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Probabilities of majority and minority violation in proportional representation

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  • Schwingenschlögl, Udo

Abstract

Apportionment methods are used in proportional representation systems for rounding electoral vote proportions to integer numbers of seats in parliament. Many criteria are known to judge this adjustment process and to decide whether a specific method is suitable for practical use. As in general it is not possible to fulfill all desired criteria together, it is necessary to consider probabilities of violated criteria for specific apportionment methods. This paper demonstrates how to calculate the probability of such violations for the important majority and minority criteria by means of a recently developed geometric-combinatorial approach. Results are given for several popular apportionment methods.

Suggested Citation

  • Schwingenschlögl, Udo, 2007. "Probabilities of majority and minority violation in proportional representation," Statistics & Probability Letters, Elsevier, vol. 77(17), pages 1690-1695, November.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:17:p:1690-1695
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    References listed on IDEAS

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    1. Udo Schwingenschlögl & Mathias Drton, 2004. "Seat allocation distributions and seat biases of stationary apportionment methods for proportional representation," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(2), pages 191-202, September.
    2. Lothar Heinrich & Udo Schwingenschlögl, 2006. "Goodness-of-fit Criteria for the Adams and Jefferson Rounding Methods and their Limiting Laws," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(2), pages 191-207, October.
    3. Udo Schwingenschlögl & Friedrich Pukelsheim, 2006. "Seat Biases in Proportional Representation Systems with Thresholds," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(1), pages 189-193, August.
    4. Schwingenschlögl, Udo & Drton, Mathias, 2006. "Seat excess variances of apportionment methods for proportional representation," Statistics & Probability Letters, Elsevier, vol. 76(16), pages 1723-1730, October.
    5. Mathias Drton & Udo Schwingenschlögl, 2005. "Asymptotic seat bias formulas," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 62(1), pages 23-31, September.
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