-regarding preferences in monetary decisions, research has been trying to pinpoint the exact causes of human benevolence. Besides pure altruism, studies have shown that reasons like “warm-glow”, self- and social signalling play a significant role in determining decision-making. These aspects can be prominent given some circumstances and be the main driver of generosity. In the previously mentioned study by Kellner, Reinstein and Riener (2015), the authors explore the possibility of conditional giving. They ran two experiments, in the lab and in the field, examining donations before subjects knew if they won the lottery and after they got to know the result. They found that men give significantly more when they commit before the result of the lottery is known. These results are attributed to reputational concerns that men were proven to be more sensitive to (e.g. Jingping, 2013). There was also a question of whether higher donations follow from income uncertainty or collection uncertainty. The lab experiment showed that uncertainty regarding the collection of the donation is responsible for the increased giving, as it allows for the (self)signalling to be cheaper and make reputational investment more worth it.
Kellner et al.’s (2015) study is the closest in its contents to the subject and method used in this research. However, there are a couple of differences. First of all, the possibility of donation in the loss scenario is included in the conditional treatment. It can be considered a robustness check, as it was introduced to see whether signalling
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will also have a prominent role even when it is clearly “cheaper” than in the case where donation is possible only when the lottery was won. If subjects are true to themselves, there should be no difference in treatments, but they would give more if they leave things for luck to decide, or if the act of committing in advance plays a role. Also, the inclusion of a loss condition is an interesting check for how people react to a prospect of loss in comparison to the same amount of money in certainty. Considering Prospect Theory (Kahneman and Tversky, 1979) people would react stronger to potential losses than gains – it is therefore possible that, faced with the prospect of losing some endowment, people share less. Secondly, the situation was framed differently in these experiments. In the design of Kellner et al. (2015) subjects were clearly told that they must decide before the result of the lottery is known or afterwards – they used between-subject design. In this study, subjects face decisions where they either know for sure how much they have, or they face some endowment uncertainty – therefore, stress is placed on the certainty vs. uncertainty aspect. Within-subject design allows us to see whether people confronted with both type of choices still decide to share different amounts depending on the setting. Randomization is used to mitigate possible satiation effect2. Additionally, this study includes probabilistic treatments that are
aimed at examining whether uncertainty can not only increase the donations, but also be a reason for decreasing them.
It is important to stress why in this study we will also consider gender effects. There have been numerous examples where the behaviour of subjects differed depending on gender in the domain of other-regarding preferences. Andreoni and Vesterlund (2001) find that men give more when the price is low and are more extreme when it comes to their choices – they are either selfish or selfless, women turn to be more equalitarian. Cox and Deck (2006) on the other hand, show that women are more sensitive to price of sharing. Price of sharing is related to the aspect of uncertain conditional donations, because signalling is cheaper in this instance – in Kellner et al. (2015) men prove to be more responsive to the price defined in such a way. Other studies also point that social cues have a larger effect on men (Rigdon et al., 2009),
2 Reinstein (2010) writes about satiation of warm-glow, which could be a reason why donations
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who also show to be more sensitive to reporting about others’ donations – then they tend to share more (Jones and Linardi, 2014; Meier, 2007). Gender differences in risk attitudes might also play a role in this study, given the fact that the experiment includes decisions under uncertainty. A number of studies showed that women generally tend to be more risk-averse (Byrnes, Miller and Schafer, 1999). Finally, females showed to be more sensitive to details of the experimental design than males (Croson and Gneezy, 2009).
Considering the nature of conditional donations, the act of committing might be a meaningful factor influencing them. Commitment on its own has been investigated as a possible way to increase charitable giving. Breman (2011) conducted a field study where donors were asked to increase their donations either immediately, in one month or in two months. She found that future commitment result in significantly higher donations. The potential explanation is that the costs of the donation are incurred in the future, but positive feelings associated with the donation, “warm-glow”, can be realized at the moment of commitment. In this study the conditional treatment is also designed to show how the earlier commitment influences donations, but time when the donation is made cannot be manipulated.
Commitments towards future actions are inherently related to uncertainty and risk.
Therefore, when modelling human behaviour in this domain it is worth to consider and include how people’s generosity is affected by those factors. Brock et al. (2013), Krawczyk and Le Lec (2010) and Karni et al. (2008) tested other-regarding preferences in risky environments. They conducted an adjusted dictator game experiment, where subjects shared prospects to win a prize and where their risk exposure varies. They found that although people take both ex ante and ex post concerns into account, that is, share even when there is no chance for ex post fairness, still they share less when risk is involved. Major difference between this study and Brock et al. (2013) is that they fixed attainable payoff levels, whereas in this experiment they vary between 3 options: 25, 50 and 75. It follows from the fact that the focus of this research is on sharing certain amounts under income uncertainty rather than sharing risk in the income uncertainty situation.
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Risk might be a reason why people partially give up on cooperation or generosity. Klempt and Pull (2010) did research on the effect of hidden and revealed information on principal-agent relationship, the results show that agents keep more to themselves when they are informed, and according to the authors, they hide this selfishness behind risk. Generally, there is evidence that people often find excuses for their selfish behaviour, because they dislike appearing as unfair. In the study of Dana, Weber and Kuang (2007), subjects in the binary dictator game, when given an opportunity to leave the relationship between their actions and resulting outcomes uncertain, use it to behave self-interestedly. Given conditional treatment in this experiment, where subjects choose their donations according to both results of the lottery, and comparing it to probabilistic treatment, where probabilities of winning and losing are the same, but the decision about donation must be made without distinguishing between each result, there is room for dodging or at least lowering the shared amount due to risk. There is also evidence in the literature that shows no effect of endowment risk on giving, but results acquired in this matter are largely dependent on how this risk is structured. In the study of Van Koten et al. (2013), they found no effect of endowment risk on the dictator game sharing, however in their design subjects can choose to share a percentage of their endowment, while risk is reflected in the mean-preserving spread. Therefore, it is easier to find no effect than in case where subjects need to choose a specific amount facing a large difference in their endowment. The experiment in this study employs the latter method as it allows for more flexibility of choice.
3. Methodology
For the purpose of this research, data was collected through a classroom style experiment. The experiment was conducted in both a Dutch, and a Polish secondary school, with participants aged 15-18 years old. The data has been compiled by means of hand-written responses. Instructions were provided in English and Polish depending on the target group. English was used with 86 Dutch participants – the experiment took place in bilingual classes of VWO level in the 4th and the 5th grade – and 17 Polish participants during an English class in one of the secondary schools in Warsaw. The other 100 participants from the same Polish secondary school were provided with
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instructions in Polish. In the following subsections experimental design, experimental procedures and proposed hypotheses are discussed.
3.1. Experimental design
The experiment is based on the dictator game design, where participants make decisions about how much of a given endowment they want to share with their allocated recipient. The first part of the experiment initially consisted of 10 rounds. However, after narrowing down the focus of the research, 8 rounds have been used for analysis3. All participants went through the same set of rounds. They made 3 types
of choices: certain, conditional and probabilistic. Certain choices were based on sharing fixed endowment, conditional choices were situations where endowment depended on a lottery and one could choose what amount to share conditional on the result of the lottery. Probabilistic choices involved a lottery played on the endowment where subjects had to make a decision about sharing, without knowing what the result of the lottery would be and involving no conditionality. The first round served to establish a reference point – participants had 50 coins at their disposal without any uncertainty involved. In the next rounds subjects faced decisions in a randomized order, regarding the sharing of their endowment either in a certain, conditional or a probabilistic setting. All the rounds are listed in Table 1.
Table 1. List of rounds and types of choices
Round 1, referential certain choice x | Y = 50
Round 2 – 8, randomized order Conditional choices There is 50% chance that Y = 50 and 50%
chance that Y = 25 x | Y = 50
x | Y = 25
There is 50% chance that Y = 50 and 50% chance that Y = 75 x | Y = 50 x | Y = 75 Probabilistic choices x | Y = [50%, 50; 50%, 25] x | Y = [50%, 50; 50%, 75] x | Y = [50%, 25; 50%, 75] Certain choices x | Y = 25 x | Y = 75
Note: x stands for the shared part of the endowment, Y is the initial endowment
3 Two probabilistic rounds were excluded: 1. 20% of earning 50 and 80% of earning 75, 2. 20% of
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Conditional choices are specified in this way to depict a situation where commitment is possible before knowing the outcome of the lottery and therefore to check whether this setting can impact subjects’ decision making – a more specified explanation on why decisions in this instance are expected to differ is provided in the Hypotheses section (3.3). Certain choices serve as control for examining the impact of conditionality, when subjects decide before the result of the lottery is known. Probabilistic choices serve as more risky extension of conditional choices. They are introduced to check whether subjects use this risk as an excuse to reduce the amount they share.
In the second part of the experiment, subjects completed Holt and Laury’s (2002) test for risk aversion4. It was aimed at identifying potential influences of risk attitudes on
decision making in the treatments involving risk. Besides the risk aversion test, subjects also gave answers to basic background questions: age, biological gender and social status/wealth.
3.2. Experimental procedures
Participants were informed that they are going to take part in an economic experiment and each of the sessions was supervised by their teacher. Each participant received the instruction sheet and 10 answer sheets, already in a randomized order, so they had all the necessary materials on their desks.5 All the participants were told that they
were matched with an anonymous partner that is also a participant in the experiment. It was made clear that their decisions will have real consequences in the form of rewards – that the number of coins in the game was equivalent to some given sum of money as a canteen voucher. Participants did not know the conversion rate, but they knew that the more coins they had, the larger their reward would be. Real money wasn’t used due to the specificity of working with secondary school children, but canteen vouchers provided a close equivalent. During 2 sessions other material rewards were also used, e.g. sweets, notebooks, pens. Not every choice was rewarded. In total 55 choices were converted into rewards based on a lottery after each session. The final conversion rate amounted to 50 coins being equal to 3 EUR in the Netherlands
4 Results of the risk aversion test are provided in Appendix 6.2.
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and 6 PLN in Poland. Each participant of the experiment played the role of the dictator. Participants were not set specific time limits for their answer, but to keep their engagement and to make sure that each round was finished at approximately similar times after 30 seconds they would hear a ringtone indicating that they should have made their decision. Answer sheets were collected at the end of the experimental session, but participants had no possibility to correct/change the choices they already made.
3.3. Hypotheses
This study is aimed at showing whether income uncertainty can translate into different sharing patterns. The first hypothesis reflects relatively recent findings that conditional choices and committing some amount of money before the endowment level is known can result in larger donations (Kellner et al., 2015).
1st Hypothesis
Conditional choice in case of winning the lottery will result in higher contributions in comparison to situations where income is certain.
This hypothesis contradicts expected utility maximization, where utility would only be derived from actual donations, taking only final outcomes into account. Therefore, making a decision based on a prospect rather than a sure situation would not change the decision about sharing as long as final outcomes are the same.
Our hypothesis can be explained by social/private image concerns. When committing to giving some amount of money in advance, but only with some probability, it becomes cheaper to donate than if it was going to be realized with certainty. The act of giving, even unrealized, can already provide utility due to “warm-glow” and reputational concerns. The utility function in this scenario can be formulated as follows: 𝑈(𝑌, 𝑔) = 𝑢(𝑌) + 𝑝[𝑢(𝑌 − 𝑔) − 𝑢(𝑌)] + 𝑝𝜃𝑤(𝑔) + 𝑟 (1) Initial endowment is represented by 𝑌, 𝑔 stands for the shared number of coins, 𝑝 is the probability of winning the lottery – in this case the possibility of winning 75 coins. 𝜃 is an indicator whether a person wants to give money due to intrinsic utility from giving. Utility from reputation is represented by 𝑟. For people that do not have the
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intrinsic drive to share, the following constraint defines whether they decide to share due to reputational reasons:
−𝑝[𝑢(𝑌 − 𝑔) − 𝑢(𝑌)] < 𝑟 (2) The smaller the 𝑝 is, the more attractive reputational benefits are to people without intrinsic giving drive (𝜃 = 0). Also, the defining element is that people that do gain intrinsic utility from giving (𝜃 = 1) have to increase their 𝑔 to be able to distinguish themselves from the other “unfair” group, in case they also have an incentive to share. Therefore, making donations uncertain and conditional should result in more sharing. Secondly the research tries to show whether higher uncertainty will be negatively reflected in the level of contributions. Past studies have indicated that risk lowered shared amounts, in this instance we check how conditional choices can compare to probabilistic options, once freedom of adjusting one’s decision to the outcome is taken away.
2nd Hypothesis
Conditional choices result in higher contributions in comparison to situations with larger income uncertainty (probabilistic options), where choices cannot be made according to each result of the lottery.
Based on the argumentation provided under the first hypothesis, uncertainty of donations can result in boosting reputational utility and translate into more sharing in case of winning the lottery. In this instance, in probabilistic choices, there’s no possibility to profit from the same type of uncertainty, because one cannot control what the initial endowment will be. This also creates the possibility to decrease sharing and to make an excuse out of income uncertainty. Both of these reasons can result in difference between these treatments.
An alternative hypothesis could be formulated with the use of expected utility maximization. Given optimal donations in the conditional choices (3) and the optimal donation in the probabilistic treatment (4), with probability p=1/2 that was used in the experiment, we should expect the equality of both treatments given the same expected values (5).
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𝑔0 𝑔1 = 𝑎𝑟𝑔𝑚𝑎𝑥𝑔0𝑔1(1 − 𝑝)𝑣(𝑌0− 𝑔0, 𝑔0) + 𝑝𝑣(𝑌1− 𝑔1, 𝑔1) (3) 𝑔 = 𝑎𝑟𝑔𝑚𝑎𝑥𝑔(1 − 𝑝)𝑣(𝑌0− 𝑔, 𝑔) + 𝑝𝑣(𝑌1− 𝑔, 𝑔) (4)
𝑔 = 1
2(𝑔0+ 𝑔1) (5)
Indexes 0 and 1 describe lower and higher value in conditional choices with respect to initial endowments and then corresponding shared amounts.
Both hypotheses are tested by comparing medians and distributions in the relevant treatments. Additionally, to check the influence of risk, difference between certain 50 and the probabilistic treatment [50%,25; 50%,75] is tested.
4. Results
There are 203 observations for all but 2 treatments, collected during 9 experimental sessions. Both subject pools, Polish and Dutch, were very similar in age, gender proportions and social/wealth status. In the total sample there is an even division between males and females (100 and 102 respectively6). Average sharing across all
treatments was at 25,5%, taking base endowment into account, which is in line with findings from other dictator games (Engel, 2010). Between 72 – 77% of subjects, depending on treatment, decided to share a positive amount. Men on average gave slightly more [13.48 to 11.83]. Table 2 below shows descriptive statistics for each treatment.
Table 2. Descriptive statistics - amounts shared in each treatment
Treatment Mean Std. Dev. Min (Max) Obs.
Certain 50* 11.68473 10.75649 0 (50) 203 Certain 25 7.374384 6.585142 0 (25) 203 Certain 75 20.97537 17.4343 0 (75) 203 Conditional 25 6.374384 6.533822 0 (25) 203 Conditional 5025 Conditional 5075 Conditional 75 12.14286 11.80788 18.50739 10.72123 11.41076 15.93998 0 (50) 0 (50) 0 (75) 203 203 203 Probabilistic 25/50 9.653266 9.879853 0 (50) 199 Probabilistic 50/75 14.97044 14.37989 0 (75) 203 Probabilistic 25/75 11.83168 13.38044 0 (75) 202
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4.1. Conditional treatments vs. Certain treatments
Based on the descriptive statistics, it is already visible that conditional treatments result in lower amounts shared. Due to lack of data normality, non-parametric Wilcoxon signed-rank test was employed to compare distributions and medians in the treatments. In the conditional treatment that resembles Kellner et al. (2015), subject chose how much to share if they won the lottery, from 75 coins. In this instance, treatment with certain 75 coins, that can be interpreted as the result of the lottery, indicates a higher level of sharing than in the conditional equivalent, rejecting equality of medians with p-value 0.0050. Conditional 50 from the conditional treatment with an alternative result of 25, which is also a winning result from the two, is statistically no different from Certain 50 (p-value 0.1431). Results are summarized in Table 3. In the conditional treatment, where the endowment turns to be 25, subjects share 6 coins, while in certainty, without any lottery, it is 7 coins. The difference is small but proves to be statistically significant with p-value 0.0047. Interestingly, in the loss condition, where subjects have the lowest possible amount in the game (25), it is the female respondents that drive the difference (p-value 0.0073).
Table 3. Wilcoxon signed-rank test results (z-statistics) wrt. differences between conditional and certain choices.
H0 Total Female Male
Conditional 75 (win) = Certain 75 -2.809*** (0.0050) -1.766* (0.0773) -2.254** (0.0242) Conditional 50 (win) = Certain 50 1.464 (0.1431) -1.601 (0.1095) -0.459 (0.6462) Conditional 50 (loss) = Certain 50 -0.514 (0.6076) -0.913 (0.3611) 0.294 (0.7687) Conditional 25 (loss) = Certain 25 -2.830*** (0.0047) -2.682*** (0.0073) -1.321 (0.1864) Note: p-value in parentheses, *** - significant at 1% level, ** - significant at 5% level, * - significant at 10% level
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Figure 1. Amounts shared in the conditional and certain choice with 25 coins
Larger sharing in the Certain treatment might be related to preference for certainty, even if the difference is considerably small. Therefore, we ran a regression to check if risk attitude can have any explanatory value when it comes to these results. Coefficients prove to be distinctly insignificant possibly due to the very small difference that needed to be accounted for. The results are provided in the Appendix 6.1. Nevertheless, in the face of median comparisons provided, we can surely reject the first hypothesis stating that conditional treatments do not result in more sharing than certain choices.
4.2. Conditional treatments vs. Probabilistic treatments
When it comes to the second hypothesis, same direct comparisons as in the previous case are not possible. Probabilities and outcomes are the same for both treatments, but the way decisions are made differs. In the conditional choice there are two responses to two scenarios, in the probabilistic choice they are brought into one. Therefore, for comparison purposes, both responses in the conditional treatment are divided in half according to the given probabilities (50%) and added together. We find no significant differences between the treatments.
Total Female Male
Conditional 6,37 5,6 7,22 Certain 7,37 7,04 7,78 0 1 2 3 4 5 6 7 8 9 Conditional Certain
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Table 4. Wilcoxon signed-rank test results (z-statistics) wrt. differences between conditional and probabilistic choices.
H0 Total Female Male
Conditional (25, 50)/2 = Probabilistic 25,50 1.300 (0.1935) 1.287 (0.1981) 0.560 (0.5753) Conditional (75, 50)/2 = Probabilistic 50, 75 0.575 (0.5654) 0.912 (0.3619) -0.068 (0.9461)
Note: p-values in parentheses
Based on the above, we reject the second hypothesis in favour of the alternative hypothesis employing expected utility maximization.
Next to the tests conducted to directly test presented hypothesis, we check whether risk has any influence on sharing when expected values are the same. It is related to the aspect investigated within the second hypothesis – if risk can be a reason for people to diminish amount of sharing. Therefore, we compare two rounds – one where subjects share from certain 50 coins, and one where there is a 50% chance they will have either 25 or 75 coins. The results are presented in Table 5.
Table 5. Wilcoxon signed-rank test results (z-statistics) wrt. differences between certain and probabilistic choices.
H0 Total Female Male
Certain 50 = Probabilistic 50% (25, 75) 0.560 (0.5757) 0.020 (0.9839) 0.801 (0.4230) Number of coins shared
Certain 50 11.68473 10.98039 12.52
Probabilistic 50% (25, 75) 11.83168 11.23529 12.56566
Note: p-values in parentheses
We find no significant difference between these treatments. It seems that risk formulated in this way had no impact on subjects’ decision on sharing. In the following section, the overall results and possible implications are discussed.
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5. Discussion and conclusion
The results section provided us with several findings. The research question was formulated as follows: Can conditionality and uncertainty of income result in different sharing patterns given the level of contributions with income certainty? Two main hypotheses based on social and self-signalling, stating that conditional choices should result in higher level of sharing, were rejected. However, coming back to the research question, we do find some different sharing patterns. Although numerical differences are small, comparing conditional choices and certain choices showed that certain choices result in slightly more sharing. Comparison of conditional choices and probabilistic choices as well as certain choices and probabilistic choices pointed at no difference between treatments – showing that expected utility maximization could be the correct way of describing human behaviour.
There are several reasons for the observed results. First of all, adding a “loss” option to conditional choices might have had a significant impact on the shared amount. Signalling could not be as “successful” because if somebody decided to share more in the winning option then it raises a question why they would not share in the loss option – sharing more in only one option does not build reputation as much. Yet, this explanation on its own does not explain why certain options would result in more sharing. What could be the case is that the loss option in the conditional treatment is more exposed to negative impact of the prospect of loss and the certain option with the same numerical value (25) could be treated as a separate situation that does not suffer from the same kind of concept, because the value is simply given. Looking at the results however, we see that also in the case of winning (75) people decide to share more in certainty. This could be attributed to some preference for certainty, but as we see from the comparison between certain and probabilistic treatment, there seem to be no influence of risk. There is also the aspect of gender differences – women defined the difference between certain 25 and conditional 25 treatment. A plausible explanation to this finding is that females were more responsive to the experimental design that stressed differences between certain options and conditional ones – as it was presented in the study of Croson and Gneezy (2009). Based on Andreoni and
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Vesterlund (2001)’s research they show that females react to tiny differences in the initial endowment in the dictator game setting, whereas males do not.
It is noteworthy that these differences although statistically significant, numerically might not provide substantial evidence to draw economically significant conclusions with respect to them. Assuming that, both hypotheses were rejected in favour of expected utility maximization. There are differences between studies that found some violations in this domain, and this research – mostly they can be attributed to the experimental design. First, in this study within-subject design was used. The direct benefits of this decision are that individual effects can be controlled for and one can be sure that found effects are not due to different samples, also a smaller number of participants is needed to find a statistically significant effect. However, in this instance where subjects are faced with multiple choices of the same nature, any potential difference might have been driven away by the repetitiveness of the same action and lack of certain emotional impact that could have played a role if it was a one-shot situation. Regardless, based on this study we can see that increased conditional giving does not happen in situations where collection in both options (loss and win) is certain. Also, probabilistic options did not provide evidence that people use risk as an excuse for lower level of sharing. The provided results indicate that income uncertainty does not contribute significantly to different sharing patterns. More research should however clarify how much impact different probabilities of loss and gain have on level of sharing, as this study operated only under one set of 50% probability. Further investigation is encouraged to check whether there is preference for certainty in choices involving other-regarding concerns.
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6. Appendix
6.1. Linear regression of difference between conditional and certain choice with 25 coins (dependent variable)
Coefficient Robust Std. errors t P > |t| r_aversion .1183193 .2981762 0.40 0.692 Dutch (nationality) -2.200309 1.397287 -1.57 0.117 English (language of instruction) 1.295135 1.421418 0.91 0.363 Male -.8234831 .9923129 -0.83 0.408 Constant 1.061744 1.950626 0.54 0.587 Model R-squared – 0.0144
6.2. Histogram of subjects’ risk aversion based on Holt and Laury’s test
Number of safe choices Risk aversion
0, 1 Highly risk loving
2 Very risk loving
3 Risk loving
4 Risk neutral
5 Slightly risk averse
6 Risk averse
7 Very risk averse
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6.3. Instructions for participants (English version)
Instructions Part 1
Welcome to the experiment. Please do not use your mobile phones and read the instructions carefully. If you have any questions about the instructions, please raise your hand and one of the observers will come to your desk to answer your question. Please do not talk to other participants during the experiment. If you wish to stop participating at any point, you are allowed to do so – however please communicate that to one of the observers.
The experiment consists of 2 parts. This is Part 1.
Part 1 will consist of 10 rounds. During each round you will be required to make a decision based on a given description. This means you have 10 decisions to make. You have been assigned to the decision-making group. During each round you will be randomly matched to another participant that does not have any decision-making power. Each round you will have a certain amount of capital at your disposal. Your task is to decide how much of this capital you want to give to the participant you have been assigned to. The other participant does not have any initial capital.
In the experiment you will face certain, conditional, and probabilistic choices:
Example 1. Certain choice:
You have 20 coins to distribute. How many would you like to give to the other participant? You can give from 0 to 20 coins – remember to indicate an integer number (a whole number, not a fraction).
Example 2. Conditional choice:
You have a 50-50 chance that you will lose some of your capital – with a 50% chance your capital remains 20 coins, with a 50% chance it becomes 10 coins. How many would you like to give to the other participant?
If your capital remains 20 coins: ___ If your capital becomes 10 coins: ___
Example 3. Probabilistic choice:
You have an 80% chance that you will lose some of your capital – there is an 80% chance that your capital remains 20 coins, and a 20% chance that it will become 10 coins. How many would you like to give to the other participant? You have to make the decision before you know exactly how much capital you have.
Each of your decisions will be linked to real rewards. Based on the lottery after the experiment, 10 decisions will be randomly chosen for the reward. You will be able to exchange the remaining number of coins for sweets, notebooks or canteen vouchers depending on the number of coins you have left. Therefore, make each of your decisions as if it could be the one that gets chosen in the final lottery.
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Part 2
Instructions Your ID number: _________
Your decision sheet shows ten decisions listed below. You have a choice between "Option A" and "Option B." The probability of each event is expressed in fractions from 0/10 to 10/10.
Fraction 0/10 is an equivalent of a 0% chance that the given result will occur, 1/10 is a 10% chance that the given result will happen, 2/10 is a 20% chance and so on, 10/10 is a certain event.
In Decision 1 at the top of the table below, you decide between two sets of lotteries – Option A, where there is a 10% chance you gain $2.00 and a 90% you gain $1.60, and Option B, where you face a 10% chance of winning $3.85 and a 90% chance of winning $0.10. As you move down the table, the chances of the higher payoff for each option increase.
Please indicate your preference for each pair of options (either Option A or Option B) in the column on the right.
Option A Option B Choice
1/10 of $2.00, 9/10 of $1.60 1/10 of $3.85, 9/10 of $0.10 2/10 of $2.00, 8/10 of $1.60 2/10 of $3.85, 8/10 of $0.10 3/10 of $2.00, 7/10 of $1.60 3/10 of $3.85, 7/10 of $0.10 4/10 of $2.00, 6/10 of $1.60 4/10 of $3.85, 6/10 of $0.10 5/10 of $2.00, 5/10 of $1.60 5/10 of $3.85, 5/10 of $0.10 6/10 of $2.00, 4/10 of $1.60 6/10 of $3.85, 4/10 of $0.10 7/10 of $2.00, 3/10 of $1.60 7/10 of $3.85, 3/10 of $0.10 8/10 of $2.00, 2/10 of $1.60 8/10 of $3.85, 2/10 of $0.10 9/10 of $2.00, 1/10 of $1.60 9/10 of $3.85, 1/10 of $0.10 10/10 of $2.00, 0/10 of $1.60 10/10 of $3.85, 0/10 of $0.10 Background questions
Please indicate the following by marking the right square: • Biological gender: ⬜ male ⬜ female
• Age: _________
• How would you compare your level of wealth (your family) to the Dutch/Polish average household?
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6.4. Answer sheets (English version)
a) Basic design of answer sheets
Round ____ Your ID number: _______________________ You have 50 coins to distribute. How many coins would you like to give to the other participant? You can give from 0 to 50 coins – remember to indicate an integer number.
Put your answer in the box to the right:
[remember to indicate an integer number]
b) Formulations for each type of treatment Certain choices:
• You have 25 coins to distribute. How many coins would you like to give to the other participant? You can give from 0 to 25 coins – remember to indicate an integer number.
• You have 75 coins to distribute. How many coins would you like to give to the other participant? You can give from 0 to 75 coins – remember to indicate an integer number.
Conditional choices:
• You have a 50-50 chance that you will lose some of your capital – with a 50% chance your capital remains 50 coins, with a 50% chance that it becomes 25 coins. How many coins would you like to give to the other participant?
If your capital remains 50 coins, you decide to give: ______ If your capital becomes 25 coins, you decide to give: ______
• There’s a 50-50 chance that you win 25 coins extra – with a 50% chance your capital remains 50 coins, with a 50% chance it becomes 75 coins. How many coins would you like to give to the other participant?
If your capital remains 50 coins, you decide to give: ______ If your capital becomes 75 coins, you decide to give: ______
Probabilistic choices:
• You have a 50% chance that you will lose some of your capital – with a 50% chance your capital remains at 50 coins, with a 50% chance it becomes 25 coins. How many coins would you like to give to the other participant? You have to make the decision before you know exactly how much capital you have.
• You have a 50% chance that you will gain some extra capital – with a 50% chance your capital remains 50 coins, with a 50% chance it becomes 75 coins. How many coins would you like to give to the other participant? You have to make the decision before you know exactly how much capital you have.
• You have a 50% chance that you will gain or lose some capital – with a 50% chance your capital amounts to 75 coins, with a 50% chance it becomes 25 coins. How many coins would you like to give to the other participant? You have to make the decision before you know exactly how much capital you have.
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