Paper Info
Title
Positional scoring-based allocation of indivisible goods.
Abstract
We define a family of rules for dividing m indivisible goods among agents, parameterized by a scoring vector and a social welfare aggregation function. We assume that agents' preferences over sets of goods are additive, but that the input is ordinal: each agent reports her preferences simply by ranking single goods. Similarly to positional scoring rules in voting, a scoring vector $$s = (s_1, \\ldots , s_m)$$s=(s1,ź,sm) consists of m nonincreasing, nonnegative weights, where $$s_i$$si is the score of a good assigned to an agent who ranks it in position i. The global score of an allocation for an agent is the sum of the scores of the goods assigned to her. The social welfare of an allocation is the aggregation of the scores of all agents, for some aggregation function $$\\star $$ź such as, typically, $$+$$+ or $$\\min $$min. The rule associated with s and $$\\star $$ź maps a profile to (one of) the allocation(s) maximizing social welfare. After defining this family of rules, and focusing on some key examples, we investigate some of the social-choice-theoretic properties of this family of rules, such as various kinds of monotonicity, and separability. Finally, we focus on the computation of winning allocations, and on their approximation: we show that for commonly used scoring vectors and aggregation functions this problem is NP-hard and we exhibit some tractable particular cases.
Year
DOI
Venue
2017
10.1007/s10458-016-9340-x
Autonomous Agents and Multi-Agent Systems
Keywords
Field
DocType
Computational social choice,Resource allocation,Fair division,Indivisible goods,Preferences
Monotonic function,Parameterized complexity,Mathematical economics,Ranking,Fair division,Voting,Ordinal number,Computer science,Resource allocation,Artificial intelligence,Machine learning,Social Welfare
Journal
Volume
Issue
ISSN
31
3
1387-2532
Citations 
PageRank 
References 
5
0.39
20
Authors
7
Name
Order
Citations
PageRank
Dorothea Baumeister117618.73
Sylvain Bouveret225117.61
Jérôme Lang32838260.90
Nhan Nguyen47916.95
Trung Thanh Nguyen566949.68
Jörg Rothe61324110.98
Abdallah Saffidine712619.72