Experiments where participants have to choose between receiving more or less money: A considerable minority chose to receive less; this result holds in different experimental environments

More or Less Money? An Experimental Study on Receiving Money. Sigve Tjøtta. Journal of Behavioral and Experimental Economics, MAr 26 2019. https://doi.org/10.1016/j.socec.2019.03.007

Highlights
•    I run experiments where participants have to choose between receiving more or less money.
•    A considerable minority chose to receive less money
•    This result holds in different experimental environments
•    This result may compromise interpretation of many experiments.

1 Introduction
A surprising result from one experiment is the point of departure for this paper. The participants were asked to choose between receiving more money or less. The experiment followed standard procedures. I used a randomized payment scheme in which only a subset of the participants were paid. It was a double-blinded design in which neither the participants nor the experimenters could identify the choices made by specific participants. To my surprise, a substantial minority, 28.6% of 91 participants, decided to receive less money. Deciding to receive less money in itself is not a surprise as this is common in many standard experiments such as dictator, ultimatum, and public goods games. Choosing less money in these situations may reflect the decision maker’s strategic behavior or concern toward the other subjects. In the dictator game, choosing less money may reflect concern for the recipient. The strength of the dictator game is that it separates the decision maker’s concern for the recipient from strategic considerations toward the recipient. The more or less money choice goes one step further from the dictator game as it removes explicitconsideration of others participants.If participants in experiments prefer receiving less money than more, the interpretation of economic experiments may be compromised. The result can be explained in at least three ways, and all may affect the interpretations of other experiments. First, subjects’ choice to receive less money, may reflectan experimenter demand effect (Hoffman et al. 1994, Zizzo (2010), and Chlaß and Moffat 2017). Second, subjects may have social preferences toward the experimenter, perceiving they are playing a dictator game with the experimenter. Choosing less money leaves more money for the experimenter. This explanation, however, may also be problematic for the interpretation of experiment results whenever subjects fail to maximize their joint payoff. For
4example, rejecting an offer in an ultimatum game or less trust in a trust game results in the subjects passing on money to the experimenter. Choosing non-cooperation in a public good game increases the payoff for oneself, but it also leaving money to the experimenter. Third, the interpretation of economic experiments is often restricted to a reference group of subjects who play against each other (Fehr and Schmidt 1999:821–822,Bolton and Ockenfels 2000:171).In the more or less money choice the reference groupis reduced to the decision maker only. Therefore, choosing less money may suggest that subjects care about how they perceive themselves. If this self-esteem restricts the subjects’ behavior in more or less money decision, it may also influence their behavior in other experiments. For example, dictators giving to an anonymous recipient is often interpreted, as the dictator preferringequality inthepayoff or following a norm for equityand social-esteem (Ellingsen and Johannesson 2008, Dreber et al.2013, and Hauge 2016).1However, among those that chose to receive less money in my experiment, a clear majority, 88,5 % of the 26 particpants, choose an even split in the corresponding dictator game. Hence, giving in a dictator game can be explained by self-esteem, not social preference or social-esteem, as usually is done.2As I used a randomized payment another selfish explanation is that subjectsdo magical thinking, they believe that claiming less money instead of more increases their probability of winning(Arad 2014). 1For an interpretation of dictator giving as a social preference for inequality see Fehr and Schmidt (1999), Bolton and Ockenfels (2000), Charness and Rabin (2002), Falk and Fischbacher (2006),and Cappelen et al.(2007). This interpretation is an ongoing discussion in the literature (List 2007, Levitt and List 2007, List 2009, Berg and Gigerenzer 2010, Binmore and Shaked 2010, Fehr and Schmidt 2010, Eckel and Gintis 2010, Wilson 2010, Smith and Wilson 2014, and Kimbrough and Ostroknutov 2015).2As the more or less money choice resembles the dictator game, the result that participants prefer getting less money for more are in line with experimental findings that dictator’s giving depend on context (Dana et.al. (2006), List (2007), and Bardsley (2008)).
5If the experimenter demand effect, social preference toward the experimenter, self-esteem, or magical thinkingare that strong in the more or less money experiment, they may also be strong in other experiments. Therefore, the interpretation of manyexperiments may be compromised. Whether these explanations actually carry over to other experiments is an empirical question. Such investigations are beyond the scope of this paper. The aimof this paper is to investigate whether the result that some participants choose to receive less money instead of more holds in other experimental situationsandwhether it translates tothe general population. I createdexperimental situations thatwouldmake accepting more money seem more appropriate for the subjects. Table 1 presents the overall results and features of the decision situations:(1) The experience of participating in experiments (reported in experiments3 and 4). (2) Strengthening the participants’ entitlement to the money (Experiment 5). (3) According to the social heuristic hypothesis, deliberations before the actual choice of more or less money should tilt the decision in the direction of accepting more money (Rand et al. 2014) (experiments6 and 7).The participants were also asked to explain their choice of more or less money in an open-ended question(experiments 6 and 7). Theseopen-ended experiments were performed inthe Norwegian Citizen Panel, a web-based survey of randomized sample of the Norwegian population aged 18 to 76 years. Finally,I elicitednorms in the situations of receiving more or less money using the elicitation procedures developed by Krupka and Weber (2013)(experiments 8 and 9). The overall result is that a considerable minority of the participants in the experiments chose to receive less money instead of more;see Table 1. In Experiment5 -the only one where the participant could choose to receive incrementallyless money-themajority, 64.5% of 200
6participants,decidedto receive less money. In the norm elicitation experiments, aminority stated that choosingto receive all the moneyis inappropriate. I used a randomized payment scheme in all experiments;in each experiment, a percentage of the participants were randomly drawn to receive money. The prices and frequencies of winning are shown in Table 1. For a subject choosing less money instead of more, the expected forgoing of money ranges from, low 0.43 kroner in Experiment 7, to high, 50 kroner in Experiment 5. These numbers correspond to expected hourly payment of 26 and 3000 kroner, respectively.3Clearly, using randomized payment schemes and very low probabilities of being paid in some of the experiments may raise the question whether the result holds for experiments in which all are paid. Manyexperiments, however, use random payment schemes in which either some subjects are paid, or subjects make multiple decisions and only a fraction of them are paid (Azrieli et al., 2018, Charness et al., 2016). It is also some empirical evidence that higher, less likely nominal payment may be more salient than lower, more certain payment (Charness et al., 2016, p. 142). Furthermore, comparing a randomized payment scheme with a standard payment scheme, there seems to be no difference in the pattern of givingin a standard dictator game and behavior in the ultimatum game (Charness et al., 2016 and Clot et al.2018). However, in experiments where the moral dimension may be more salient, as it may be in the more or less money experiment reported here, with a randomized payment schemethe benefit of signaling social esteem or self-esteemis chosen by certainty while the monetary cost of signaling is paid only in a fraction of the times (Charness etal. 2016: 148). This asymmetry between cost and 3The estimated hourly wage is based on that subjects used on average one minute.
7benefit may cause difference in results between experiments with randomized payment schemes and experiments in which all are paid.4Table 1: Overall results for experiments. EXP.N TypeDescription Payment lotteryfrequency Less money1 91ClassroomMore or Less andDictator, within-subjects design500 kroner4/9128.6%2 151Classroom More or Less and Dictator,between-subjects design500 kroner4/15136.0%3, 4181ClassroomExperiencedvs. Inexperiencedsubjects.More or Less and Dictator,between-subjects design500 kroner4/18130.4%5200Lab, 20 sessionsStrengthen Entitlements.More or Less and Dictator,between-subjects design500 kroner1/1064.5%61,019Web-basedaExplaining, ex post their choices in an open-ended question 1800 kroner1/101922.6%71,861Web-basedaDeliberation, Inexperience vs. Experienced, explaining choices ex post and ex ante 1800 kroner1/186129.2%8120Lab, 4 sessionsNorm elicitation500 kroner12/120 19.0%b940ClassroomNorm elicitation 500 kroner10/157 38.0%bNotes: The payment in all the experiments is conditional on winning in a lottery; the column withthePayment Lottery shows the prices in Norwegian kroner and frequency of winning. a)The Norwegian Citizen Panel, a web-based survey of a cross-section of the Norwegian population aged 18 to 76 years old. See Ivarsflaten et al.(2015). b) Percentage that states that it is ―very socially inappropriate‖ or ―socially inappropriate‖ to keep all the money for themselves. The point of departure forthis paper wasratherunusual as it started with asurprising result.In hindsight, perhapsI should not have been surprised becausein someuniversally experienced 4I thank an anonymous reviewer for pointing out this mechanism. Note that in Experiment 5, in which the expected cost of signaling is highest (50 kroner), as many as 64.5 % chose to receive less money.
8situationsoutside the lab, people selectless instead of more money. For example, customers return to a shop if they discover that the cashier forgot to charge them for anitem. People routinely take found wallets to the lost and found, and they do likewise in field experiments (Stoop 2014). Similar results are reported in the experimental literature. In a meta-study of 72 studies with more than 32,000 subjects across 43 countries using the lying set-up introduced by Fischbacher and Föllmi-Heusi (2013), the subjects forewent, on average, about three-quarters of the gains from lying (Abeler et al.2016:2). Many participants reported non-maximizing payoff numbers more often than their truthful likelihood (Abeler et al.2016:8). The ―No Die‖ treatment in Fischbacher and Föllmi-Heusi (2013), resembled the more or less choice the most: The participants were asked to pick a number between 1 and 6 with the same incentivized payoff as in the roll die treatment. Among the participants (n=34), 15% chose to receive less money instead of more.Arad (2014) reports that a considerable number of participants in pickingbetween lotteries that differ only in theirprizes, selected lotteries with prizes less than the maximum prize.She explains her results with magical thinking. By choosing the lottery with the lowest price participants believe this would increase their chancesof winning. Magical thinking may be an explanation for choosing less money for more as I usedrandomized payment scheme in all experiments. Among those 454 participants that picked less money in experiments 6 and 7, 10.6% explained their choice as magical thinking. The results presented in this paper may be driven by norms common to Norwegians but less common elsewhere. In general, behavior in experiment has been shown to vary across societies (Henrich et al.2010, Herrmann et al.2008), and itmay also do so in the ―more or less
9money‖ experiment. However behavior in standard experiments in Norwegian samples doesnotdeviate radically from behavior in similar experiments from samples in Western countries. Reigstad et al. (2017) comparedpro-social behavior in different games conducted in Norway and the US and found that pro-social behavior is very similar in the two countries, both across individuals and over time. Cappelen et al. (2015) compared Norwegian students’ behavior in dictator game and found that their behavior was not substantially different from thatreported in the meta-study by Engel (2011). Inexperiments 1-5, I also conducted standard dictator games, and the behavior of the dictator does not deviate radically from the results previously reported in the literature.