Junta Distributions and the Average-Case Complexity of Manipulating Elections

Abstract

Encouraging voters to truthfully reveal their preferences in an election has long been an important issue. Recently, computational complexity has been suggested as a means of precluding strategic behavior. Previous studies have shown that some voting protocols are hard to manipulate, but used N P-hardness as the complexity measure. Such a worst-case analysis may be an insufficient guarantee of resistance to manipulation.Indeed, we demonstrate that N P-hard manipulations may be tractable in the averagecase. For this purpose, we augment the existing theory of average-case complexity with some new concepts. In particular, we consider elections distributed with respect to junta distributions, which concentrate on hard instances. We use our techniques to prove that scoring protocols are susceptible to manipulation by coalitions, when the number of candidates is constant.

Hybrid Elections Broaden Complexity‐Theoretic Resistance to Control

“…Regarding average-case NP-hardness, a well-known theory developed by Levin [48], the theory is lovely, but only a handful of problems have been shown to be average-case NP-hard, and not a single one of those in any way involves elections. Regarding frequency of hardness, there have been a number of recent results (as a few examples as a starting point for the interested reader, we mention [49,50,51,52,53,54,55] and the references therein, and we in the full TR version of this paper provide a more detailed discussion) showing that certain NPhard election issues can be frequently simple, but to the best of our knowledge, none of those papers obtains such results for any control problem. Briefly put, issues of average-case NP-hardness and of frequency of correctness are clearly very interesting, are rightly gaining attention, and we highly commend them to the reader while also mentioning that the field's understanding of such results and ability to obtain them is still quite limited and currently doesn't exist at all for the case of control problems (except see the comment of the next paragraph, which in a sense says that our work at least preserves good behavior in this regard).…”

Manipulative elicitation – A new attack on elections with incomplete preferences

“…In another direction, it would be interesting to conduct extensive experimentation to study usefulness of our approach in practice. This is specially important since computational intractability is known to provide only a weak barrier in other forms of election manipulation [PR07].…”

Risk-limiting Audits and the Margin of Victory in Nonplurality Elections

“…This has led to several alternative ways of thinking about the complexity of manipulation, for example by extending the types of manipulation (Faliszewski, Hemaspaandra, and Hemaspaandra, 2011), designing approximation algorithms (Brelsford, Faliszewski, Hemaspaandra, Schnoor, and Schnoor, 2008), using average-case complexity (Procaccia and Rosenschein, 2007), or random models for errors (Friedgut, Kalai, andNisan, 2008, Isaksson, Kindler, andMossel, 2010). Some researchers believe that the hardness of manipulation is a desirable property, especially in elections done automatically by computer agents (Faliszewski, Hemaspaandra, and Hemaspaandra, 2010).…”