Majority decisions based on difference of votes

Abstract

In this paper a class of voting procedures, located between simple and unanimous majorities, is introduced and characterized. Given two alternatives, the winning alternative is the one with a number of votes exceeding that obtained by the other in a previously fixed quantity. Moreover, a subclass of these voting procedures has been considered, by demanding additionally a number of votes greater than a previously fixed threshold. The main results of this paper are characterizations of these voting procedures through aggregation functions of fuzzy preferences associated with quasiarithmetic means and OWA operators.

Consensus-Based Agglomerative Hierarchical Clustering

“…The first condition is equivalent to the property of self-duality (see García-Lapresta and Llamazares [13,Proposition 5]). The second condition is weaker than the original of Yager [31], called strongly decaying, that requires strict inequalities w i < w j .…”

Monotonicity-based consensus states for the monometric rationalisation of ranking rules with application in decision making

“…Other properties such as simple majority [95], absolute majority [139] or majorities based on difference of votes [65] have no immediate relation with monotonicity of the votrix or the votex.…”

Consistent collective decisions under majorities based on difference of votes

“…The concept and the definition of majorities based on difference of votes was introduced in García-Lapresta and Llamazares (2001) and was later axiomatically characterized in Llamazares (2006), and subsequently in Houy (2007). These rules involve crisp preferences, i.e.…”

“…This paper is devoted to analyze and compare the probabilities of consistent collective decisions over three alternatives for a class of majorities rules: majorities based on difference of votes (García-Lapresta and Llamazares 2001;Llamazares 2006;Houy 2007). Given two alternatives, these majorities based on differences focus on requiring to an alternative, to be declared the winner, to reach a number of votes that exceeds the number of votes for the other alternative in a quantity fixed before the voting process.…”