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Abstentions in the German Bundesrat and ternary decision rules in weighted voting systems

Listed author(s):
  • Birkmeier Olga

    (University of Augsburg, Institute for Mathematics, Augsburg, Deutschland)

  • Käufl Andreas

    (University of Augsburg, Institute for Mathematics, Augsburg, Deutschland)

  • Pukelsheim Friedrich
Registered author(s):

    Ternary decision rules allowing for abstentions,besides Yea- and Nay-votes, are analyzed. The German Bundesrat serves as a prime example. We show that the decision-making efficiency of the Bundesrat would increase if abstentions were allowed. A general formula for the mean success margin of a ternary decision rule is derived assuming selfdual and permutationally invariant distributions. The ternary Penrose–Banzhaf model is discussed in detail, and the influence probabilities of voters and a rule´s influence sensitivity are evaluated.

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    File URL: https://www.degruyter.com/view/j/stnd.2011.28.issue-1/stnd.2011.1066/stnd.2011.1066.xml?format=INT
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    Article provided by De Gruyter in its journal Statistics & Risk Modeling.

    Volume (Year): 28 (2011)
    Issue (Month): 1 (March)
    Pages: 1-16

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    Handle: RePEc:bpj:strimo:v:28:y:2011:i:1:p:1-16:n:2
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    1. Edward M. Bolger, 2002. "Characterizations of two power indices for voting games with r alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(4), pages 709-721.
    2. Annick Laruelle & Federico Valenciano, 2005. "Assessing success and decisiveness in voting situations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(1), pages 171-197, January.
    3. Josep Freixas & William S. Zwicker, 2003. "Weighted voting, abstention, and multiple levels of approval," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(3), pages 399-431, December.
    4. Josep Freixas, 2005. "Banzhaf Measures for Games with Several Levels of Approval in the Input and Output," Annals of Operations Research, Springer, vol. 137(1), pages 45-66, July.
    5. Paulo P. Côrte-Real & Paulo T. Pereira, 2004. "The voter who wasn’t there: Referenda, representation and abstention," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(2), pages 349-369, April.
    6. Dan Felsenthal & Moshé Machover, 2005. "Voting power measurement: a story of misreinvention," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(2), pages 485-506, December.
    7. Olga Ruff & Friedrich Pukelsheim, 2010. "A probabilistic synopsis of binary decision rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(3), pages 501-516, September.
    8. J. Bilbao & J. Fernández & A. Losada & J. López, 2000. "Generating functions for computing power indices efficiently," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(2), pages 191-213, December.
    9. Freixas, Josep & Zwicker, William S., 2009. "Anonymous yes-no voting with abstention and multiple levels of approval," Games and Economic Behavior, Elsevier, vol. 67(2), pages 428-444, November.
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