Partial strategyproofness: Relaxing strategyproofness for the random assignment problem

Mennle, Timo; Seuken, Sven

doi:10.1016/j.jet.2020.105144

Cited by 30 publications

(28 citation statements)

References 27 publications

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“…However, BM is criticized for failing strategyproofness (Abdulkadiroglu et al, 2006), which has motivated the development of variants of BM. Most notably, Mennle and Seuken (2021) showed that the adaptive Boston mechanism (ABM) (Alcalde, 1996;Dur, 2019) Harless (2018) proposed the immediate division + mechanism and proved it satisfies sd-WEF.…”

Section: Related Work and Discussionmentioning

confidence: 99%

Favoring Eagerness for Remaining Items: Designing Efficient, Fair, and Strategyproof Mechanisms

Guo¹,

Sikdar²,

Xia³

et al. 2021

Preprint

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In the assignment problem, items must be assigned to agents who have unit demands, based on agents' ordinal preferences. Often the goal is to design a mechanism that is both fair and efficient. In this paper, we first prove that, unfortunately, the desirable efficiency notions rank-maximality, ex-post favoring-higher-ranks, and ex-ante favoring-higher-ranks, which aim to allocate each item to agents who rank it highest over all the items, are incompatible with the desirable fairness notions strong equal treatment of equals (SETE) and sd-weak-envy-freeness (sd-WEF) simultaneously.In light of this, we propose novel properties of efficiency based on a subtly different notion to favoring higher ranks, by favoring "eagerness" for remaining items and aiming to guarantee that each item is allocated to agents who rank it highest among remaining items. Specifically, we propose ex-post favoring-eagerness-for-remaining-items (ep-FERI) and ex-ante favoring-eagerness-for-remaining-items (ea-FERI). We prove that the eager Boston mechanism satisfies ep-FERI and sd-WSP, and that the uniform probabilistic respecting eagerness mechanism satisfies ea-FERI. We also prove that both mechanisms satisfy SETE and sd-WEF, and show that no mechanism can satisfy stronger versions of envyfreeness and strategyproofness while simultaneously maintaining SETE, and either ep-FERI or ea-FERI.

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Section: Related Work and Discussionmentioning

confidence: 99%

Favoring Eagerness for Remaining Items: Designing Efficient, Fair, and Strategyproof Mechanisms

Guo¹,

Sikdar²,

Xia³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…In the present situation we consider the restriction to the housing allocation model, so that each "school" is a single object. Mennle and Seuken (2014) discuss what they call the Adaptive Boston mechanism (they call the original variant Naive Boston). In this case, in round i, all remaining agents submit a bid for their highest remaining object, rather than for the highest object for which they have not yet bid, as in the naive version.…”

Section: Order Bias Of Common Algorithmsmentioning

confidence: 99%

“…In this case, in round i, all remaining agents submit a bid for their highest remaining object, rather than for the highest object for which they have not yet bid, as in the naive version. It is well known that the both variants are Pareto efficient but violate strategyproofness (Mennle and Seuken, 2014;Abdulkadiroglu and Sönmez, 2003), although the adaptive version does satisfy a weaker incentive property known as partial strategyproofness (Mennle and Seuken, 2014;Mennle and Seuken, 2021).…”

Section: Order Bias Of Common Algorithmsmentioning

confidence: 99%

Order Symmetry: A New Fairness Criterion for Assignment Mechanisms

Freeman¹,

Pritchard²

2021

Preprint

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We introduce a new fairness criterion, order symmetry, for assignment mechanisms that match n objects to n agents with ordinal preferences over the objects. An assignment mechanism is order symmetric with respect to some probability measure over preference profiles if every agent is equally likely to receive their favorite object, every agent is equally likely to receive their second favorite, and so on. When associated with a sufficiently symmetric probability measure, order symmetry is a relaxation of anonymity that, crucially, can be satisfied by discrete assignment mechanisms. Furthermore, it can be achieved without sacrificing other desirable axiomatic properties satisfied by existing mechanisms. In particular, we show that it can be achieved in conjunction with strategyproofness and ex post efficiency via the top trading cycles mechanism (but not serial dictatorship). We additionally design a novel mechanism that is both order symmetric and ordinally efficient. The practical utility of order symmetry is substantiated by simulations on Impartial Culture and Mallows-distributed preferences for four common assignment mechanisms.

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“…We use the same model as in (Mennle and Seuken, 2017): A setting pN, M, qq consists of a set of agents N (n " #N ), a set of objects M (m " #M ), and a vector q " pq 1 , . .…”

Section: Formal Modelmentioning

confidence: 99%

“…A weaker incentive concept is lexicographic dominance-strategyproofness (LD-strategyproofness), which requires that a mechanism makes truthful reporting a dominant strategy for those agents who have lexicographic preferences over the objects. 1 In (Mennle and Seuken, 2017), we have introduced partial strategyproofness, a new, intermediate incentive concept that parametrizes the spectrum of incentive concepts between SD-and LD-strategyproofness.…”

Section: Introductionmentioning

confidence: 99%

Local Sufficiency for Partial Strategyproofness

Mennle¹,

Seuken²

2020

Preprint

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In (Mennle and Seuken, 2017), we have introduced partial strategyproofness, a new, relaxed notion of strategyproofness, to study the incentive properties of nonstrategyproof assignment mechanisms. In this paper, we present results pertaining to local sufficiency for partial strategyproofness: We show that, for any r P r0, 1s, r-local partial strategyproofness implies r 2 -partial strategyproofness, and we show that this is the tightest polynomial bound for which a guarantee can be proven. Our results unify the two prior local sufficiency results for strategyproofness (Carroll, 2012) and lexicographic dominance-strategyproofness (Cho, 2012).

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Partial strategyproofness: Relaxing strategyproofness for the random assignment problem

Cited by 30 publications

References 27 publications

Favoring Eagerness for Remaining Items: Designing Efficient, Fair, and Strategyproof Mechanisms

Favoring Eagerness for Remaining Items: Designing Efficient, Fair, and Strategyproof Mechanisms

Order Symmetry: A New Fairness Criterion for Assignment Mechanisms

Local Sufficiency for Partial Strategyproofness

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