Limiting Dictatorial rules

Torres, Ricard

doi:10.1016/j.jmateco.2004.06.002

Cited by 8 publications

(3 citation statements)

References 24 publications

(35 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recall that a choice demands some ranking. This is usually done by combining ordered preference lists into a single consensus value, as in a reviewing procedure [49,50]. We outline the MLR, which is based directly on rankings and not on the scores.…”

Section: Maximum Likelihood Rulementioning

confidence: 99%

A Theory of Best Choice Selection through Objective Arguments Grounded in Linear Response Theory Concepts

Ausloos,

Rotundo,

Cerqueti

2024

Physics

View full text Add to dashboard Cite

In this study, we propose how to use objective arguments grounded in statistical mechanics concepts in order to obtain a single number, obtained after aggregation, which would allow for the ranking of “agents”, “opinions”, etc., all defined in a very broad sense. We aim toward any process which should a priori demand or lead to some consensus in order to attain the presumably best choice among many possibilities. In order to specify the framework, we discuss previous attempts, recalling trivial means of scores—weighted or not—Condorcet paradox, TOPSIS (Technique for Order Preference by Similarity to Ideal Solution), etc. We demonstrate, through geometrical arguments on a toy example and with four criteria, that the pre-selected order of criteria in previous attempts makes a difference in the final result. However, it might be unjustified. Thus, we base our “best choice theory” on the linear response theory in statistical physics: we indicate that one should be calculating correlations functions between all possible choice evaluations, thereby avoiding an arbitrarily ordered set of criteria. We justify the point through an example with six possible criteria. Applications in many fields are suggested. Furthermore, two toy models, serving as practical examples and illustrative arguments are discussed.

show abstract

Section: Maximum Likelihood Rulementioning

confidence: 99%

A Theory of Best Choice Selection through Objective Arguments Grounded in Linear Response Theory Concepts

Ausloos,

Rotundo,

Cerqueti

2024

Physics

View full text Add to dashboard Cite

show abstract

“…Mihara (1997) and Lauwers and Van Liedekerke (1995) are remarkable examples of earlier works that impose anonymity axioms in addition to the standard Arrow axioms. Recently, many works have tried to clarify various anonymity axioms, or to introduce some other requirements, such as continuity (Gomberg et al 2005;Torres 2005;Salonen and Saukkonen 2005). Kirman and Sondermann (1972) and Hansson (1976) characterize the power structure behind social choice.…”

Section: Introductionmentioning

confidence: 99%

The possibility of Paretian anonymous decision-making with an infinite population

Cato

2019

Soc Choice Welf

View full text Add to dashboard Cite

This paper considers the trade-off between unanimity and anonymity in collective decision-making with an infinite population. This efficiency-equity trade-off is a fundamental difficulty in making a normative judgment in a conflict between generations. In particular, it is known that this trade-off is quite sensitive in the formulation of unanimity axioms. In this study, we consider the trade-off in a preference-aggregation framework instead of the standard utility-aggregation framework. We show that there exists a social welfare function that satisfies I-strong Pareto, independence of irrelevant alternatives, and finite anonymity. This contrasts with an impossibility result in the standard utility-aggregation framework, and this means that the trade-off is also sensitive for background frameworks of aggregations.

show abstract

“…A survey of this literature can be found in Lauwers (1998), and as can be seen from more recent works the exploration along this direction continues today [see e.g. Torres (2005)]. Consistent with the recurrent trend to obtain close connections between Arrow's impossibility theorem and the Gibbard-Satterthwaite theorem (see Theorem 2), Mihara (2000) eventually showed that a result analogous to that in Kirman and Sondermann (1972) holds for social choice functions when we require coalitional strategy-proofness [see also Rao et al (2018)].…”

Section: Introductionmentioning

confidence: 99%

Impossibility theorems with countably many individuals

Ninjbat

2018

SERIEs

View full text Add to dashboard Cite

The problem of social choice is studied on a domain with countably many individuals. In contrast to most of the existing literature which establish either non-constructive possibilities or approximate (i.e. invisible) dictators, we show that if one adds a continuity property to the usual set of axioms, the classical impossibilities persist in countable societies. Along the way, a new proof of the Gibbard-Satterthwaite theorem in the style of Peter Fishburn's well known proof of Arrow's impossibility theorem is obtained.

show abstract

Limiting Dictatorial rules

Cited by 8 publications

References 24 publications

A Theory of Best Choice Selection through Objective Arguments Grounded in Linear Response Theory Concepts

A Theory of Best Choice Selection through Objective Arguments Grounded in Linear Response Theory Concepts

The possibility of Paretian anonymous decision-making with an infinite population

Impossibility theorems with countably many individuals

Contact Info

Product

Resources

About