Social Numbers
Creators: name: Kappes, Andreas
Publisher: name: Open Science Framework
Year: 2022
Subjects: subject: Social Psychology
subject: Social and Behavioral Sciences
subject: Psychology
subject: FOS: Psychology

description: Research Question In this project, we ask if the social decision making is influenced by the number of social partners involved in the decision. Specifically, we predict that humans make qualitatively different decisions depending on whether they can individuate social partners (i.e., in the small number range) or not (i.e., in the large number range). Sample size We will recruit 144 participants via Amazon Turk. Predictions and Analysis plan: 1. Does the number of victims count in the small vs. large number range? We use trolley dilemma type scenarios, where we manipulate both the number of people who are saved and the number of people who are killed, using the following combinations: 1. Save 4 while killing a. 2 (ratio: 2:1) b. 3 (ratio: 4:3) 2. Save 40 while killing a. 20 (ratio: 2:1) b. 30 (ratio: 4:3) 3. Save 400 while killing a. 200 (ratio: 2:1) b. 300 (ratio: 4:3) Predictions and analyses: • Model: o acceptability ~ number_range * number_ratio + (1|participant) + (1|scenario) o The number range is the number of saved and the ratio the contrast between a and b. o Number range will be coded as a factor, with 4 as the base level • People should be less willing to kill in (1) than in (2) or (3) o Main effect of number_range • If the effect is driven by harm aversion, the difference between 1a and 1b should be smaller than between 2a and 2b and than between 3a and 3b. o Interaction between number range and number ratio o Potentially interaction between number range and number ratio after removing Condition 1. • If the effect is driven by the net number of saved individuals, the difference should be greater between 3a and 3b than between 2a and 2b, and people should be more willing to kill in 3 than in 2; if it is psychophysically driven by the Weber ratio, the relative willingness to kill should be the same in 2 and 3. o Main effect of number range interaction between number range and number ratio after removing Condition 1. o Evidence for null:  For each of Conditions 2 and 3: Calculate within-participant difference score between Conditions 2a and 2b and Conditions 3a and 3b, respectively.  Subtract the difference scores.  Fit two normal distributions to these difference, one fitting the mean and one setting the mean to zero, calculate the likelihood of the difference given these distributions, adjust the likelihoods of the different numbers of parameters using the Bayesian Information Criterion and the Akaike Information Criterion, and calculate the likelihood ratio for the null model (i.e. the one where the mean is set to zero). Long-term follow up: Parametrically manipulate the Weber ratio 2. Does the number of saved count in the small vs. large number range In the small number case, people might be driven by the number of victims, while, in the large number case, they might go for the ratio between the saved and the sacrificed. This can be tested by manipulating the number of the saved individuals. 4. Kill 2 for saving a. 3 (ratio: 2:3) b. 4 (ratio: 1:2) 5. Kill 20 for saving a. 30 (ratio: 2:3) b. 40 (ratio: 1:2) 6. Kill 200 for saving a. 300 (ratio: 2:3) b. 400 (ratio: 1:2) Predictions and analyses: • Model: o acceptability ~ number_range * number_ratio + (1|participant) + (1|scenario) o The number range is the number of killed and the ratio the contrast between a and b. • Number range will be coded as a factor, with 2 as the base level • Difference between (a) and (b) is stronger in 5 or 6 (where people go for the ratio) than in 4, where people go for the number of victims o Interaction between number range and ratio • However, it also possible that people are overall less sensitive to the number of saved than to the number of victims. o Unclear how this should be tested. Having a combined model of Conditions 1 to 6, with an additional factor whether number of victims or the number of saved is manipulated, and expect a triple interaction? Not sure this make sense 3. Does the first victim has a special status? We will use trolley dilemma type scenarios, where vary the number of victims. In all conditions, 40 people will be saved if the participant is willing to kill 1, 2 or 10 people. Prediction and analyses: • Model: o acceptability ~ number_killed + (1|participant) + (1|scenario) o number_killed is treated as a factor with 10 as the base level • People will be more likely to kill 10 people than to kill a single person due to the singleton effect. o Main effect of number_killed for the 1 vs. 10 contrast • They are more likely to kill 2 people than to kill 10 people. o Main effect of number_killed for the 2 vs. 10 contrast Experimental conditions for Experiments 1 to 3. As the 2 vs. 4 comparison is used in both Experiment 1 and Experiment 2, we end up with a total of 9 conditions for Experiment 1 and 2, and another 3 conditions for Experiment 3: # Victims # Saved Experiment 2 4 1, 2 3 4 1 2 3 2 20 40 1, 2 30 40 1 20 30 2 200 400 1, 2 300 400 1 200 300 2 1 40 3 2 40 3 10 40 3 Counterbalancing for Experiment 1 to 3 • Condition-Scenario assignment. We have 12 conditions and 12 scenarios. In total, there are thus 12! = 479,001,600 ways to assign scenarios to conditions. We will thus use a Latin square design, yielding 12 assignments. • Condition order. The order of the conditions is randomized. 4. Are people more altruistic when dealing with smaller numbers of social partners? In the first set of experiment, people will become more utilitarian in the large number range (at least when we manipulate the number of victims). In this experiment, we ask if participants are less utilitarian (and altruistic) when they have to deal with more social partners because they cannot use the large number system to track individual beneficiaries, which, in turn, would lead to socially undesirable outcomes. Specifically, we use a dictator game where participant have to give up amount A for it to be provided to recipients. Critically, a bank will step in so that all recipients receive the amount A at the same cost to the participant. There will be 2, 3, 4 (small number range), 200, 300 or 400 (large number range) recipients; for good measure, we also a single participant. Predictions: • A will be greater in the small number range than in the large number range. • A will be greater for 3 recipients than for 1 recipient, but not for 300 recipient than for 100. • Factorial prediction for A ~ [number range] x [2 vs. 3 vs. 4] o Main effect of number range o Interaction between number range and 2 vs. 3 vs. 4 Note: We discussed including 20, 30 and 40 as well, but then we wouldn’t have a factorial design. Instruction wording. Scenario 1: Tip in a restaurant (for N&gt;1) The Electric Dairy is a luxury restaurant chain with an unusual way of determining the tips for their waiters. Diners receive a £100 discount they can keep for themselves. However, they can also give up a portion of the discount as tip. The Electric Dairy will then step in to give that amount to all of their N waiters. How much they give up and how much they keep to themselves is entirely up to the diner and unknown to the staff at the Electric Dairy. For example, if a diner keeps the discount to themselves, the waiters receive nothing; if a diner gives £20, they get to keep £80, but all N waiters get £20; and if a diner gives £80, they get to keep £20, but all N waiters get £80. If you were dining at the Electric Dairy, how much of your £100 discount would you give up? Scenario 2: Economic game (for N&gt;1) Vernon Hermann is an economist interested in how much people value each other. He invites panels of N people. Unbeknownst to the other panel members, one panel member is chosen to receive £100. This member can either decide to keep the money to her or himself, or to give up a portion of this money so that all the other panel members receive that amount. For example, the chosen panel member decides to keep everything, the other panel members receive nothing; if the panel member decides to give up £20, the panel member gets to keep £80, and each of the other N panel members receives £20; and if the chosen panel member decides to give £80, the panel member gets to keep £20, and each of the other N panel members receives £80. If you were the chosen panel member, how much of your £100 would you give up?