Stepwise ordinal efficiency for the random assignment problem

Ramezanian, Rasoul; Feizi, Mehdi

doi:10.1016/j.jmateco.2020.10.005

Cited by 7 publications

(8 citation statements)

References 5 publications

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“…As illustrated in Example 5, neither the eating algorithm nor the RP necessarily provides a strict favoring upper ranks random assignment. Nevertheless, we show that a modified eating algorithm, à la Ramezanian and Feizi (2021b), where no agent can eat an object unless all the others ranking the object better are full, provides a random assignment that is strict favoring upper ranks.…”

Section: Mechanismmentioning

confidence: 95%

“…We continue sharing anything that remained from the object equally among those still hungry agents with the highest rank for those objects, as long as no agent is willing to eat anymore because there is nothing left from the object to share or all agents are full. Ramezanian and Feizi (2021b), in their Proposition 5, proved that the outcome of the modified eating algorithm is stepwise ordinal efficient, which itself is a stronger notion than ordinal efficiency. Moreover, in their Lemma 1, it is proved that at every step s of the algorithm, any object a, which is the sth-best object of an agent i, get exhausted or agent i gets full.…”

Section: Mechanismmentioning

confidence: 99%

“…Proof. Given Lemma 1 of Ramezanian and Feizi (2021b), at each step s of the modified eating algorithm, given an object a that is a sth-best of an agent i, that is, rank a s ( , ) = i ≻ , we have two possible cases: either object a get exhausted, or agent i gets full at step s. In the former case, for all other agents such as j that rank a s ( , ) >…”

Section: Mechanismmentioning

confidence: 99%

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The object allocation problem with favoring upper ranks

Feizi

2022

Int J of Economic Theory

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We introduce (strict) favoring upper ranks, which is an extension of favoring higher ranks for random assignments. We demonstrate that ex post favoring ranks implies (strict) favoring upper ranks, and envy‐freeness implies favoring upper ranks. Moreover, for at least four agents, no mechanism satisfies strict favoring upper ranks and either equal division lower bound or equal treatment of equals and lower invariance. Finally, we proved that the (modified) eating algorithm provides a random assignment that is (strict) favoring upper ranks.

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Section: Mechanismmentioning

confidence: 95%

Section: Mechanismmentioning

confidence: 99%

Section: Mechanismmentioning

confidence: 99%

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The object allocation problem with favoring upper ranks

Feizi

2022

Int J of Economic Theory

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“…Remark: Part (i) of sd-rank-fairness corresponds to non-wastefulness defined in Section 2 of this paper. Part (ii) of sd-rank-fairness is equivalent to respect for rank defined by Harless (2018) and stepwise ordinal efficiency defined by Ramezanian and Feizi (2020). Bogomolnaia and Moulin (2001) showed that sd-efficiency is a refinement of ex post efficiency.…”

Section: Two New Axiomsmentioning

confidence: 99%

“… Actually, Bogomolnaia (2015),Harless (2018), andRamezanian and Feizi (2020) have considered random assignment rules with similar intuition.…”

mentioning

confidence: 99%

The probabilistic rank random assignment rule and its axiomatic characterization

Chen,

Harless,

Jiao

2021

Preprint

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This paper considers the problem of randomly assigning a set of objects to a set of agents based on the ordinal preferences of agents. We generalize the well-known immediate acceptance algorithm to the afore-mentioned random environments and define the probabilistic rank rule (PR rule). We introduce two new axioms: sd-rank-fairness, 1 and equal-rank envy-freeness. Sd-rank-fairness implies sd-efficiency. 2 Equal-rank envy-freeness implies equal treatment of equals. Sd-rank-fairness and equal-rank envy-freeness are enough to characterize the PR rule.

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