A geometric model of sensitivity of multistage elections to change

This paper geometrically compares multistage, multiple, and positional elections. The method of comparison shows that multiple stage elections are not necessarily more sensitive to small scale manipulation or other small scale effects. In particular, when all rank-order outcomes matter, multistage elections are in general less sensitive to perturbation, while in the case where the election’s outcome simply produces a singular winner and stages are not closely correlated, some multistage elections show similar or higher levels of intrinsic vulnerability to manipulation, error, and fraud as positional or multiple elections. In elections where the outcome simply produces a singular winner, a plurality vote is identified as less vulnerable in a single stage election than in multiple stages, while an antiplurality vote is identified as more vulnerable in a single stage than in multiple stages.