Coalition Formation Analysis
Also known as: Minimal Winning Coalition Theory, Riker Size Principle, Coalition Theory, Government Coalition Analysis
Coalition formation analysis is the formal study of which subset of parties will combine to form a governing or decision-making coalition when no single party commands a majority. William Riker's 1962 The Theory of Political Coalitions supplied the foundational logic: under pure office-seeking, rational politicians form minimal winning coalitions and, by the size principle, the smallest winning coalition possible, so that the spoils of office are divided among as few partners as necessary. Michael Laver and Norman Schofield's 1990 Multiparty Government enriched this with policy-seeking motives, showing that coalitions also tend to be ideologically connected. The framework predicts coalition membership from seat shares and party positions.
Key highlights
- Derives sharp, parsimonious predictions about coalition membership from nothing more than seat shares and, optionally, policy positions.
- Cleanly separates and then recombines the two great motivations — office and policy — clarifying the logic behind each prediction.
- Provides falsifiable benchmarks (minimal winning, minimum size, connected winning) against which observed governments can be scored.
- Connects naturally to cooperative game theory and power-index analysis, embedding coalition choice in a broader formal tradition.
Intuition
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How it works
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When to use it
Use coalition formation analysis when no party holds a majority and you need to predict, or explain, which combination of parties will govern, support a cabinet, or pass a measure — the central question of multiparty parliamentary politics. The office-seeking (minimal-winning, minimum-size) predictions are most useful when the spoils of office dominate motivations and policy differences are secondary; the policy-based (connected winning) predictions are appropriate when ideology constrains who can credibly govern together. The framework also informs analysis of legislative voting coalitions and any setting where a majority must be assembled from indivisible blocs. It is less suited to cases dominated by a single formateur's bargaining advantage or by detailed portfolio negotiations, where the structural government-formation bargaining model is the better tool, and to two-party systems where coalition choice does not arise.
Strengths & limitations
- Derives sharp, parsimonious predictions about coalition membership from nothing more than seat shares and, optionally, policy positions.
- Cleanly separates and then recombines the two great motivations — office and policy — clarifying the logic behind each prediction.
- Provides falsifiable benchmarks (minimal winning, minimum size, connected winning) against which observed governments can be scored.
- Connects naturally to cooperative game theory and power-index analysis, embedding coalition choice in a broader formal tradition.
- The pure size principle systematically under-predicts the surplus-majority and minority governments that occur frequently in practice.
- It treats office benefits as a fixed, perfectly divisible prize, abstracting from the lumpiness and importance of specific portfolios.
- Static criteria ignore the sequential bargaining and formateur advantage that shape which feasible coalition actually forms.
- Identifying the relevant policy dimension and parties' positions on it is empirically demanding and can change the connected-coalition prediction.
Common pitfalls
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Applications
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Frequently asked
What is the difference between a minimal winning coalition and a minimum-size coalition?
A minimal winning coalition is one with no surplus members: every party in it is needed for the majority, so dropping any one would make the coalition lose. A minimum-size coalition is the strongest version of Riker's size principle — among all winning coalitions it has the smallest total seat weight. Every minimum-size coalition is minimal winning, but not every minimal winning coalition is minimum-size, because a coalition can have no redundant members yet still hold more total seats than some other winning combination.
Why do the pure office-seeking predictions often fail empirically?
Riker's size principle assumes politics is a zero-sum division of fixed office spoils, but real coalitions frequently include surplus partners or even fall short of a majority (minority governments). This happens because parties also pursue policy, because uncertainty about partners' reliability rewards extra seats as insurance, because external threats or constitutional supermajority requirements favor oversized coalitions, and because some parties are excluded as anti-system regardless of size. Incorporating policy connectedness and bargaining dynamics improves the predictions substantially.
How does coalition formation analysis differ from the government formation model?
Coalition formation analysis is a cooperative, selection-among-coalitions approach: given seat shares and positions, it identifies which subsets of parties are winning, minimal, smallest, or ideologically connected. The government formation model is a non-cooperative, sequential bargaining framework in which a formateur is recognized, proposes a government and a division of portfolios, and partners accept or reject — generating a proposer advantage and explaining portfolio allocation. The two are complementary: coalition theory characterizes the feasible and attractive coalitions; the bargaining model explains how one of them is actually chosen and how the spoils are split.
Sources
- 1.Riker, W. H. (1962). The Theory of Political Coalitions. Yale University Press.ISBN 9780300001754
- 2.Laver, M., & Schofield, N. (1990). Multiparty Government: The Politics of Coalition in Europe. Oxford University Press.ISBN 9780198280798
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Cite this page
ScholarGate. (2026, June 22). Coalition Formation Analysis. ScholarGate. https://scholargate.app/political-economy/coalition-formation-analysis