Median voter theorem

In political science and social choice theory, Black's median voter theorem 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 does not apply, and rational social choice is in fact possible if using a Condorcet method.

This is sometimes reframed into the median voter property, a voting system criterion which says electoral systems should choose the candidate most well-liked by the median voter. Ranked choice voting and plurality fail this property, while approval,^[1]^[2] Coombs' method, and all Condorcet methods^[3] satisfy 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. 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.

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,^[4] basing this on his model of economic competition.^[4]^[5] 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.^[2]^[6]^{[note 1]}

^ 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.
^ P. Dasgupta and E. Maskin, "The fairest vote of all" (2004); "On the Robustness of Majority Rule" (2008).
^ ^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.

Cite error: There are <ref group=note> tags on this page, but the references will not show without a {{reflist|group=note}} template (see the help page).

[1] 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.

[:0-2] 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.

[3] P. Dasgupta and E. Maskin, "The fairest vote of all" (2004); "On the Robustness of Majority Rule" (2008).

[Holcbome-4] Holcombe, Randall G. (2006). Public Sector Economics: The Role of Government in the American Economy. Pearson Education. p. 155. ISBN 9780131450424.

[SiC-5] Hotelling, Harold (1929). "Stability in Competition". The Economic Journal. 39 (153): 41–57. doi:10.2307/2224214. JSTOR 2224214.

[6] 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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