Efficient Lower Bounding of Single Transferable Vote Election Margins

Abstract: The single transferable vote (STV) is a system of preferential proportional voting employed in multi-seat elections. Each ballot cast by a voter is a (potentially partial) ranking over a set of candidates. The margin of victory, or simply 'margin', is the smallest number of ballots that need to be manipulated to alter the set of winners. Knowledge of the margin of an election gives greater insight into both how much time and money should be spent on auditing the election, and whether uncovered mistakes throw the election result into doubt -- requiring a costly repeat election -- or can be safely ignored without compromising the integrity of the result. Lower bounds on the margin can also be used for this purpose, in cases where exact margins are difficult to compute. There is one existing approach to computing lower bounds on the margin of STV elections, while there are multiple approaches to finding upper bounds. In this paper, we present improvements to this existing lower bound computation method for STV margins. The improvements lead to increased computational efficiency and, in many cases, to the algorithm computing tighter (higher) lower bounds.