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Xavier Mora

Publications and source records attributed to Xavier Mora.

9 recordsLinked to original sources
arXiv2019

The method of Enestr\"om and Phragm\'en for parliamentary elections by means of approval voting

We study a method for proportional representation that was proposed at the turn from the nineteenth to the twentieth century by Gustav Enestr\"om and Edvard Phragm\'en. Like Phragm\'en's better-known iterative minimax method, it is assumed that the voters express themselves by means of approval voting. In contrast to the iterative minimax method, however, here one starts by fixing a quota, i.e. the number of votes that give the right to a seat. As a matter of fact, the method of Enestr\"om and Phragm\'en can be seen as an extension of the method of largest remainders from closed lists to open lists, or also as an adaptation of the single transferable vote to approval rather than preferential voting. The properties of this method are studied and compared with those of other methods of the same kind.

econ.TH↗
arXiv2015

Fraction-like rates from preferential voting

A method is given for determining a mixed social choice out of a paired-comparison matrix. The method combines a projection procedure introduced in previous papers of the same authors and a classical method due to Zermelo. The resulting method is proved to have certain desirable properties, which include: compliance with a majority principle, clone consistency, and continuity of the mixing fractions with respect to the data.

math.CO↗
arXiv2015

Social choice rules driven by propositional logic

Several rules for social choice are examined from a unifying point of view that looks at them as procedures for revising a system of degrees of belief in accordance with certain specified logical constraints. Belief is here a social attribute, its degrees being measured by the fraction of people who share a given opinion. Different known rules and some new ones are obtained depending on which particular constraints are assumed. These constraints allow to model different notions of choiceness. In particular, we give a new method to deal with approval-disapproval-preferential voting.

cs.AI↗
arXiv2014

Choosing by means of approval-preferential voting. The path-revised approval choice

Approval-preferential voting is problematical since it combines two different kinds of information that could by themselves lead to different choices. This article analyses the problem and studies a new proposal to deal with it. The existing methods are overviewed with special attention to several desirable properties that are not always met. Particular emphasis is made on certain rather unknown views of Condorcet about this subject. The proposed procedure definitely aims for a choice in the spirit of approval voting. However, it still makes use of the preferential information so as to improve the approval one. This is done by means of the path scores, in common to Schulze's method for preferential voting. The resulting method, that we call path-revised approval choice, is shown to enjoy several good properties. In particular, it fulfils in a well-defined sense Condorcet's latest view that a surely good option should prevail over a doubtfully best one.

cs.GT↗
arXiv2012

A continuous rating method for preferential voting. The incomplete case

A method is given for quantitatively rating the social acceptance of different options which are the matter of a preferential vote. In contrast to a previous article, here the individual votes are allowed to be incomplete, that is, they need not express a comparison between every pair of options. This includes the case where each voter gives an ordered list restricted to a subset of most preferred options. In this connection, the proposed method (except for one of the given variants) carefully distinguishes a lack of information about a given pair of options from a proper tie between them. As in the special case of complete individual votes, the proposed generalization is proved to have certain desirable properties, which include: the continuity of the rates with respect to the data, a decomposition property that characterizes certain situations opposite to a tie, the Condorcet-Smith principle, and clone consistency

math.OC↗
arXiv2012

A general method for deciding about logically constrained issues

A general method is given for revising degrees of belief and arriving at consistent decisions about a system of logically constrained issues. In contrast to other works about belief revision, here the constraints are assumed to be fixed. The method has two variants, dual of each other, whose revised degrees of belief are respectively above and below the original ones. The upper [resp. lower] revised degrees of belief are uniquely characterized as the lowest [resp. highest] ones that are invariant by a certain max-min [resp. min-max] operation determined by the logical constraints. In both variants, making balance between the revised degree of belief of a proposition and that of its negation leads to decisions that are ensured to be consistent with the logical constraints. These decisions are ensured to agree with the majority criterion as applied to the original degrees of belief whenever this gives a consistent result. They are also also ensured to satisfy a property of respect for unanimity about any particular issue, as well as a property of monotonicity with respect to the original degrees of belief. The application of the method to certain special domains comes down to well established or increasingly accepted methods, such as the single-link method of cluster analysis and the method of paths in preferential voting.

cs.AI↗
arXiv2011

A continuous rating method for preferential voting. The complete case

A method is given for quantitatively rating the social acceptance of different options which are the matter of a complete preferential vote. Completeness means that every voter expresses a comparison (a preference or a tie) about each pair of options. The proposed method is proved to have certain desirable properties, which include: the continuity of the rates with respect to the data, a decomposition property that characterizes certain situations opposite to a tie, the Condorcet-Smith principle, and a property of clone consistency. One can view this rating method as a complement for the ranking method introduced in 1997 by Markus Schulze. It is also related to certain methods of one-dimensional scaling or cluster analysis.

math.OC↗
arXiv2008

A continuous rating method for preferential voting

A method is given for quantitatively rating the social acceptance of different options which are the matter of a preferential vote. The proposed method is proved to satisfy certain desirable conditions, among which there is a majority principle, a property of clone consistency, and the continuity of the rates with respect to the data. One can view this method as a quantitative complement for a qualitative method introduced in 1997 by Markus Schulze. It is also related to certain methods of one-dimensional scaling or cluster analysis.

math.OC↗