Voting theory is plagued by seemingly contradictory results, called voting paradoxes. For example, different methods of tallying votes can result in different election results; these voting paradoxes give contradictory answers to the question of what the voting population “really” wants. This paper studies voting paradoxes brought about by considering the effect of dropping one or more candidates in an election after the voting data has already been collected. Dropping a candidate may change the election results for the remaining candidates. This paper adopts an algebraic framework to approach this voting theoretic problem.