Abstract
Same parliaments, to form a committee of size \(q\), use a voting process like the following: every parliamentary member votes for one out of a fixed set of candidates, and those \(q\) candidates receiving more votes are elected for the committee. Assuming total discipline of vote, this is a game form in which players are the parliamentary groups. We investigate, according to some natural hypotheses about preferences, the likely distribution of the members of this committee. The main results are: (a) when fractional votes are allowed, there is a complete agreement between the distribution among the groups of the elected candidates that are outcomes of a Nash equilibrium and the distribution that, according to the size of the groups, would compute the Jefferson-d’Hondt allocation rule, and (b) when fractional votes are not allowed, there is a near agreement for a majority of situations.
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Notes
After completing our work, we have been aware of the paper Cox (1991), which proves a close analogue to our Proposition 1 (a), but in a context of large elections instead of a chamber with disciplined voters. We thank Alberto Penadés for this information.
This procedure for resolving ties is better than a pure random tie breaking from the point of view of both computation and practical relevance. The selection of such an order O can be made according to the information provided by the base situation, but it needs to be a public knowledge among the players at the time of selecting their voting actions. We thank an associate editor for clarifying our ideas on this point.
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Acknowledgments
This research has been supported by the Research Project ECO2008-05895-C02-02, Ministerio de Ciencia e Innovación, Spain. The authors are indebted to José Luis Jimeno and also to a referee and an associate editor. Their very helpful comments and suggestions have led to a significant improvement in the paper.
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Pérez, J., De la Cruz, O. Implementation of Jefferson-d’Hondt rule in the formation of a parliamentary committee. Soc Choice Welf 42, 17–30 (2014). https://doi.org/10.1007/s00355-012-0718-7
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DOI: https://doi.org/10.1007/s00355-012-0718-7