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Group Decisions: Choosing a Winner by Voting

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Handbook of Group Decision and Negotiation

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Abstract

Voting is one of the several methods for making group decisions. A large number of voting systems have been developed for a seemingly same purpose, i.e., to find out the collective will. The basic motivation for the study of voting systems is the fact that different systems often produce different outcomes when applied to a given set of voter opinions. In some contexts we are able to single out plausible outcomes, e.g., candidates who – given a distribution of opinions in the electorate – ought to be elected for the system to be called reasonable or democratic in some specific sense. Social choice theorists have developed various plausibility criteria for the evaluation of voting systems. After discussing the classic paradoxes of social choice, we review the main criteria as well as the most important results in social choice theory. We also present some techniques for the analysis of opinion distributions. Finally, we discuss some profile restrictions and their relevance for the voting system choice.

This is a substantially updated version of Nurmi (2010).

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Notes

  1. 1.

    In the theory of voting, the concept of agenda refers to the order in which various policy proposals or candidates are voted upon. The notion is thus more specific than the agenda concept appearing in such expressions as “the European Union has a hidden agenda,” “what do we have on the agenda today,” etc.

  2. 2.

    A more extensive description of the procedures can be found in, e.g., Felsenthal and Nurmi (2018, Ch. 3).

  3. 3.

    For further distinctions among monotonicity-related paradoxes, see Felsenthal and Tideman (2013) as well as Felsenthal and Nurmi (2017) and Felsenthal and Nurmi (2019).

  4. 4.

    Y (N, respectively) in the table means that the desideratum represented by the column is satisfied (not satisfied) by the procedure represented by the row. For an evaluation of 20 procedures in terms of a more extensive set of criteria, see Felsenthal and Nurmi (2018).

  5. 5.

    The exceptions are range voting and majority judgment which both are independent of irrelevant alternatives. They are also based on somewhat non-standard voter input, viz., not just rankings, but grade values of alternatives are required.

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Author information

Authors and Affiliations

  1. Department of Philosophy, Contemporary History and Political Science, University of Turku, Turku, Finland

    Hannu Nurmi

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  1. Hannu Nurmi
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Correspondence to Hannu Nurmi .

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Editors and Affiliations

  1. Wilfrid Laurier University Dept. Mathematics, Waterloo, ON, Canada

    D. Marc Kilgour

  2. University of Strathclyde Strathclyde Business School, Glasgow, UK

    Colin Eden

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Nurmi, H. (2020). Group Decisions: Choosing a Winner by Voting. In: Kilgour, D., Eden, C. (eds) Handbook of Group Decision and Negotiation. Springer, Cham. https://doi.org/10.1007/978-3-030-12051-1_11-1

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  • DOI: https://doi.org/10.1007/978-3-030-12051-1_11-1

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