Median voter theorem

In political science and social choice, the 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 theorem was first set out by Duncan Black in 1948.^[1] 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.

A different argument due to Anthony Downs and Harold Hotelling is only loosely-related to Black's median voter theorem, but is often confused with it. This model argues that politicians in a representative democracy will converge to the viewpoint of the median voter,^[2] because the median voter theorem implies that a candidate who wishes to win will adopt the positions of the median voter.^[2]^[3]^[4] However, this argument only applies to systems satisfying the median voter property, and cannot be applied to systems like ranked choice voting (RCV) or plurality voting outside of limited conditions (see § Hotelling–Downs model).^[5]^[6]^[7]

^ 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.
^ ^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.
^ Anthony Downs, "An Economic Theory of Democracy" (1957).
^ McGann, Anthony J.; Koetzle, William; Grofman, Bernard (2002). "How an Ideologically Concentrated Minority Can Trump a Dispersed Majority: Nonmedian Voter Results for Plurality, Run-off, and Sequential Elimination Elections". American Journal of Political Science. 46 (1): 134–147. doi:10.2307/3088418. ISSN 0092-5853.
^ 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.
^ Mussel, Johanan D.; Schlechta, Henry (2023-07-21). "Australia: No party convergence where we would most expect it". Party Politics. 30 (6): 1040–1050. doi:10.1177/13540688231189363. ISSN 1354-0688.

[1] 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.

[holcombe-2006-2] Holcombe, Randall G. (2006). Public Sector Economics: The Role of Government in the American Economy. Pearson Education. p. 155. ISBN 9780131450424.

[hotelling_harold-1929-3] Hotelling, Harold (1929). "Stability in Competition". The Economic Journal. 39 (153): 41–57. doi:10.2307/2224214. JSTOR 2224214.

[downs-1957-4] Anthony Downs, "An Economic Theory of Democracy" (1957).

[5] McGann, Anthony J.; Koetzle, William; Grofman, Bernard (2002). "How an Ideologically Concentrated Minority Can Trump a Dispersed Majority: Nonmedian Voter Results for Plurality, Run-off, and Sequential Elimination Elections". American Journal of Political Science. 46 (1): 134–147. doi:10.2307/3088418. ISSN 0092-5853.

[myerson-1993-6] 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.

[7] Mussel, Johanan D.; Schlechta, Henry (2023-07-21). "Australia: No party convergence where we would most expect it". Party Politics. 30 (6): 1040–1050. doi:10.1177/13540688231189363. ISSN 1354-0688.

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