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The median voter theorem in political science and social choice theory, developed by Duncan Black, states that if voters and candidates are distributed along a one-dimensional spectrum and voters have single-peaked preferences, any voting method that is compatible with majority-rule will elect the candidate preferred by the median voter. The median voter theorem thus shows that under a realistic model of voter behavior, Arrow's theorem, which essentially suggests that ranked-choice voting systems cannot eliminate the spoiler effect, does not apply, and therefore that rational social choice is in fact possible if the election system is using a Condorcet method.
This is sometimes reframed into the median voter property, a voting system criterion that says electoral systems should choose the candidate most well-liked by the median voter. Systems that fail the median voter criterion exhibit a center-squeeze phenomenon, encouraging candidates to take more extreme positions than the broader population would prefer. Some voting systems satisfy the median voter property, including all Condorcet methods,[1] approval voting,[2][3] and Coombs' method; others, such as instant-runoff voting ("ranked choice voting") and plurality voting, fail it. Score voting satisfies the property under strategic and informed voting (where it is equivalent to approval voting), or if voters’ ratings of candidates are linear with respect to ideological distance.
The theorem was first set out by Duncan Black in 1948.[4] He wrote that he saw a large gap in economic theory concerning how voting determines the outcome of decisions, including political decisions. Black's paper triggered research on how economics can explain voting systems. In 1957 Anthony Downs expounded upon the median voter theorem in his book An Economic Theory of Democracy.[5]
A related assertion was made earlier (in 1929) by Harold Hotelling, who argued politicians in a representative democracy would converge to the viewpoint of the median voter,[6] basing this on his model of economic competition.[6][7] However, this assertion relies on a deeply simplified voting model, and is only partly applicable to systems satisfying the median voter property. It cannot be applied to systems like ranked choice voting (RCV) or first-past-the-post at all, even in two-party systems.[3][8][note 1]
- ^ P. Dasgupta and E. Maskin, "The fairest vote of all" (2004); "On the Robustness of Majority Rule" (2008).
- ^ Cox, Gary W. (1985). "Electoral Equilibrium under Approval Voting". American Journal of Political Science. 29 (1): 112–118. doi:10.2307/2111214. ISSN 0092-5853. JSTOR 2111214.
- ^ a b Myerson, Roger B.; Weber, Robert J. (March 1993). "A Theory of Voting Equilibria". American Political Science Review. 87 (1): 102–114. doi:10.2307/2938959. hdl:10419/221141. ISSN 1537-5943. JSTOR 2938959.
- ^ Black, Duncan (1948-02-01). "On the Rationale of Group Decision-making". Journal of Political Economy. 56 (1): 23–34. doi:10.1086/256633. ISSN 0022-3808. S2CID 153953456.
- ^ Anthony Downs, "An Economic Theory of Democracy" (1957).
- ^ a b Holcombe, Randall G. (2006). Public Sector Economics: The Role of Government in the American Economy. Pearson Education. p. 155. ISBN 9780131450424.
- ^ Hotelling, Harold (1929). "Stability in Competition". The Economic Journal. 39 (153): 41–57. doi:10.2307/2224214. JSTOR 2224214.
- ^ Mussel, Johanan D.; Schlechta, Henry (2023-07-21). "Australia: No party convergence where we would most expect it". Party Politics. doi:10.1177/13540688231189363. ISSN 1354-0688.
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