Sharif Digital Repository

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 Kirchgassner. 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... 

One of the most famous criteria to measure the optimality of the election result in the metric space is the amount of distortion. In this framework, the cost of choosing each candidate is considered equal to the total distance of the community members from that candidate. With this definition, the candidate who has the lowest selection cost among all the candidates is called the optimal candidate. The amount of distortion for an electoral mechanism is equal to the maximum amount of the cost of selecting the selected candidate divided by the cost of selecting the desired candidate. It turns out that no deterministic voting mechanism can guarantee a distortion value better than 3. Various...