Strategic Voting under the Qualified Majority Rule

This is an analysis of strategic voting under the qualified majority rule. Existing formal analyses of the plurality rule predict the complete coordination of strategic voting: A strict interpretation of Duverger’s Law. This conclusion is rejected. Unlike previous models, the popular support for each option is not commonly certain. Agents base their vote on both public and private signals of popular support. When private signals are the main source of information, the uniquely stable equilibrium entails only limited strategic voting and hence partial coordination. This is due to the surprising presence of negative feedback: An increase in strategic voting by others reduces the incentive for a rational voter to act strategically. The theory leads to the conclusion that multi-candidate support in a plurality electoral system is perfectly consistent with rational voting behaviour. 1. Duverger’s Law and Strategic Voting Duverger (1954) introduced his Law to political economy by noting that “the simple-majority single-ballot system favors the two-party system”. His aim was to evaluate the effect of voting systems on the structure and number of political parties. Duverger’s writings envisaged an ongoing process involving both voters and political parties with bipartism as an eventual conclusion. More recent authors have offered a stricter version of Duverger’s Law. The models of Cox (1994), Palfrey (1989) and Myerson and Weber (1993) predict strict bipartism as the outcome of any plurality rule election. Palfrey’s (1989) “mathematical proof” claims that: “. . . with instrumentally rational voters and fulfilled expectations, multicandidate contests under the plurality rule should result in only two candidates getting any votes.” Date: Printed on February 14, 2000, in preparation for submission to the Journal of Political Economy. This paper is based on Part III of Myatt (1999), and is in submission under the title “A New Theory of Strategic Voting”. Stephen D. Fisher inspired this work with his extensive empirical research on tactical voting in Britain, and with many hours of conversation on the topic. Grateful thanks are also due to Geoff Evans, David Firth, Robin Mason, Iain McLean, Wolfgang Pesendorfer, Kevin Roberts, Hyun Shin, Chris Wallace, Peyton Young and seminar participants at Edinburgh, Johns Hopkins, Keele, LSE, Oxford, Princeton, Southampton and UCL for helpful comments. 1 STRATEGIC VOTING UNDER THE QUALIFIED MAJORITY RULE 2 These authors consider a population of agents each casting a single vote, where the candidate with the largest number of votes wins. They claim that the uniquely stable equilibrium outcome involves positive support for only two candidates. This outcome is the result of strategic voting — agents voting for other than their preferred candidates. Indeed, the prediction is that agents fully coordinate in their strategic behaviour. ...................................................................................................................................................................................................................................................................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..... ..... ..... ..... ..... ..... ..... ..... ...... ....... ....... ....... ....... ....... ....... ...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .