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Finding the Threshold of Exclusion for all single seat and multi-seat scoring rules: Illustrated by results for the Borda and Dowdall rules

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  • Grofman, Bernard
  • Feld, Scott L.
  • Fraenkel, Jon

Abstract

We provide a general analytic approach for calculating the Threshold of Exclusion (TE) for the single-seat and the multi-seat versions of all scoring rules, an infinitely large class of voting systems (Fishburn, 1973; Young, 1975; Saari, 1994, 1995). We offer specific results for two rules used for parliamentary elections at the national level: Borda (Black, 1958), used for national elections to special reserved seats for Hungarian and Italian ethnic minorities in Slovenia, and the unique and little known electoral system used for legislative elections on the Pacific Island state of Nauru, the Dowdall rule. When voters are required to provide a complete ranking of all candidates, we find that Borda does not, in general, operate as a majoritarian system in that a supermajority of roughly 2/3rd is required to guarantee electing a candidate of choice. In contrast, we find that, as district magnitude increases, the Threshold of Exclusion for the Dowdall rule tends to zero, in the same way as do list systems of proportional representation (PR). However, in contrast to the case for list PR rules, TE for Dowdall can still be relatively close to 12 for small district magnitudes.

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  • Grofman, Bernard & Feld, Scott L. & Fraenkel, Jon, 2017. "Finding the Threshold of Exclusion for all single seat and multi-seat scoring rules: Illustrated by results for the Borda and Dowdall rules," Mathematical Social Sciences, Elsevier, vol. 85(C), pages 52-56.
    • Handle: RePEc:eee:matsoc:v:85:y:2017:i:c:p:52-56
    DOI: 10.1016/j.mathsocsci.2016.11.004
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    1. Gallagher, Michael, 1992. "Comparing Proportional Representation Electoral Systems: Quotas, Thresholds, Paradoxes and Majorities," British Journal of Political Science, Cambridge University Press, vol. 22(4), pages 469-496, October.
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    Cited by:

    1. Salvatore Barbaro, 2024. "Electoral Methods and Political Polarization," Working Papers 2411, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    2. Aleksei Y. Kondratev & Alexander S. Nesterov, 2020. "Measuring majority power and veto power of voting rules," Public Choice, Springer, vol. 183(1), pages 187-210, April.

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