Algorithmic Game Theory

The Price of Anarchy in Bilateral Network Formation in an Adversary Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 Lasse Kliemann The Query Complexity of Correlated Equilibria . . . . . . . . . . . . . . . . . . . . . . 268 Sergiu Hart and Noam Nisan The Money Pump as a Measure of Revealed Preference Violations . . . . . 269 Bart Smeulders, Laurens Cherchye, Bram De Rock, and Frits C.R. Spieksma Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 The Complexity of Fully Proportional Representation for Single-Crossing Electorates Piotr Skowron, Lan Yu, Piotr Faliszewski, and Edith Elkind 1 University of Warsaw, Poland 2 Nanyang Technological University, Singapore 3 AGH University of Science and Technology, Poland Abstract. We study the complexity of winner determination in single-crossing elections under two classic fully proportional representation rules—Chamberlin– Courant’s rule and Monroe’s rule. Winner determination for these rules is known to be NP-hard for unrestricted preferences. We show that for single-crossing preferences this problem admits a polynomial-time algorithm for Chamberlin– Courant’s rule, but remains NP-hard for Monroe’s rule. Our algorithm for Chamberlin–Courant’s rule can be modified to work for elections with bounded singlecrossing width. To circumvent the hardness result for Monroe’s rule, we consider single-crossing elections that satisfy an additional constraint, namely, ones where each candidate is ranked first by at least one voter (such elections are called narcissistic). For single-crossing narcissistic elections, we provide an efficient algorithm for the egalitarian version of Monroe’s rule. We study the complexity of winner determination in single-crossing elections under two classic fully proportional representation rules—Chamberlin– Courant’s rule and Monroe’s rule. Winner determination for these rules is known to be NP-hard for unrestricted preferences. We show that for single-crossing preferences this problem admits a polynomial-time algorithm for Chamberlin– Courant’s rule, but remains NP-hard for Monroe’s rule. Our algorithm for Chamberlin–Courant’s rule can be modified to work for elections with bounded singlecrossing width. To circumvent the hardness result for Monroe’s rule, we consider single-crossing elections that satisfy an additional constraint, namely, ones where each candidate is ranked first by at least one voter (such elections are called narcissistic). For single-crossing narcissistic elections, we provide an efficient algorithm for the egalitarian version of Monroe’s rule.

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