Beyond seat share: evaluating voting-power indices in government formation

Abstract

This thesis evaluates whether cooperative game-theoretic voting-power indices improve empirical explanations of government formation relative to models based solely on parliamentary seat share. While seat share is the dominant measure of bargaining power in the coalition formation literature, it captures numerical size rather than strategic necessity - two quantities that diverge substantially in fragmented multiparty legislatures. Four indices are examined: the Banzhaf Power Index and Shapley-Shubik Value, which compute pivotality across all winning coalitions, and the Deegan-Packel and Holler-Packel indices, which restrict attention to minimal winning coalitions only. The analysis covers 4,939 party-election observations from 626 elections across 37 parliamentary democracies between 1945 and 2023, using nested logistic regression models evaluated through four complementary criteria: McFadden pseudo-R², likelihood ratio test, Bayesian Information Criterion, and area under the ROC curve. The results are asymmetric. The all-coalitions family consistently outperforms seat share across both outcome variables and all four criteria. The minimal-winning-coalition family does not, because its restriction to minimal winning coalitions embeds an assumption about rational behaviour that the empirical record systematically violates. For researchers operationalising bargaining power in coalition research, the Banzhaf or Shapley-Shubik index is the appropriate structural measure; seat share, while interpretable, is a less precise substitute.