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.