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A note on the direct democracy deficit in two-tier voting

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  • Maaser, Nicola
  • Napel, Stefan

Abstract

A large population of voters with single-peaked preferences are partitioned into disjoint constituencies. Collective decisions are taken by their representatives, one from each constituency, according to a weighted voting rule. It is assumed that each representative’s ideal point perfectly matches that of the respective constituency median and that top-tier decisions are in the voting game’s core. The resulting representative-democratic voting outcomes generally differ from those of a direct-democratic, single-tier system. The expected discrepancy varies with the voting weight allocation. It is minimized by weights proportional to constituency population sizes only if citizens differ sufficiently more between than within constituencies. Weights proportional to the square root of population sizes perform better if all citizens have independent and identically distributed ideal points.

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  • Maaser, Nicola & Napel, Stefan, 2012. "A note on the direct democracy deficit in two-tier voting," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 174-180.
    • Handle: RePEc:eee:matsoc:v:63:y:2012:i:2:p:174-180
    DOI: 10.1016/j.mathsocsci.2011.10.008
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    1. Le Breton, Michel & Lepelley, Dominique & Macé, Antonin & Merlin, Vincent, 2017. "Le mécanisme optimal de vote au sein du conseil des représentants d’un système fédéral," L'Actualité Economique, Société Canadienne de Science Economique, vol. 93(1-2), pages 203-248, Mars-Juin.
    2. Kirsch, Werner & Toth, Gabor, 2022. "Collective bias models in two-tier voting systems and the democracy deficit," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 118-137.
    3. Kurz, Sascha & Maaser, Nicola & Napel, Stefan, 2018. "Fair representation and a linear Shapley rule," Games and Economic Behavior, Elsevier, vol. 108(C), pages 152-161.
    4. Yukio Koriyama & Jean-François Laslier & Antonin Macé & Rafael Treibich, 2013. "Optimal Apportionment," Journal of Political Economy, University of Chicago Press, vol. 121(3), pages 584-608.
    5. Sascha Kurz, 2014. "Measuring Voting Power in Convex Policy Spaces," Economies, MDPI, vol. 2(1), pages 1-33, March.
    6. Imma Curiel, 2014. "A multifaceted analysis of the electoral system of the Republic of Suriname," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 24(4), pages 29-49.
    7. Sascha Kurz & Nicola Maaser & Stefan Napel & Matthias Weber, 2014. "Mostly Sunny: A Forecast of Tomorrow's Power Index Research," Tinbergen Institute Discussion Papers 14-058/I, Tinbergen Institute.

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