Decision-making through Dominance Plausible Rule: New characterizations

Camacho, Franklin; Pérez, Ramón Pino

doi:10.1016/j.mathsocsci.2021.05.003

Cited by 2 publications

(1 citation statement)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This lifting was proposed by Leal and Pino Pérez [34] as a variant of Moulin lifting, introduced by Hervé Moulin [40], and the leximax lifting (cf. [6,9,13,14,16]). In order to define it, we will use the precise-leximax orders over V ↓ X .…”

Section: Orderings and Liftingsmentioning

confidence: 99%

Taxonomy of powerful voters and manipulation in the framework of social choice functions

2023

Self Cite

View full text Add to dashboard Cite

In this work we pursue the study of manipulability of social choice functions through "liftings", that is, mappings which extend orderings over points to orderings over subsets of points. We discover a very weak notion of monotony which is closely related to independence of irrelevant alternatives. This allows us to establish an interesting and general theorem on manipulability. We show that this theorem is indeed equivalent to Arrow-Sen Theorem in the class of nonmanipulable social choice functions. As a consequence of this general theorem we obtain a manipulation theorem for linear profiles in the style of Gibbard-Satterthwaite Theorem but for social choice functions instead of voting schemes. We introduce the notion of nominator, which is a natural generalization of the notion of pairwise nominator introduced by Kelly. Then, we establish that, in the presence of rational properties over liftings, a social choice function is either manipulable, or it admits a nominator. In addition, we do a comparative study on different types of powerful voters (dictators, nominators, pairwise nominators and weak-dictators) present in the literature. Although, in general, they are non-equivalent notions, we show that under some natural conditions, modulo nonmanipulability, the last three are equivalent or even all the notions are equivalent.

show abstract