Living Ethics Journal

By Steven Zhang, Daniel Cardwell.

Abstract:

Human behavior shows a preference for minimizing loss when presented with probabilistically distinct choices. An example of this is that, when presented with the choice of either a 100% chance of receiving $5 or an 80% chance of receiving $6, the former is almost universally preferred, despite the choices being mathematically equivalent. This is likewise the basis for the business model of insurance companies, which operate on the premise that consumers will be willing to pay a smaller sum each month in exchange for protection from greater potential losses. The purpose of this study is to evaluate responses when given the option between a guaranteed losing outcome and an outcome with the risk of incurring greater losses, but also the possibility of avoiding loss altogether

Methods:

The experiment involves ten pairs of participants, for a total of 20 participants. These pairs are then randomly assigned to either the control or experimental group. All participants begin with $30 of Monopoly money, which can be exchanged for candy at an exchange rate of $1=1 M&M at the end of the experiment. This exchange rate is made known to the participants prior to the experiment. Both groups take turns to bid for a sum of $20.

Procedure:

In group one, which we designate the control group, the loser of the bid loses all of their money and receives no candy. If, at any point, a player backs out, they will receive no candy. Players are allowed to wager more than the amount they have (ie: if a player wagers $50 and wins, the result will be a net loss of $30, meaning they receive no candy).

In group two, which we designate the experimental group, both players must pay their most recent bid, regardless of whether or not they win. If the value wagered exceeds $20, the participant must still pay the wagered amount (ie: if a player wagers $21 and wins, they must pay $21 while receiving $20, resulting in a net loss of $1)

Following the experiment, participants are polled on the following three questions:

1. What were your reasons for continuing to bid?
2. Did you ever consider backing out for any reason?
3. Did the incentive of candy, or the risk of losing it, affect your decision?

Data for the control and experimental groups are separated. Responses to the first question are grouped into four categories: “desire for candy”, “preference to avoid loss of candy”, “preference to win regardless of reward”, and “did not wish to bid”. This data will be compared with the final bids of participants to determine motives.

Responses to the second question are split into four categories according to the following criteria:

	Affirmative	Negative
Won
Lost

Results:

Figure 1:

Figure 2: 

Final Bids of Control Group

Final Bids of Experimental Group

Figure 3: 

First Poll Question Results for Control Group

Desire for candy	Preference for avoiding loss	Preference to win	Did not wish to bid
2	4	1	3

Second Poll Question Results for Control Group

	Affirmative	Negative
Won	1	4
Lost	5	0

Figure 4: 

First Poll Question Results for Experimental Group

Desire for candy	Preference for avoiding loss	Preference to win	Did not wish to bid
3	6	1	0

Second Poll Question Results for Experimental Group

	Affirmative	Negative
Won	3	2
Lost	5	0

Figure 5: 

Lastly, the plot of final bids of participants in the control and experimental groups, as shown in Figure 1, is revised to exclude participants who responded “no” to the third poll question. As such, only participants who indicated that either the incentive of candy or the risk of losing it affected their decision are included. 

Discussion: 

When comparing final bids between the control and experimental groups (Figure 1), both groups display similar medians of $29 for the control group and $28 for the experimental group. The experimental group shows a left-skewed distribution, with the majority of final bids falling around $30 (the point at which continuing to bid results in a net loss for both players) (Figure 2). The control group, however, shows a bimodal distribution, with the most common results clustered around $0 and $50 (the threshold past which the payoff of winning is equal to that of losing). 

Analysis of control group: 

The control group provides a scenario where the option that minimizes loss is unambiguous, as participants who lose the bid lose the entirety of their money. Because participants are allowed to bid more than their starting balance of $30, the only point at which continuing to bid is disincentivized is once a participant has bid $50 or more, since after that point, regardless of whether they win, their resulting balance will be $0. As a result, a plurality of final bids, comprising roughly the two upper quartiles, fall around $50. A notable exception to this is the subset of participants choosing to withdraw after bidding a lower amount. This subset, comprising roughly the bottom quartile, withdrew after final bets below the lowest final bid of the experimental group once outliers are omitted. 

The third poll question asks participants whether the incentive of candy, or the risk of losing it, affected their decision. The purpose of this is to ascertain which participants were incentivized to win, so as to remove the confounding variable of personal preference for the candy offered (M&Ms). The omitting of results from participants who responded “no” (Figure 5) serves to include only results from participants who felt incentivized to play as if it were a realistic scenario. When only these results are concluded, the data shows a left-skewed distribution similar to that of the experimental, but with the majority of final bids clustering around $50 instead of $30. 

Analysis of experimental group: 

When examining Figure 5, both groups show similarly clustered distributions, but the final bids of the experimental group fall $20 lower than that of the control group. This suggests both groups evaluate risk similarly, where both participants are likely to avoid immediate loss in favor of increasing the potential for future loss. Both groups also evaluate the point at which the potential for future loss outweighs the immediate loss of withdrawing similarly. Participants in both groups most commonly withdrew at the point where withdrawing results in a net loss equal to the entirety of their balance. The only difference is that because losing participants in the control group must lose all their money, whereas losing participants in the experimental group only must pay their last bid, this point is different for both groups ($50 versus $30). 

Conclusion: 

Participants in this experiment showed a clear preference for taking greater short-term risks. In the experimental group, the most optimal strategy was to immediately withdraw, as that ensures that, despite losing, the participants retains their initial balance of $30. However, no participant in the experimental group pursued this strategy. Instead, all participants chose to bid, hoping that their opponent would withdraw. An analysis of the results of the first poll question (Figure 3) reveals that twice as many participants chose “preference for avoiding loss” as their incentive to continue bidding than participants who chose “desire to win”. This shows that, despite taking the greater short-term risk and choosing to continue bidding, participants were still more concerned about the long-term risk of losing than they were about the reward of winning. 

The results of this study match the prediction for the control group made in our hypothesis, where participants will bid progressively higher amounts until they reach $50, but does not support our prediction for the experimental group, as we predicted more participants would withdraw after bidding small amounts, preferring to minimize the potential for future loss. However, the premise of the hypothesis is supported, as participants overwhelmingly cited the preference to avoid loss as a greater factor in their decision than the desire for reward.