Arrovian aggregation for preferences over sets

2007 ◽  
Vol 53 (3) ◽  
pp. 255-258
Author(s):  
Levent Kutlu
Keyword(s):  
Arrovian Aggregation ◽  
Preferences Over Sets

scholarly journals Arrovian Aggregation of Convex Preferences

Econometrica ◽  
2020 ◽  
Vol 88 (2) ◽  
pp. 799-844
Author(s):  
Florian Brandl ◽  
Felix Brandt
Keyword(s):  
Social Welfare ◽  
Complete Characterization ◽  
Choice Functions ◽  
Maximal Elements ◽  
The Social ◽  
Outcome Space ◽  
Convex Preferences ◽  
Finite Set ◽  
Arrovian Aggregation

We consider social welfare functions that satisfy Arrow's classic axioms of independence of irrelevant alternatives and Pareto optimality when the outcome space is the convex hull of some finite set of alternatives. Individual and collective preferences are assumed to be continuous and convex, which guarantees the existence of maximal elements and the consistency of choice functions that return these elements, even without insisting on transitivity. We provide characterizations of both the domains of preferences and the social welfare functions that allow for anonymous Arrovian aggregation. The domains admit arbitrary preferences over alternatives, which completely determine an agent's preferences over all mixed outcomes. On these domains, Arrow's impossibility turns into a complete characterization of a unique social welfare function, which can be readily applied in settings involving divisible resources such as probability, time, or money.

Arrovian aggregation in economic environments: how much should we know about indifference surfaces?

2005 ◽  
Vol 124 (1) ◽  
pp. 22-44 ◽  
Author(s):  
Marc Fleurbaey ◽  
Kotaro Suzumura ◽  
Koichi Tadenuma
Keyword(s):  
Arrovian Aggregation

Modelling and learning user preferences over sets

2010 ◽  
Vol 22 (3) ◽  
pp. 237-268 ◽  
Author(s):  
Kiri L. Wagstaff ◽  
Marie desJardins ◽  
Eric Eaton
Keyword(s):  
User Preferences ◽  
Preferences Over Sets

The MarCon algorithm: A systematic market approach to distributed constraint problems

1999 ◽  
Vol 13 (3) ◽  
pp. 217-234 ◽  
Author(s):  
H. VAN DYKE PARUNAK ◽  
ALLEN C. WARD ◽  
JOHN A. SAUTER
Keyword(s):  
Mechanical Design ◽  
Machine Intelligence ◽  
Common Interest ◽  
Systematic Method ◽  
New Approach ◽  
Market Approach ◽  
Preferences Over Sets

MarCon (Market-based Constraints) applies market-based control to distributed constraint problems. It offers a new approach to distributing constraint problems that avoids challenges faced by current approaches in some problem domains, and it provides a systematic method for applying markets to a wide array of problems. Constraint agents interact with one another via the variable agents in which they have a common interest, using expressions of their preferences over sets of assignments. Each variable integrates this information from the constraints interested in it and provides feedback that enables the constraints to shrink their sets of assignments until they converge on a solution. MarCon originated in a system for supporting human product designers, and its mechanisms are particularly useful for applications integrating human and machine intelligence to explore implicit constraints. MarCon has been tested in the domain of mechanical design, in which its set-narrowing process is particularly useful.

COALITION FORMATION GAMES: A SURVEY

2006 ◽  
Vol 08 (04) ◽  
pp. 613-641 ◽  
Author(s):  
JANA HAJDUKOVÁ
Keyword(s):  
Coalition Formation ◽  
Coalition Structure ◽  
Transferable Utility ◽  
New Models ◽  
Stability Definition ◽  
Preferences Over Sets

In this paper we give an overview of various methods used to study cooperation within a set of players. Besides the classical games with transferable utility and games without transferable utility, recently new models have been proposed: the coalition formation games. In these, each player has his own preferences over coalitions to which he could belong and the quality of a coalition structure is evaluated according to its stability. We review various definitions of stability and restrictions of preferences ensuring the existence of a partition stable with respect to a particular stability definition. Further, we stress the importance of preferences over sets of players derived from preferences over individuals and review the known algorithmic results for special types of preferences derived from the best and/or the worst player of a coalition.

STABILITY OF PARTITIONS UNDER $\mathcal{WB}$-PREFERENCES AND $\mathcal{BW}$-PREFERENCES

2004 ◽  
Vol 03 (04) ◽  
pp. 605-618 ◽  
Author(s):  
KATARÍNA CECHLÁROVÁ ◽  
JANA HAJDUKOVÁ
Keyword(s):  
Existence Problem ◽  
Open Questions ◽  
Preferences Over Sets

Let a set of players be given and suppose that players have strict preferences over other players. The preferences are then extended to preferences over sets using the best (worst) player of a set and the worst (best) player as a tie-breaker. For such set-preferences we study the structure and computational questions connected with the existence problem of stable partitions. In the end, we review the known results for stable partitions under various preferences and point out some open questions.

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