Coalition Formation Game

Robert Welz

JGU Mainz

05 November 2026

The Game

How do party goals affect electoral competition and coalition formation?

  • Work in groups: each group represents a party.
  • Choose an ideological position, compete in an election, and negotiate a government.
  • Your goal: maximize your own party’s points.

Preparation

  1. Form 3–7 parties
  2. Each party secretly draws a motive: office, policy, or both. Keep it secret until the final scoring stage.
  3. At game setup, we select:
    • Possible voter distributions and the number of cabinet portfolios (5–10).
    • Whether opposition parties can receive policy points.
  4. The app generates 1,000 voters on an ideological scale from 0 (left) to 100 (right).

The Election

  1. Every party chooses a position between 0 and 100.
  2. Voters choose the ideologically nearest party; ties are resolved randomly.
  3. Votes are translated proportionally into 100 parliamentary seats.
  4. The app displays the composition of parliament.

An absolute majority requires 51 seats.

Coalition Bargaining

  • Formateur: The party with the most seats makes the first proposal.
  • Parties respond in descending order of seat share and may make counterproposals.
  • Negotiate four things:
    1. Which parties form the government.
    2. Which party gets the head of government.
    3. How the ministerial portfolios are allocated.
    4. The government’s agreed policy position (0–100).

How to Score

Party motive Points
Office 10 Points per portfolio
Policy \(60 - \lvert Coalition Position-PartyPosition\rvert\)
Both \(\dfrac{OfficePts.+PolicyPts.}{2}\)
  • Head of Governments grants 20 Points!
  • Negative policy points are possible.
  • Office points are available only to coalition parties.
  • At setup, we decide whether opposition parties can earn policy points. If not, their policy component is zero.

Example: One Party, Three Motives

Party A is at position 30. The coalition agrees on 50. Party A holds 3 portfolios and the head of government.

  • Office component: \(3\times10=30\).
  • Policy component: \(60-|30-50|=40\).
  • Head-of-government bonus: 20.
If Party A’s motive is… Final score
Office \(30+20=\mathbf{50}\)
Policy \(40+20=\mathbf{60}\)
Both \((30+40)/2+20=\mathbf{55}\)

Let’s go!

https://robertwelz-coalition-game.share.connect.posit.cloud/