Compromise Rules Revisited

Decision makers often face a dilemma when they have to arbitrate between the quantity of support for a decision (i.e., the number of people who back it) and the quality of support (i.e., at which level to go down in voters’ preferences to obtain sufficient level of support). The trade-off between the quality and quantity of support behind alternatives led to numerous suggestions in social choice theory: without being exhaustive we can mention Majoritarian Compromise, Fallback Bargaining, Set of Efficient Compromises, Condorcet Practical Method, Median Voting Rule, Majority Judgement. Our point is that all these concepts share a common feature which enables us to gather them in the same class, the class of compromise rules, which are all based upon elementary scoring rules described extensively by Saari. One can exploit his results to analyze the compromise rules with relative ease, which is a major point of our paper.

1. This method was implemented in December 2016 to select a candidate for the 2017 French presidential election. Via the website https://laprimaire.org/, 50.64% of the 32,685 participants gave the grade “very good” to Charlotte Marchandise, who was selected. Eventually, she could not participate in the 2017 French presidential elections, as she did not get the support of 500 elected officials, a necessary condition to register as a candidate.

2. The term efficient compromise has also been used in the literature by Börgers and Postl (2009). When two persons with opposite preferences have to choose among three alternatives, it is the alternative that maximizes ex ante the weighted sum of von Neumann Morgenstern (vNM) utilities of the voters. Their primary objective is to understand whether this solution is implementable when the vNM utilities are privately observed. Our model is not as precise, as we ignore the utilities of the agents in this paper, and just focus on their ranking; hence, Börgers and Postl’s “utilitarian” efficient compromise is not defined in our context.

3. Also called the Veto Rule, or the Negative Plurality Rule in the literature.

4. For more on scoring rules using thresholds, see Saari (1994).

5. Recall that our refined q-partisan compromise is what Brams and Kilgour (2001) call q-approval compromise.

6. See Young (1974, 1975)

7. This is precisely described for the three candidate case in Saari (1999).

8. Alternative a is a weak Condorcet winner at profile p if \(N_{a,b}(p)\ge N_{b,a}(p)\) for all \(b\in A,b\not =a.\)

Authors and Affiliations

1. Normandy University, UNICAEN, CNRS, UMR [6211], CREM, MRSH bureau 131, Université de Caen Normandie, 14032, Caen Cedex, France

   Vincent Merlin

2. Department of Economics, İstanbul Bilgi University, Kazım Karabekir Cad. No: 2/13, 34060, Eyüp, Istanbul, Turkey

   İpek Özkal Sanver

3. Murat Sertel Center for Advanced Economic Studies, İstanbul Bilgi University, Kazım Karabekir Cad. No: 2/13, 34060, Eyüp, Istanbul, Turkey

   İpek Özkal Sanver

4. Université Paris-Dauphine, Université PSL, CNRS, LAMSADE, 75016, Paris, France

   M. Remzi Sanver

Corresponding author

Correspondence to M. Remzi Sanver.

This Project has been supported by the ANR-14-CE24-0007-01 (CoCoRICoCoDEC) and the PICS CNRS exchange programme. The work of Sanver has been partly supported by the Project IDEX ANR-10-IDEX-0001-02 PSL* “MIFID”.

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