The presentation by the two mathematicians raised the question of whether the expression of a preference should be the consequence of a binary choice, or whether it is more complex to express. Because an election is not always a choice between two peers, but can also be a choice among a larger number, ranking can be considered as a way of expressing preferences. By complicating the notion of majority in this way, Balinski and Laraki's proposal makes it possible to reflect on the true meaning of election.
The proposal to adopt majority judgment as a new voting modality stems from a twofold observation: the expression of opinions through majority voting does not necessarily reflect collective preferences; when more than two candidates are in the running, the results of the vote may be contradictory by virtue of Condorcet's and Arrow's paradoxes. According to Balinski and Laraki, if candidates are judged on the basis of a common scale of ordinal mentions, the ballot can 1) always identify a winner, 2) neutralize Condorcet's and Arrow's paradoxes, and 3) ensure the equality of voters' votes. In this way, the majority decision must identify the candidate the voters really want: it takes into account the opinion of all voters on all candidates, and gives voters complete freedom to express their opinions.
While majority voting certainly makes it possible to go beyond the idea that an election is an elimination, the discussion raised the thorny issue of the homogenization of judgment criteria between voters. It was also recalled that proportional representation was another way of escaping the majority paradox, in the case of the election of an assembly. Finally, questions were raised about the persuasiveness of majority voting and the conditions under which it can be implemented - in particular, should there be a proliferation of local democratic experiments pending wider adoption?
