Efficient reallocation under additive and responsive preferences

Aziz, Haris; Bíró, Péter; Lang, Jérôme; Lesca, Julien; Monnot, Jérôme

doi:10.1016/j.tcs.2019.05.011

Cited by 37 publications

(45 citation statements)

References 20 publications

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“…One of the tools of the study is the search for Pareto optimal solutions in a multi-agent environment. Recently, new fast algorithms have been developed to verify and support the achievement of Pareto optimality Aziz et al (2019).…”

Section: Objective Functions Allocation Strategies and Matching Algorithms For Kidney Exchange Programsmentioning

confidence: 99%

Operations research in Hungary: VOCAL 2018

Bertok

Csendes

Galambos

2021

Cent Eur J Oper Res

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Section: Objective Functions Allocation Strategies and Matching Algorithms For Kidney Exchange Programsmentioning

confidence: 99%

Operations research in Hungary: VOCAL 2018

Bertok

Csendes

Galambos

2021

Cent Eur J Oper Res

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“…Thus, apparently the NecPR requirement is too strong and the PDDPR and PosPR requirements are too weak, while the ND-DPR requirement hits a sweet spot between 'recall' and 'precision': it allows us to solve many instances (= high 'recall') and most solutions are satisfactory (= high 'precision'). 5…”

Section: Ndd-proportionality In Simulationsmentioning

confidence: 99%

Fair Allocation with Diminishing Differences

Segal-Halevi¹,

Hassidim

Aziz

2020

jair

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Ranking alternatives is a natural way for humans to explain their preferences. It is being used in many settings, such as school choice, course allocations and residency matches. In some cases, several "items" are given to each participant. Without having any information on the underlying cardinal utilities, arguing about fairness of allocation requires extending the ordinal item ranking to ordinal bundle ranking. The most commonly used such extension is stochastic dominance (SD), where a bundle X is preferred over a bundle Y if its score is better according to all additive score functions. SD is a very conservative extension, by which few allocations are necessarily fair while many allocations are possibly fair. We propose to make a natural assumption on the underlying cardinal utilities of the players, namely that the difference between two items at the top is larger than the difference between two items at the bottom. This assumption implies a preference extension which we call diminishing differences (DD), where X is preferred over Y if its score is better according to all additive score functions satisfying the DD assumption. We give a full characterization of allocations that are necessarily-proportional or possibly-proportional according to this assumption. Based on this characterization, we present a polynomial-time algorithm for finding a necessarily-DD-proportional allocation if it exists. Using simulations, we show that with high probability, a necessarily-proportional allocation does not exist but a necessarily-DD-proportional allocation exists, and moreover, that allocation is proportional according to the underlying cardinal utilities. We also consider chore allocation under the analogous conditionincreasing-differences. (Avinatan Hassidim), UNSW Sydney and Data61 CSIRO, Australia. haris.aziz@unsw.edu.au (Haris Aziz)A preliminary version of this paper was published in the proceedings of IJCAI 2017 [42]. In the present version, the proofs are substantially revised and simplified, omitted proofs are included, and there are two new sections: one on division of chores (section 9) and one on binary utilities (section 10).

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“…In the literature of exchange with multiple endowments, which is what we are dealing with in this paper, several strategy-proof rules have been developed by weakening the core-selecting property (Pápai, 2003(Pápai, , 2007Todo et al, 2014). Various restriction over the preference domain have also been considered in the literature, such as binary domain (Luo & Tang, 2015), asymmetric preferences (Sun, Hata, Todo, & Yokoo, 2015), and additive preferences (Sonoda, Fujita, Todo, & Yokoo, 2014;Aziz, Biró, Lang, Lesca, & Monnot, 2016).…”

Section: Related Workmentioning

confidence: 99%

A Complexity Approach for Core-Selecting Exchange under Conditionally Lexicographic Preferences

Fujita¹,

Lesca²,

Sonoda³

et al. 2018

jair

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Core-selection is a crucial property of rules in the literature of resource allocation. It is also desirable, from the perspective of mechanism design, to address the incentive of agents to cheat by misreporting their preferences. This paper investigates the exchange problem where (i) each agent is initially endowed with (possibly multiple) indivisible goods, (ii) agents' preferences are assumed to be conditionally lexicographic, and (iii) side payments are prohibited. We propose an exchange rule called augmented top-trading-cycles (ATTC), based on the original TTC procedure. We first show that ATTC is core-selecting and runs in polynomial time with respect to the number of goods. We then show that finding a beneficial misreport under ATTC is NP-hard. We finally clarify relationship of misreporting with splitting and hiding, two different types of manipulations, under ATTC.

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Efficient reallocation under additive and responsive preferences

Cited by 37 publications

References 20 publications

Operations research in Hungary: VOCAL 2018

Operations research in Hungary: VOCAL 2018

Fair Allocation with Diminishing Differences

A Complexity Approach for Core-Selecting Exchange under Conditionally Lexicographic Preferences

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