We consider distributed elections, where there is a center and k sites. In such distributed elections, each voter has preferences over some set of candidates, and each voter is assigned to exactly one site such that each site is aware only of the voters assigned to it. The center is able to directly communicate with each of the sites. We are interested in designing communication-efficient protocols, allowing the center to maintain (i.e., declare) a candidate which, with arbitrary high probability, is guaranteed to be a winner, or at least close to being a winner. We consider various single-winner voting rules, such as variants of Approval voting and scoring rules, tournament-based voting rules, and several round-based voting rules. For these voting rules, we show that, using communication which is logarithmic in the number of voters, it is possible for the center to maintain such approximate winners. We complement our protocols with lower bounds. Our results have implications in various scenarios, such as aggregating customer preferences in on-line shopping websites or supermarket chains and collecting votes from different polling stations of political elections.
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 on the number of clones as well as on how each voter orders the clones within the block. 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.