Online Supporting Materials

A. Experiment Instruction (Translated from the original version in Chinese)

Welcome!

In what follows, you are going to participate in some activities for about 40 minutes. You will use the computer to participate in the activities. Please do not open other browsers to work on other tasks. Use of cell phone and consumption of food are not allowed during the process. If you have any question, please raise your hand and we will come to assist you.

You are going to participate in a game and interact with others in the room. The rules of the game are articulated as follows: In each round of the game, you would be given 10 tokens and decide whether to donate any amount to a public account. Donation to the public account would be multiplied by 4 and then evenly distributed to everyone in the room (including yourself). And the tokens you do not donate would be kept to yourself. The tokens you have at the end (those you keep plus those you receive from the public account) are redeemable to money: The more tokens you have, the more money you would get.

You would use the pseudo-ID number and password we provide to you to log on to the online game. Your real identity would NOT be used or revealed in the game. If you choose to drop out in the middle of the game, we will pay you a show-up fee, but not the additional payoff from the game.

It is emphasized that in what follows you are participating in a REAL game with other participants in the room. No deception is used in the game. Note that how much you would get from the experiment depends on not only your personal decision-making, but also how others make their decisions.

You are going to take on 5 games. Each game is independent of one another. The token balance in your account at the end of a game would be recorded and it would be renewed to zero in the beginning of the next new game. At the end of today’s experiment, we will choose one of the 5 games by lottery to pay you in proportion to the balance of tokens you earn in the chosen game.

B. Selection of Snapshots of the User Interface

(Translated from the original version in Chinese)

* Note: The numbers in bold and italic in the following context are for illustration only and they would be endogenously generated by the computer program in reference to participants’ behavior in the experiment.

1. In the beginning of an experiment trial

Let us review the rules of the game again. In each round of the game, you would be given 10 tokens and decide whether to donate any amount to a public account. Donation to the public account would be multiplied by 4 and then evenly distributed to everyone in the room (including yourself). And the tokens you do not donate would be kept to yourself. The following table illustrates an example of the outcomes of the decisions made by you and the 15 others. The numbers in the cells show how many tokens you would get.

When every other donates 10tokens / When every other donate 0 token
When you donate 10 tokens / 40 / 2.5
When you donate 0 token / 47.5 / 10

Keep in mind, however, the example above is for your reference only. In the following game, you can choose any token(integer) between 0 and 10 for donation to the public account. Similarly, other participants are engaging in the same decision-making as you are.

2.1 Decision-making phase (for individual decision makers in round 1):

Current Token Balance: 30(1 token = NT$ 3)

You are going to play the game with 15 other participants

Now you are given 10 tokens. Please indicate how many of them you would like to donate to the public account:______

2.2 Decision-making phase (for group leaders post round 1):

Current Token Balance: 60(1 token = NT$ 3)

You are going to play the game with 3 other subgroup representatives.

Now you are given 10 tokens. Please indicate how many of them you would like to donate to the public account. Note again that being a representative your decision will represent your group members’ decisions. Before making the decision, you may want to view the decisions made by part of your group members in the previous round:

3, 5, 8, 7,…….

2.3 Announcement of the PGG result

Below is the result of the 1st round.

You donated 7 tokens to the public account. The distribution of the other 15 players’ donations is:

Mean: 4.23

Median: 5

Maximum: 8

Minimum: 0

According to the result, in this round you have received 20.61 tokens that would be deposited to your account.

3.1 Voting phase

We are entering a new round of the game and the rule of the game is the same as before. However, not every of you would play in the next round; instead, you would elect representatives to make decisions on others’ behalf.

Every player in the room is assigned to different subgroups. A representative would be elected from each subgroup. His or her decision made in the game would apply to his/her group members. For example, suppose that player A, B, and C are in one subgroup and player A is elected as the representative. Then player B and C would not make decisions and their donation to the public account would be copied from player A’s donation.

Now please review the donation records of your group members made in last round. Please cast your vote on the one you prefer to be the representative. The candidate who receives the highest votes would be the representative. Lottery would be used to break a tie in ballot counts.

Candidates’ donation records / 1 / 4 / 7 / 6 / 8 / 9
(Please fill the circle) /  /  /  /  /  / 

3.2 Announcement of the election result (for the leaders)

After 2 round(s) of election, you are now elected as the representative to make decisions on behalf of 4 persons (equivalent to 25 % of the whole group). The structure of your representativeness is shown as follows. You will represent these people to play the game with 3 other subgroup representatives in the following round.

C. Empirical Assessment of the Parameter p in the Experiment

The preference parameter p is by assumption a continuous variable in the model, while the position of the candidate that actors voted for in the experiment (P) is discrete (integer). To estimate the parameter p requires an interpolation of actors’ choices (P) made in the experiment. In our simulation model, given a number of candidates (l) ranked from low to high by cooperativeness, actor i, whose voting preference is pi, would vote for the kth position candidate if . Therefore, if we observed in the experiment that actor i casted his/her vote on the kth position candidate, the estimation of his/her preference of leadership would be: , which is the mid-point of (k-1)/l and k/l.

D. Supporting Tables and Figures

Table S1- Conditions under which direct election chooses more cooperative leaders than indirect election does in the simulation

Preference / Preference Variation / Electorate Composition / Groups Size
Strong / Weak / Large / Small / Random / Homophilous / Large / Small
√ / √ / √ / √ / √
√ / √ / √ / √
√ / √ / √ / √

Note: The check sign specifies that the condition of a factor (shaded in gray) be fulfilled. Each row represents a combination of conditions wherein direct election would choose more cooperative leaders than indirect election.Whereas a factor has both conditions checked, it means that in either condition, when combined with the conditions of other factors specified inthe same row, direct election would generate more cooperative leadership.

Table S2 - Tobit regression on public goods contribution in the final two rounds

Independent Variables / Estimates
Delegated Leadership
(0=default treatment; 1=voting treatments) / 6.72***
(0.76)
Voting Schemes
(0=indirect election; 1=direct election) / 4.80***
(0.65)
Electorate Composition
(0=homophilous; 1=random) / 3.48***
(0.55)

Note: *** p<0.001, ** p<0.01, * p<0.05

Standard errors are clustered within subjects and reported in the parentheses

Table S3 - Logistic regression on the likelihood of voting for self

Independent Variables / Estimates
Voters’ Ranking in Cooperativeness / 2.29***
(0.35)
Voting Scheme
(0=indirect election; 1=direct election) / -1.68***
(0.14)
Electorate Composition
(0=homophilous; 1=random) / 0.27
(0.14)

Note: *** p<0.001, ** p<0.01, * p<0.05

Standard errors are clustered within subjects and reported in the parentheses

Figure S1The mean cooperativeness of the top leaders elected in the different election systems against different preference structures of actors. Plots in the left (right) column represent random (homophilous) electorates.

Figure S2The mean cooperativeness of the elected leaders against different group sizes (horizontal axis). Plots in the left (right) column represent random (homophilous) electorates. The curves at the upper (lower) positions in each figure represent strong (weak) preferences for cooperators as leaders.

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