Approximation and Hardness of Shift-Bribery.

In the Shift-Bribery problem we are given an election, a preferred candidate, and the costs of shifting this preferred candidate up the voters' preference orders. The goal is to find such a set of shifts that ensures that the preferred candidate wins the election. We give the first polynomial-time approximation scheme for the Shift-Bribery problem for the case of positional scoring rules, and for the Copeland rule we show strong inapproximability results.