Intelligence and leadership selection

The experiment will use a 2x2 between subject design. It will vary the institution and the stage game.

2023-05-01

2023-06-30

The key outcome variables in this experiment are:

1. How subjects vote in the Majority treatment in Stage 3
2. Who subjects vote for in the Presidential treatment in Stage 3
3. The actions and strategies played by elected Leaders in Stage 3

We are interested in all these outcomes conditional on Raven score, obtained from Stage 1.

1. Voting at the individual level is a binary variable - 1 or 0 (Majority treatment)
2. Subjects can vote for 1 of five candidates in their group (including themselves). Only information given is about their earnings (Presidential treatment)
3. Actions are binary variables 1 or 0, and strategies can be estimated from actions in the repeated game using ML (Presidential treatment)

These outcomes all conditional on Raven score from Stage 1.

1. Subjects actions and strategies in Stage 2.

1. Actions are binary variables 1 or 0, and strategies can be estimated from actions in the repeated game in Stage 2 using ML

The experiment will use a 2x2 between subject design. It will vary the institution used for groups to make a decision and the stage game. It will also be concerned with the Raven score of subjects.

The experiment will use a 2x2 between subject design, and will consist of 3 stages.

Stage 1
We elicit a comprehensive range of subject characteristics using both incentivised tasks and surveys. We collect Raven score, risk preferences, social preferences, field of study, age, gender. Subjects are provided with no feedback about their decisions or payoffs until the end of the experiment. We will use the Raven test to measure intelligence, using 18 items from the Advanced Progressive Matrices (set E).

Stage 2

Subjects are matched into pairs and play a repeated game with random stopping time (0.75), with exponential distribution according to a predetermined pseudorandom sequence. Subjects play the game for a random number of times (0.75 continuation rule) according to a predetermined pseudorandom sequence, with random, anonymous rematching, to allow them to learn about the game, the incentives. They are provided with feedback, and are paid for one randomly chosen game at the end of the experiment.

Stage 3

Third, subjects are then randomised and put into two groups of 5. The group then collectively plays the repeated game until it ends. The repeated game is played for ten rounds.

-Treatment 1 Majority Voting – All group members must vote on which action to take in the game in each period of the game. Whichever action is voted for with majority, that action is implemented. They cannot abstain.

-Treatment 2 Presidential – At the start of each repeated game, group members vote for 1 member of the group to be the leader. The leader is selected by majority vote. The leader then plays the game on behalf of the group for the entirety of the repeated game, selecting actions. Payoffs for all group members are determined by the leader’s actions. Once the repeated game ends, they vote again for the next round of play. When voting for a leader, subjects are provided information about the average earnings of each subject in their group from each period of the games from Stage 2. They are not provided with individual characteristics.

All subjects, whether elected or not, must take an action in the repeated game even though it is irrelevant – this means they cannot select the president to avoid the cognitive cost of choosing.

In a second dimension we will vary the repeated game used in Stage 2 and 3, using the Prisoner's Dilemma or Battle of the Sexes. We will use the payoffs taken from Proto et al. (2019, JPE).

Similarly, we will follow Proto et al. (2019, JPE) and divide subjects by the average Raven score into High and Low Raven subjects, once all sessions have been completed.

Pre-determined pseudo randomised sequence

session level randomisation

Yes

40 sessions in total

We plan to collect 40 sessions worth of data, with ten subjects in each session. This means we will use a total of 400 subjects.

Ten sessions per treatment.

Many of our outcome variables are binary. We consider the minimum detectable effect size using session level averages. If group or individual level averages are consider, the minimum detectable effect size is considerably larger. Binary variables - between subject, session level averages alpha (significance) = 0.05 n1=10 n2=10 sd1=0.25 sd2=0.25 power=0.8 The minimum detectable effect size is a 0.33 difference between variables between any two treatments. Binary variables - session level, binary variables, paired averages (high vs low raven) To detect an effect of 0.3 power=0.8 sd=0.25 alpha (significance)=0.05 correlation between averages =0.5 We would need 8 sessions to detect this effect size using session level data.