Coalition Formation under Representation and Ideological Positioning

Treatment 1-1-1: no representation [A - 1 member, B - 1 member, C - 1 member]
Treatment 3-3-3: balanced representation [A - 3 members, B - 3 members, C - 3 members]
Treatment 4-2-4: small, centrist third party [A - 4 members, B - 2 members, C - 4 members]
Treatment 2-4-4: small, extreme third party [A - 2 members, B - 4 members, C - 4 members]

2026-05-25

2027-03-31

Measured variables include participants’ agreed bargaining allocations, whether bargaining reaches an agreement, individual risk aversion, and prosocial parameters and categories.

Agreed bargaining allocations can be further investigated for the type: (proportional, equal division, centrist dominance, real voting
weights across teams, real voting weights across team members), coalition types (by a mainstream party and a small third party, or by two mainstream parties), and specific payoffs for each team.

We also collect all chat discussions and bargaining offers, including their content, timing, and status. In addition, data from the side tasks: risk elicitation (BRET), prosocial games, and cognitive assessments are recorded for each participant.

1. Design overview
There are three groups A, B, and C, each consisting of several members (representing parliamentary seats). No single group holds more than 50% of the seats, meaning that a governing coalition must consist of at least two parties.

Furthermore, there are position constraints affecting coalition effectiveness. Party B is centrist, positioned between Party A (left) and Party C (right). If a government formed by distant parties, such as (A + C) or (A + B + C), is deemed ineffective, resulting in a payoff of 0. Coalitions formed by adjacent parties, such as (A + B) or (B + C), can coordinate policies effectively and yield a payoff of 100.

This constraint eliminates superadditivity in standard coalition formation settings. As a result, the game operates as a dual-bargaining environment, where simultaneous negotiations take place between A and B, as well as between B and C.

Some treatments involve representation, where one participant negotiates on behalf of the team. In the baseline treatment, teams consist of 1 member and each participant negotiates for their personal payoffs.

Coalition bargaining is repeated in 4 rounds.

To avoid framing bias related to political preferences, each participant is assigned into a "Team" based on the result of the modified Minimal Group Paradigm task in each round.

2. Treatments
Treatment 1-1-1: no representation [A - 1 member, B - 1 member, C - 1 member]
Treatment 3-3-3: balanced representation [A - 3 members, B - 3 members, C - 3 members]
Treatment 4-2-4: small, centrist third party [A - 4 members, B - 2 members, C - 4 members]
Treatment 2-4-4: small, extreme third party [A - 2 members, B - 4 members, C - 4 members]

3. Stages
3.1. Modified Minimal Group Paradigm task
Subjects are asked to rate their preferences for several pairs of paintings by two artists A and C. Based on the results, 3 teams are formed: Team A (those with strong preference for Artist A), Team B - balanced, and Team C (those with strong preference for Artist C). In case of a tie, individuals could be randomly assigned to one of two bordering groups (e.g. A or B).

The task is based on the Klee-Kandinsky task (Tajfel 1970) from social psychology. The purpose of the task is to create groups with unified identities based on trivial distinctions (Klee and Kandinsky were abstract painters with similar styles). In our modification, the task also selects extreme and balanced groups, which represent realistic political scenarios.

In 4 repeated rounds of bargaining, the artist pairs are updated based on real artists with similar styles. The team labels for different rounds are:
Round 1: Team A (strong preference for Artist A), Team B - balanced, and Team C (strong preference for Artist C).
Round 2: Team F (strong preference for Artist F), Team G - balanced, and Team H (strong preference for Artist H).
Round 3: Team L (strong preference for Artist L), Team M - balanced, and Team N (strong preference for Artist N).
Round 4: Team P (strong preference for Artist P), Team Q - balanced, and Team R (strong preference for Artist R).

After the task, subjects are told what team they are assigned to based on their preferences. The sizes of all teams are also shown.

3.2. Individual preferences
We collect preferences of each participant for:
- The ideal payoffs their team should aim for in negotiation.
- The minimum payoffs their team should aim for in negotiation (amount below this should not be accepted).
- What coalition is preferred (only for the centrist team B)
- Whether they would like to represent the team in negotiation (only for treatments with representation).

3.3. Negotiation representatives
Treatment 1-1-1 (no representation) skips this stage.
In Treatment 3-3-3, three negotiations take place simultaneously. Each member participates in a separate negotiation. One of the three outcomes is randomly chosen to determine the payoffs for the round.
In Treatment 4-2-4 and 2-4-4, two members in each team are randomly chosen as negotiation representatives. Two negotiations take place simultaneously. One of the two outcomes is randomly chosen to determine the payoffs for the round. The two members in teams of four wait until both negotiations finish.

3.4. Group communication
Members chosen to represent the team in negotiations are announced.
Individual preferences previously collected are shown to the team.
Team members can freely communicate in a chatbox.

Treatment 1-1-1 (no representation) skips this stage.

3.5: Bargaining

Bargaining is conducted in an unstructured format.

Subjects representing Team B can negotiate both with Teams A and C. Subjects representing Teams A and C can only negotiate with Team B.

Each bargaining pair negotiates over splitting a payoff of 100. Within each bargaining pair (A and B; B and C), subjects can (1) propose, retract, accept, or reject different allocations; and (2) communicate freely with each other.

A coalition is formed when one pair agrees on an allocation. The payoff for each team is equally divided for each team member. For example, if team A has 4 members and reaches a payoff of 40, each member receives 10 for the round. The remaining team excluded in the coalition gets a payoff of zero.

When the time limit is reached and no agreement is reached, all teams receive a payoff of zero. Bargainers can quit early and earn a payoff of zero for the team.

The sample bargaining screens for representatives of Teams A and B are attached. For Team C: bargaining screens look similar to screens of Team A, but instead, the half on the left (negotiation between A and C) is greyed out, while the active negotiation is on the right (between B and C).

4. Conversion rate in bargaining
As each treatment has a different number of participants in coalition bargaining, we use a different conversion rate of the 100 payoff points:
- For treatment 1-1-1 (group of 3): 1 payoff point is worth 15 JPY. 100 payoff points is worth 1500 JPY.
- For treatment 3-3-3 (group of 9): 1 payoff point is worth 45 JPY. 100 payoff points is worth 4500 JPY.
- For treatment 4-2-4 and 2-4-4 (group of 10): 1 payoff point is worth 50 JPY. 100 payoff points is worth 5000 JPY.
These rates ensure similar average payments across treatments.

5. Other tasks and questionnaire
- Bomb Risk Elicitation Task (BRET) to measure risk aversion
- Modified dictator game, modified ultimatum game: Bayle (2025) to elicit the inequality aversion and the behavioral symmetry (in a Kantian morality perspective)
- NLE task to measure cognitive ability without relying on the standard CRT
- Questionnaire:
-- Self-declared risk preference
-- Political leaning (on a left-right spectrum) and affiliation (support for a particular political party)
-- How participants make their decisions in the modified Minimal Group Paradigm task
-- Sociodemographic information: age, gender, degree, academic major, nationality

Not available

Randomization by computer will determine grouping.

Treatment randomization for each session.

No

Data collection will take place at Waseda University’s laboratory in Japan, targeting student participants. The collection period is scheduled from May 2026 to February 2027.

Each session will include either 18 participants (treatments 1-1-1 and 3-3-3) or 20 participants (treatments 4-2-4 and 2-4-4). These numbers ensure a new group composition of different participants are formed in each round. They also ensure sufficient anonymity, preventing participants from identifying their partners.

For treatments 1-1-1 and 3-3-3: We plan to recruit 18 participants per session. In each round, the 18 participants are divided into 6 groups of 1-1-1 (1 negotiation) or 2 groups of 3-3-3 (3 concurrent negotiations). Therefore, each round records 6 observations (bargaining outcomes). With 4 rounds, each session has 24 observations. We plan to conduct two sessions (36 participants) for each of these treatments, resulting in a total of 48 observations per treatment.

For treatments 4-2-4 and 2-4-4: We plan to recruit 20 participants per session. In each round, the 20 participants are divided into 2 groups of 4-2-4 or 2-4-4, each with 2 concurrent negotiations. Therefore, each round records only 4 observations (bargaining outcomes). With 4 rounds, each session has 16 observations. We plan to conduct three sessions (60 participants) for each of these treatments, resulting in a total of 48 observations per treatment.

With this sample size and a significance level of 0.05 (alpha), the power analysis yields a value of 0.83.

192 bargaining outcomes, 48 bargaining outcomes per treatment.

We plan to recruit 192 subjects in order to achieve a power of 0.83 for an alpha of 0.05.

With this sample size and a significance level of 0.05 (alpha), the power analysis yields a value of 0.83.

Analysis plan