Keep your distance: Land division with separation

Elkind, Edith; Segal-Halevi, Erel; Suksompong, Warut

doi:10.1016/j.comgeo.2023.102006

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Reinforcement1

Score-unanimity and Range-respect1

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2023

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Cited by 1 publication

(2 citation statements)

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“…Proof. We prove this for the sum rule; the proofs for the max and min rules can be found in the full version [14].…”

Section: Reinforcementmentioning

confidence: 83%

See 1 more Smart Citation

Settling the Score: Portioning with Cardinal Preferences

Elkind,

Suksompong,

Teh

2023

Frontiers in Artificial Intelligence and Applications

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We study a portioning setting in which a public resource such as time or money is to be divided among a given set of candidates, and each agent proposes a division of the resource. We consider two families of aggregation rules for this setting—those based on coordinate-wise aggregation and those that optimize some notion of welfare—as well as the recently proposed Independent Markets mechanism. We provide a detailed analysis of these rules from an axiomatic perspective, both for classic axioms, such as strategyproofness and Pareto optimality, and for novel axioms, which aim to capture proportionality in this setting. Our results indicate that a simple rule that computes the average of all proposals satisfies many of our axioms, including some that are violated by more sophisticated rules.

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“…Proof. We prove this for the sum rule; the proofs for the max and min rules can be found in the full version [14].…”

Section: Reinforcementmentioning

confidence: 83%

“…Proof. We prove the result for the max rule; the proof for the min rule can be found in the full version [14]. For m = 2, let x be the output vector of the max rule.…”

Section: Score-unanimity and Range-respectmentioning

confidence: 89%