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• W3111415601 abstract "Consensus halving refers to the problem of dividing a resource into two parts so that every agent values both parts equally. Prior work has shown that when the resource is represented by an interval, a consensus halving with at most n cuts always exists, but is hard to compute even for agents with simple valuation functions. In this paper, we study consensus halving in a natural setting where the resource consists of a set of items without a linear ordering. When agents have additive utilities, we present a polynomial-time algorithm that computes a consensus halving with at most n cuts, and show that n cuts are almost surely necessary when the agents’ utilities are drawn from probabilistic distributions. On the other hand, we show that for a simple class of monotonic utilities, the problem already becomes PPAD-hard. Furthermore, we compare and contrast consensus halving with the more general problem of consensus k-splitting, where we wish to divide the resource into k parts in possibly unequal ratios, and provide some consequences of our results on the problem of computing small agreeable sets." @default.
• W3111415601 created "2020-12-21" @default.
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• W3111415601 date "2020-01-01" @default.
• W3111415601 modified "2023-10-17" @default.
• W3111415601 title "Consensus Halving for Sets of Items" @default.
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• W3111415601 doi "https://doi.org/10.1007/978-3-030-64946-3_27" @default.
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