Int. J. of Industrial and Systems Engineering   »   2009 Vol.4, No.1

 

 

Title: Probabilistic majority rules

 

Author: Annibal Parracho Sant'Anna

 

Address: Escola de Engenharia – Universidade Federal Fluminense, Rua Passo da Patria, 156, bl. D, sl. 309, 24210-240 Niteroi-RJ, Brazil

 

Abstract: This paper is on the modelling of social choice systems. It studies the problem of aggregating individual judgements into collective decisions. Its basic framework is that of the application of majority rules to choose between two options: acceptance or rejection of a given proposition. A new probabilistic approach is developed. It is established a precise dependence condition under which majority acceptance according to any premise taken isolately is equivalent to majority acceptance when all the premises are taken together. This dependence condition is based on the hypothesis of covariance proportional to the probabilities of unfavourable evaluations. Other probabilistic rules are proposed. The case of choice among multiple options is also addressed.

 

Keywords: social choice; preference; probabilistic majority rules; decision aids; discursive dilemma; doctrinal paradox; fuzzy logic; probability; correlation; dependence structure; modelling; individual judgements; collective decisions; multiple choice.

 

DOI: 10.1504/IJISE.2009.021679

 

Int. J. of Industrial and Systems Engineering, 2009 Vol.4, No.1, pp.19 - 31

 

Available online: 30 Nov 2008

 

 

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