On the Distortion Value of the Elections with Abstention

Abstract In Spatial Voting Theory, distortion is a measure of how good the winner is. It is proved that no deterministic voting mechanism can guarantee a distortion better than 3, even for simple metrics such as a line. In this study, we wish to answer the following question: how does the distortion value change if we allow less motivated agents to abstain from the election?We consider an election with two candidates and suggest an abstention model, which is a more general form of the abstention model proposed by Kirchgässner (2003). We define the¨ concepts of the expected winner and the expected distortion to evaluate the distortion of an election in our model. Our results fully characterize the distortion value and provide a rather complete picture of the model.