Ranking Sets of Objects

Barberà, Salvador; Bossert, Walter; Pattanaik, Prasanta K.

doi:10.1007/978-1-4020-7964-1_4

Cited by 227 publications

(219 citation statements)

References 112 publications

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“…Our next result shows that we are dealing with a framework that is at least as expressive as the classical framework for ranking sets of objects [3]. 2 Consider a problem of the latter kind, with m objects.…”

Section: Outcome-based Desiderata and Ranking Sets Of Objectsmentioning

confidence: 99%

“…There are connections here to problems analysed in the literature on ranking sets of objects [14,3,11]. The question discussed in that literature is how to extend a preference order over individual objects to a preference order over nonempty sets of such objects (with the most common interpretation of those sets being that we will eventually obtain one of the objects in the set in question, but cannot control which).…”

Section: The Paradox Of Early Collective Uncertainty Resolutionmentioning

confidence: 99%

“…In the sequel, we focus on the latter, so as to be able to discuss connections to the literature on ranking sets of objects [14,3,11].…”

Section: The Single-agent Casementioning

confidence: 99%

“…Outcome-dominance is known as the Gärdenfors principle in the literature on ranking sets of objects [3]. It is a natural requirement to impose: it classifies any change of action as an improvement if it results either in a new best possible outcome to be added or in the currently worst possible outcome to be eliminated.…”

Section: Desiderata For Action Choice Functionsmentioning

confidence: 99%

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Voting on Actions with Uncertain Outcomes

Endriss

2013

Algorithmic Decision Theory

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Abstract. We introduce a model for voting under uncertainty where a group of voters have to decide on a joint action to take, but the individual voters are uncertain about the current state of the world and thus about the effect that the chosen action would have. Each voter has preferences about what state they would like to see reached once the action has been executed. That is, we need to integrate two kinds of aggregation: beliefs regarding the current state and preferences regarding the next state.

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Section: Outcome-based Desiderata and Ranking Sets Of Objectsmentioning

confidence: 99%

Section: The Paradox Of Early Collective Uncertainty Resolutionmentioning

confidence: 99%

“…In the sequel, we focus on the latter, so as to be able to discuss connections to the literature on ranking sets of objects [14,3,11].…”

Section: The Single-agent Casementioning

confidence: 99%

Section: Desiderata For Action Choice Functionsmentioning

confidence: 99%

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Voting on Actions with Uncertain Outcomes

Endriss

2013

Algorithmic Decision Theory

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“…We begin with three natural axioms, which extend the dominance principle in the comparison of sets (Barberà et al 2004, BBP in what follows). The first requires that when an element is replaced in the selection with a better one, then the selection is deemed to be more orderly.…”

Section: Introductionmentioning

confidence: 99%

Selections from ordered sets

2017

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We study the problem of evaluating whether the selection from a set is close to the ordering of the set determined by an exogenously given measure. Our main result is that three axioms, two naturally capturing "dominance", and a stronger one imposing a form of symmetry in the comparison of selections, are sufficient toWe would like to thank Vincent Anesi, Vito Peragine, Daniel Seidmann, Eyal Winter and especially Ernesto Savaglio, the Associate Editor and two anonymous referees of this journal for helpful suggestions. The final revision of the paper was carried out after Stefano Verzillo started to work at the European Commission, Joint Research Centre. The scientific output expressed does not imply a policy position of the European Commission. Neither the European Commission nor any person acting on behalf of the Commission is responsible for the use which might be made of this publication. The paper was presented at GRASS, Turin, in Nottingham, and at the Royal Economic Society Conference in Brighton. evaluate how close any selection from any set is to the given ordering of the set. This closeness is given by a very simple index, which is a linear function of the sum of the ranks of the selected elements. The paper ends by relating this index to the existing literature on distance between orderings, and also offers a practical application of the index.

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