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Improved Heuristic for Manipulation of Second-order Copeland Elections

The second-order Copeland voting scheme is NP-complete to manipulate even if a manipulator has perfect information about the preferences of other voters in an election. A recent work proposes a branch-and-bound heuristic for manipulation of secondorder Copeland elections. The work shows that there are instances of the elections that may be manipulated using the branch-and-bound heuristic. However, the performance of the heuristic degraded for fairly large number of candidates in elections. We show that this heuristic is exponential in the number of candidates in an election, and propose an improved heuristic that extends this previous work. Our improved heuristic is based on randomization technique and is shown to be polynomial in the number of candidates in an election. We also account for the number of samples required for a given accuracy and the probability of missing the accurate value of the number of manipulations in an election.