Journal of Artificial Intelligence Research 42 (2011) 529-573 Submitted 08/11; published 11/11
Cloning in Elections: Finding the Possible Winners
Edith Elkind [email protected] School of Physical and Mathematical Sciences Nanyang Technological University, Singapore Piotr Faliszewski [email protected] AGH University of Science and Technology Krakow, Poland Arkadii Slinko [email protected] Department of Mathematics University of Auckland, Auckland, New Zealand
Abstract We consider the problem of manipulating elections by cloning candidates. In our model, a manipulator can replace each candidate c by several clones, i.e., new candidates that are so similar to c that each voter simply replaces c in his vote with a block of these new candidates, ranked consecutively. The outcome of the resulting election may then depend onthenumberofclonesaswellasonhoweachvoterordersthecloneswithintheblock.We formalize what it means for a cloning manipulation to be successful (which turns out to be a surprisingly delicate issue), and, for a number of common voting rules, characterize the preference profiles for which a successful cloning manipulation exists. We also consider the model where there is a cost associated with producing each clone, and study the complexity of finding a minimum-cost cloning manipulation. Finally, we compare cloning with two related problems: the problem of control by adding candidates and the problem of possible (co)winners when new alternatives can join.
1. Introduction
In many real-life elections, some of the candidates may have fairly similar positions on major issues, yet disagree on what is the best way to implement their common goals. Under many voting rules, and most glaringly under Plurality voting, these candidates run the risk of splitting the vote and losing to a candidate with an opposing program. This phenomenon can be exploited to alter the election outcome. For instance, New York Times wrote about a Republican political operative who recruited drifters and homeless people onto the Green Party ballot and freely admitted that these candidacies may siphon some support from the Democrats and therefore help Republicans (Lacey, 2010). Such scenarios have been extensively studied in the (computational) social choice lit- erature (see Section 6 for an overview). Depending on whether the manipulation is con- templated by one of the candidates or by an external party, this issue is known as strategic candidacy problem (this term was coined in Dutta, Jackson, & Le Breton, 2001, 2002) or the problem of control by adding candidates. Inthispaperwewilladdressavariantofthisproblemthatisknownascloning.Itis characterized by the following feature: each new candidate must be very similar to one of the existing candidates. This form of manipulative behavior was first identified and studied