No-show paradoxes in Condorcet voting methods: a computational experiment

A No-show Paradox can be described in a voting context as the fact that there is a voter who would be better not voting, since she prefers the winner resulting from the election when she abstains to the winner resulting when she votes honestly. Variations of the No-show Paradox, that affects ordinal aggregation methods have been identified and analysed in the context of voting methods. A method affected by one of these types of paradox can be manipulated in the sense that a voter may obtain better results when she does not show her preferences. A stronger version of the paradox, called Strong No-show Paradox, says that there is a voter whose favourite candidate loses the election if she votes honestly, but gets elected if she abstains. All Condorcet and scoring run-off methods are known to be affected by at least one version of the paradox and almost all of Condorcet ones are known to be affected by the strong versions. The practical relevance of these paradoxes in the evaluation of a voting method depends, at least in part, on the probability of occurrence of a situation when the paradox effectively happens. As an extension of our first research step, we present now the results obtained through a random simulation that explores the occurrence of some versions of the paradox in some of the best known Condorcet voting methods.