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Back to Black: The Median Voter Revisited

Author

Listed:
  • Mathieu Martin
  • Linus Thierry Nana Noumi
  • Zéphirin Nganmeni
  • Ashley Piggins

    (CY Cergy Paris Université, THEMA)

Abstract

A long-standing foundational problem in the spatial theory of politics is the generic emptiness of the majority core when there is more than one dimension in the policy space. This implies that, in general, we cannot predict where win-motivated candidates will locate in an electoral contest decided by majority rule. We assume that the candidates face some uncertainty: they observe each voter’s ideal point in the policy space but not their indifference surfaces. Given any proper spatial voting game, we first identify the set of imprudent positions in the space. If a candidate adopts an imprudent position, then there exists a position for their opponent that will defeat them for certain. We introduce a new concept, the prudent core, as the set of positionsthat are not imprudent in this sense. We show that the prudent core is always non-empty. With majority voting and an odd number of voters, the prudent core equals the dimension-by-dimension median. The prudent core equals the majority core whenever the latter is nonempty.

Suggested Citation

  • Mathieu Martin & Linus Thierry Nana Noumi & Zéphirin Nganmeni & Ashley Piggins, 2026. "Back to Black: The Median Voter Revisited," Thema Working Papers 2026-04, THEMA (Théorie Economique, Modélisation et Applications), CY Cergy-Paris University, ESSEC and CNRS.
    • Handle: RePEc:ema:worpap:2026-04
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    References listed on IDEAS

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    1. Mathieu Martin & Zéphirin Nganmeni & Craig Tovey, 2021. "Dominance in spatial voting with imprecise ideals," Post-Print hal-04257716, HAL.
    2. Owen, G & Shapley, L S, 1989. "Optimal Location of Candidates in Ideological Space," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(3), pages 339-356.
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    5. Mathieu Martin & Zéphirin Nganmeni & Ashley Piggins & Élise F. Tchouante, 2022. "Pure-strategy Nash equilibrium in the spatial model with valence: existence and characterization," Public Choice, Springer, vol. 190(3), pages 301-316, March.
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    Keywords

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    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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