Going beyond the in-/out-group dichotomy: Investigating altruism towards middle-groups

2022-07-20

2022-08-11

1) The success in the group task:
Has a group solved the group-task successfully: yes/no? We will regress this binary outcome with a probit regression on the group-size and the chosen artist. H0: group-size and chosen artist have no statistically significant effect on the success in the group-task.

2) Allocations of coins to the different cups:
First, as an overview of the results we calculate the mean allocation x of all participants to the respective cups per treatment and per part.

3) Delta in allocation of coins to theoretical value:
We then divide this mean allocation of coins by how many coins should theoretically be put into that cup (15, if there are two cups in a part – 10 if there are three cups): x/10 respective y/15. These values can be interpreted as “for every coin that should have been put into this cup, how many coins were actually put into it”

4) Causal effect of introducing a middle-group:
We will use a difference-in-difference approach to identify the causal effect of introducing a middle-group. The control group is the “2-2” group, the treatment group the “2-3” group. The first part is the pre-treatment, the second part is the post-treatment period. We will look at two outcome measures correcting for multiple hypothesis testing: (i) When a middle-group is introduced, what is the effect on the delta in allocation of coins compared to the theoretical value for the in-group? (ii) … for the out-group? H0: there are no effects.

5) Compare this effect between the alternative middle-groups:
Treatments “2-3” and “2-3a” use two different types of middle-groups. Everything we do for the “2-3” treatment in the last part (4) of the analysis we will also do for treatment “2-3a” and then compare the coefficients and their standard deviations.

6) Effect of having had a middle-group from the beginning versus being introduced to it later:
The treatment “3-3” had the middle-group from the start, the treatment “2-3” only in the second part. To investigate the effect of this difference in experience with a middle-group, we will pool all data from the second round of these to treatments and run an OLS regression with the treatment-variable (i.e. the difference in experience) as explanatory variable. We will do this for three outcome measures correcting for multiple hypothesis testing: (i) What is the effect of being introduced to a middle-group already at the start on the delta in allocation of coins compared to the theoretical value for the in-group? (ii) … for the middle-group? (iii) … for the out-group? H0: There are no effects.

7) Analysis on the individual level:
For each participant and part we will count how many coins were put into cup x and calculate the “delta in absolute coins” by subtracting the theoretical amount of coins (10 or 15). We will plot the “delta in absolute coins per cup”-distribution of all participants in each treatment, part and cup on a x-scale [-15, +15]. We will then perform a Monte-Carlo-Simulations for each of these plots where the simulated agents indeed distribute the coins randomly as specified by the rules. The difference to the actual experimental data is that there the subjects might in fact not have followed the rules. In this case we will observe different distributions. Then for each treatment, part and cup we compare the simulated results with the actual results of the human experimental participants with a Kolmogorov-Smirnov-test.
H0: The distributions of the results of the experimental data and the simulated data are statistically not different from each other.

8) Behaviour over time:
Per treatment and round we calculate the mean contribution per cup. First, we will plot this variable over all rounds. Then we will perform an OLS regression on this variable with rounds as explanatory variable to see whether there are time trends. H0: there are no time trends.

The main feature of the present study is the introduction of “middle-groups” between in- and out-groups within the minimal group paradigm.
First, participants are asked whether they prefer a painting by Kandinsky or Klee. Based on this choice participants are grouped in groups of 3-5 where everyone chose the same painting. This is the in-group of a participant. An out-group member is described as a random participant who takes part in this study at another (unknown to the participant) university, at a different time and who chose the other painting. A member of a middle-group is described as a random participant who takes part in this study at the same university at a different time who chose the same painting. In a variation that participant is at another university.
With their respective in-group, the participants have to solve a group task. Individually they have to identify which of two paintings was made by the painter they chose in the first activity, there are five rounds of this with new paintings in each round. All the individual guesses in a group are added up, and if a group made more correct than false guesses they win a monetary reward.
As task, the experiment uses an adaption of the mind game as presented in Hruschka et al (2014) ‘Impartial Institutions, Pathogen Stress and the Expanding Social Network’. Participants are presented cups that are associated with the groups mentioned above (in-, middle-, alternative middle-, out-group). In step 1 of every round they should pick one of the cups in their head (unobservable to the experimenter), in step 2 they should roll a die (unobservable to the experimenter), in step 3 they should put 1 coin in one of the cups depending on the cup they chose in their head and the result of the die-roll. Whether participants put the coin into the “correct” cup is unobservable to the experimenter. But due to the random nature of the die-roll, it should be equal in all cups, which can be tested statistically.
The experiment consists of two parts directly after each other with 30 rounds of the above-mentioned steps in both parts, so in total 60 rounds.
There are three setups of the cups:
• In the first setup (“2”), there are only cups of the in- and out-group.
• In the second setup (“3”), there are cups of in-, middle- and out-group.
• In the third setup (“3a”), there are cups of in-, the above-mentioned alternative middle- and out-group.
We use four treatments that combine the setups in the two parts in different ways: (“first part” – “second part”):
1. 2-2
2. 2-3
3. 3-3
4. 2-3a
We plan to run this study with 4 sessions each at Heidelberg University and at Hochschule Rhein-Waal. In each session we aim to have 30-35 participants, so a total sample size of 240-280. The treatments will be randomly assigned, so will be roughly, but most likely not exactly, similar in size.

Randomization by computer (oTree / python)

1. individuals to groups 2. groups to treatments

Yes

2 different universities

240-280 university students

60-70 per treatment, 120-140 per universities, where treatments are roughly equally split over universities