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The Arrovian framework of social choice theory is flexible enough to allow for a precise axiomatic study of the voting rules that are used in political elections, sport competitions or expert committees, etc. such as the majority rule or the scoring rules. The objective of this paper is to give an account of the results that have been obtained in this direction since 1951. We first present some basic conditions for a collective decision rule to be democratic. Next, we expound in detail two fundamental results: the characterization of the majority rule by May, and the axiomatization of the family of scoring rules by Young. Afterwards, using these results, some specific scoring rules, such as the plurality vote or the Borda count, have also been characterized. Some remarks on other directions of research and open issues conclude the paper.

The axiomatic characterizations of majority voting and scoring rules