A theory of measuring, electing, and ranking

Abstract

The impossibility theorems that abound in the theory of social choice show that there can be no satisfactory method for electing and ranking in the context of the traditional, 700-year-old model. A more realistic model, whose antecedents may be traced to Laplace and Galton, leads to a new theory that avoids all impossibilities with a simple and eminently practical method, ''the majority judgement.'' It has already been tested.

Empowering Representative Voters: A Rationale and a Model for the Practice of Weighting Votes

“…A nonlinear scoring rule is the central ingredient in the Majority Judgment system developed by Balinski and Laraki (2007). It consists of taking the median rather than the mean of the gradings received by a candidate.…”

Mean-median compromise method as an innovating voting rule in social choice theory

“…Consequently, on the basis of this conviction, it is advisable to consider a new theory which pushes back the fixed limits of the arrovian framework. Michel Balinski and Rida Laraki undertook various works in this direction to propose a new framework not based on decision makers' individual preferences but on their evaluations [4,5,6]. Thus, the Balinski-Larakian model requires from actors to make a judgment on each candidate in competition.…”

“…The winner is the one who obtains the highest median. This function uses two tie-breaking rules: majority-grade and majority-gauge (see [4], [5], and [6]).  Mean-Median Compromise Method (MMCM): this method is obtained by hybridization of the BMC and MJ.…”

Consensus-based clustering under hesitant qualitative assessments

“…In the context of voting theory, it is worth mentioning that Balinski and Laraki [4,5] have proposed a voting system called Majority Judgment where voters assess the alternatives through linguistic terms ('excellent', 'very good', 'good', 'acceptable', 'poor' and 'to reject'). See Balinski and Laraki [6] for an experimental analysis of their proposal.…”

“…Thus, the distance between consecutive linguistic terms is assumed to be constant. 4 The notion of consensus measure was introduced by Bosch [8] in the context of linear orders. Additionally, Bosch [8] and Alcalde-Unzu and Vorsatz [3] provided axiomatic characterizations of several consensus measures in the context of linear orders.…”