Collective decisions and intertemporal risk choices

Participants are randomly assigned to a 3-person group to complete two behavioral tasks: a Risky Choice (RC) task and a Risky-Intertemporal Choice (RIC) task. The study implements a 2 X 2 between-subject factorial design to evaluate how group decisions are shaped by two distinct dimensions of institutional design:

1. Factor 1: Voting Rules (Threshold for Agreement)
(1) Majority Rule Treatment: A group decision is successfully reached and executed if a specific proposal receives support from at least two out of the three members (a two-thirds majority threshold).
(2)Unanimity Rule Treatment: A group decision strictly requires the unanimous support of all three group members (a consensus threshold).

2. Factor 2: Voting Weights (Power Distribution)
(1) Unweighted System Treatment: All three group members possess equal voting power (each member has exactly 1 vote). Group earnings from the selected tasks are distributed equally among all members.
(2) Weighted System Treatment: Voting power is distributed asymmetrically. One randomly designated group leader is allocated 2 votes, while the remaining two ordinary members are allocated 1 vote each. Under this setup, a total of 4 votes exist within the group. To pass a proposal under the Majority Rule, a threshold of 3 votes is required. Earnings from the task are distributed proportionally based on each member's voting weight (the leader receives a higher share of the payoff).

In all treatments, if a group fails to reach an agreement within 5 formal coordination rounds, a deadlock is declared, and all members receive a zero payoff for that specific task.

2026-06-01

2026-12-31

I define three key primary outcome variables measured at the group level (or stage-specific individual level) to evaluate the treatment effects of voting rules and voting weights:

1. Group Risk-Taking Level ($D_{3}$) Definition: The total number of risky/delayed options (Option B) selected by the group in the final approved choice list for a given task.Measurement: This variable ranges from 0 to 10 for each task. A higher value indicates a higher group propensity for risk-taking (in the RC task) or a higher willingness to accept delayed risks (in the RIC task). We denote $D_{RC,3}$ as the final group outcome in the Risky Choice task and $D_{RIC,3}$ as that in the Risky-Intertemporal Choice task.

2. The Behavioral Delayed Effect ($\triangle_{3}$)Definition: The net change in the group’s risk-taking level caused strictly by the introduction of the 4-week temporal delay.Measurement: Calculated as the difference in the number of risky choices made by the final group between the two tasks: $\triangle_{3} = D_{RIC,3} - D_{RC,3}$. A more negative value of $\triangle_{3}$ indicates higher group sensitivity to the discounting effect of time delay, while a value closer to 0 indicates higher institutional resilience against short-term discounting.

3. Strategic Preference Displacement ($\Delta D_{Stage}$)Definition: The intra-group displacement of choices across different formal stages of the collective bargaining process, which isolates the net impact of institutional interaction from baseline individual preferences.Measurement: We primarily evaluate two displacement metrics:(a) Individual-to-Proposal Shift ($D_{2} - D_{1}$): The difference between a member’s first formal group proposal ($D_{2}$) and their baseline individual choice ($D_{1}$).(b) Pure Group Interaction Effect ($D_{3} - D_{1}$): The difference between the final enacted group decision ($D_{3}$) and the initial average individual preferences ($D_{1}$).

This study employs a mixed between-within subject factorial design to rigorously evaluate the causal impacts of formal voting rules and voting weights on collective intertemporal choices under uncertainty. The unit of randomization and independent statistical inference is fixed strictly at the group level (3-person interaction sessions) to fully control for intra-group correlation.

1. Between-Subject Factors (2 × 2 Factorial Treatment Cells)
Subjects are randomly assigned to one of four distinct, mutually exclusive institutional treatment cells upon arrival at the laboratory:

Treatment 1 (U-Uw) Unanimity & Unweighted: Decisions strictly require unanimous support from all 3 members (consensus threshold). All members possess equal voting power (1 vote each).

Treatment 2 (U-W) Unanimity & Weighted: Decisions strictly require unanimous support from all 3 members. Voting power is distributed asymmetrically: one randomly designated leader holds 2 votes, while the remaining two members hold 1 vote each.

Treatment 3 (M-Uw) Majority & Unweighted: Decisions require agreement from at least two out of three members (2/3 majority threshold). All members possess equal voting power (1 vote each).

Treatment 4 (M-W) Majority & Weighted: Voting power is distributed asymmetrically (Leader has 2 votes; each ordinary member has 1 vote; total = 4 votes). The institutional passage threshold is set to a strict minimum of 3 votes.

2. Within-Subject Factors (Multi-Dimensional Risk Tasks)
Every independent group completes two sequential conditions across four formal parts (Parts A to D) to elicit baseline individual preferences and final collective outcomes:

Condition 1: Risky Choice (RC) Task: Elicits pure risk preferences using a multiple price list (MPL) framework, trading off a certain, immediate payoff (Option A) against a probabilistic, immediate reward (Option B).

Condition 2: Risky-Intertemporal Choice (RIC) Task: Imposes a 4-week temporal delay on all potential payoffs of the risky option (Option B) while keeping the certain option (Option A) immediate, thereby capturing the direct behavioral interaction of risk taking and time discounting.

3. Coordination Protocol and Deadlock Rule
Within each group task (Parts B and D), a structured, dynamic coordination protocol is executed for a maximum of 5 formal rounds. Each round sequentially consists of: (i) Simultaneous Proposal Submission, (ii) Anonymous Free-Form Group Chat Deliberation, and (iii) Simultaneous Voting. If a group fails to reach a binding collective decision matching their treatment's threshold by the end of Round 5, a complete contract deadlock is declared, and all members earn zero payoff for that task.

Not available

The experiment is conducted entirely online via a dedicated web-based behavioral platform (oTree). The unit of randomization and independent statistical inference is fixed strictly at the group level (3-person anonymous online sessions). Upon logging into the synchronized online experimental server, eligible participants are randomly and evenly matched into 3-person virtual groups under one of four institutional environments.

This study implements a multi-level randomization structure consisting of two distinct levels, with the highest and most conservative unit of statistical inference fixed at the group level (3-person virtual clusters).

1. Level 1: Session-Level Randomization (Macro Level)

Unit: Experimental Session.

Description: Before the recruitment of online participants begins, each independent online session (a synchronized virtual timeslot on the server) is predetermined and randomly assigned to one of the four institutional treatments via a computer-generated schedule. This ensures that participants logging into a specific time block are blinded and orthogonal to the specific voting thresholds and power allocations they will encounter.

2. Level 2: Intra-Session Group-Level Randomization (Micro Level)

Unit: 3-Person Virtual Cluster (Group / Matching Group).

Description: Within each synchronized online session, as individual participants finish logging in, the background algorithm of the experimental software (oTree) randomly and anonymously aggregates individuals into strictly independent 3-person virtual groups.

Yes

160 Groups

480 participants (organized into 160 independent virtual groups).

40 groups per treatment arm.

40 groups in Unanimity & Unweighted, 40 groups in Unanimity & Weighted, 40 groups in Majority & Unweighted, and 40 groups in Majority & Weighted.