
ConsensusHalving: Does it Ever Get Easier?
In the εConsensusHalving problem, a fundamental problem in fair divisi...
read it

Efficient Splitting of Measures and Necklaces
We provide approximation algorithms for two problems, known as NECKLACE ...
read it

ConsenusHalving: Does it Ever Get Easier?
In the εConsensusHalving problem, a fundamental problem in fair divisi...
read it

Strong Approximate Consensus Halving and the BorsukUlam Theorem
In the consensus halving problem we are given n agents with valuations o...
read it

A rigorous formulation of and partial results on Lorenz's "consensus strikes back" phenomenon for the HegselmannKrause model
In a 2006 paper, Jan Lorenz observed a curious behaviour in numerical si...
read it

Consensus Halving is PPAComplete
We show that the computational problem CONSENSUSHALVING is PPAcomplete...
read it

Kemeny Consensus Complexity
The computational study of election problems generally focuses on questi...
read it
Consensus Halving for Sets of Items
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 polynomialtime 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 PPADhard. Furthermore, we compare and contrast consensus halving with the more general problem of consensus ksplitting, 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.
READ FULL TEXT
Comments
There are no comments yet.