Comparing small-group and individual behavior in lottery-choice experiments.

• Author: Baker, Ronald J., II

1. Introduction

   Group decision making plays an important role in economic policy. From the Open Market Committee of the Federal Reserve, to family expenditures, to the management of mutual funds, important decisions are made by groups. (1) Although there is a long history in social psychology of studying the effects of group discussion on decision making, research addressing when and how group decisions differ from individual decisions in economic contexts with salient cash rewards has only recently appeared in the economics literature. (2) This study builds on this nascent literature by reporting the results of a series of lottery-choice experiments following the Holt-Laury (2002) format. The goal of this study is to compare the inferred-risk preferences measured by the lottery choices of three-person groups and individuals in an environment where group members must unanimously agree on the group decision after a period of unstructured discussion.

   This study consists of experiments in two treatments: nonsequenced (between-subjects) experiments that generate independent individual-choice and group-choice samples and sequenced (within-subjects) individual-group-individual experiments. The nonsequenced experiments measure whether group choices are, on average, significantly different than individuals. The sequenced experiments investigate how individual choices are aggregated into the group choice and examine whether participating in group discussion immediately impacts subsequent individual choices.

   Similar to previous research, the findings of this study show that subject composition (individual or group decision makers) does influence experimental outcomes. Specifically, although there is not a significant difference in the total number of safe-lottery choices based on subject composition in the nonsequenced experiment, lottery choice is affected by a significant interaction between subject composition and the lottery-winning percentage, defined here as the probability of attaining the high-payoff outcome in the lottery. Groups appear to deviate less from the risk-neutral set of choices in the lowest (10-30%) and highest (80-100%) winning-percentage lotteries. The sequenced experiments show that a group shift occurs such that the total number of safe-lottery choices by the group is significantly greater than the mean total safe choices of group members, and that unstructured group discussion significantly impacts subsequent individual choices.

   The paper proceeds as follows: section 2 summarizes recent related research exploring risk preferences of individuals and groups using lottery-valuation or lottery-choice experiments, the experimental procedures for the lottery-choice experiments utilized here are explained in section 3, section 4 presents the experimental results, and a summary of conclusions is offered in section 5.

2. Overview of Recent Related Lottery Experiments

   Recent studies using lotteries to elicit risk preferences have been conducted by Holt and Laury (2002), Harrison, Lau et al. (2005), Colombier et al. (2006), and Shupp and Williams (2008). (3) Holt and Laury (2002) elicited individual risk preferences using a four-phase lottery-choice experiment with probabilities of obtaining the higher monetary payoff ranging from 10% to 100%. Each phase differed by the monetary payoffs of the lotteries and whether or not subjects were paid based on their decisions. (4) Their experimental results showed that subject decisions at baseline payoff levels were consistent with risk aversion (indicated by the number of safe-lottery choices), there was no difference in inferred-risk preferences between baseline payoffs and high-hypothetical payoffs, and the magnitude of inferred-risk aversion increased from baseline to high-real payoffs. Increased risk aversion persisted as the payoffs continued to be scaled upward; however, risk preferences in the high-payoff lotteries were not consistent with those in the hypothetical high-payoff lotteries. Finally, risk preferences in baseline-payoff lotteries conducted after the high-payoff lottery phase remained consistent with the baseline-payoff lotteries conducted before the high-payoff lottery phase.

   In a comment on the Holt and Laury (2002) paper, Harrison, Johnson et al. (2005) noted that an order effect existed in the Holt-Laury lottery-choice experiments. Holt and Laury (2005) reported new data to address the magnitude of the order effect; their original conclusions were supported by the new data.

   Harrison, Lau et al. (2005) analyzed social preferences in a lottery-choice experiment. Individuals were assigned to anonymous three-person groups, and the group decision was determined by majority rule. Group members were not allowed to communicate with one another. Controlling for order effects and subject demographics, the interval regression and random-effects panel-data estimates reported found no evidence of differences in the choices of individuals and three-person majority-rule groups.

   Shupp and Williams (2008) conducted lottery-valuation experiments to compare the risk preferences revealed by individuals relative to three-person groups and to analyze how individual decisions are aggregated to form a group decision. Instead of using a lottery-choice procedure, Shupp and Williams elicited maximum willingness-to-pay bids to play each of nine lotteries with varying probabilities (10-90%) of winning $20 ($60 for groups) or nothing. Individuals were endowed with $20 (groups with $60) to cover their bids. Group decisions were formed by unanimous consent after an unstructured period of face-to-face discussion.

   Shupp and Williams (2008) analyzed their results using a certainty-equivalent ratio (CER) defined as the reported maximum willingness-to-pay divided by the expected value of the lottery. Thus a CER = 1 was consistent with risk-neutral preferences, a CER > 1 was consistent with risk-seeking preferences, and a CER < 1 was consistent with risk-averse preferences. For example, in a lottery with a 50% probability of winning $20, the expected value of the lottery is $10. If a subject reported a maximum willingness-to-pay of $10, this person would be classified as risk neutral (with a CER of 1). In contrast, if a subject reported a maximum willingness-to-pay of $7 (less than the expected value of the lottery) this person would be classified as risk averse (with a CER of 0.7). Elicited CERs showed a significant interaction between subject composition (individual or group) and the lottery-win percentage. For the lowest-risk lotteries (win percentage of at least 80%) the average group CER was near the risk-neutral benchmark and slightly greater than the average individual CER. For the highest-risk lotteries (win percentage of at most 40%) the average group CER revealed substantial risk aversion and was significantly smaller than the average individual CER. For lotteries with a winning percentage of 50-70%, average group and individual CERs were consistent with risk aversion and not significantly different.

   Shupp and Williams (2008) also conducted a follow-up experiment employing individual-then-group sequenced decisions that was designed to test the robustness of their initial (independent samples) results and to explore how individuals form a group decision. These data confirmed that group discussion led to a significant shift of the group CER away from the mean individual group-member CER toward more risk aversion in the four highest-risk lotteries. No significant individual-versus-group difference was found in the five lowest-risk lotteries.

   In a recent working paper, Colombier et al. (2006) reported individual and three-person group lottery-choice experiments in which group members cannot directly communicate, as in Harrison, Lau et al. (2005), but must come to a unanimous group decision through an iterative voting process or have a random decision imposed on the group. They interpreted their results as being inconsistent with the findings of Harrison, Lau et al. (2005) (significant differences are reported for individual-versus-group decisions) and generally consistent with implications derived from the Shupp-Williams (2008) lottery-valuation research and the research reported here.

3. Experimental Procedures

   The experimental procedure followed Holt and Laury (2002), Laury (2002), and Holt and Laury (2005). Subjects were presented with a menu of 10 lottery-choice decisions. Each decision represented a choice between a relatively "safe" lottery (with a small difference between the low-payoff and high-payoff outcome) and a more "risky" lottery (with a larger difference between the low-payoff and high-payoff outcome). Payoffs were identical in all 10 decisions; however, the probability of the high-payoff outcome increased in 10% increments from 10% in the first decision to 100% in the last decision. In each decision the subject was asked to choose which lottery he preferred to play. One of these decisions was randomly chosen for payment by throwing a 10-sided die, with the outcome of the lottery determined by a second throw. (5)

   As in Holt and Laury (2002), the total number of safe-lottery choices was used as a measurement of subject risk preferences. A subject acting as if risk neutral would choose the lottery with the highest expected monetary payoff for all winning probabilities: he would choose the safe lottery for winning probabilities p [member of] [10%,40%] and then switch to the risky lottery for the winning probabilities p [member of] [50%,100%]. (6) A subject acting as if risk averse...