Towards Formalization of Rational Voting Models on Large Electrates

Abstract

Since Downs (1957) proposed a rational voting model, which has been used to explain the statistical relationship between closeness of elections and levels of their turnouts, many articles has pointed out that discussions on the model couldn't make eligible voters have enough incentive to go to their polling places (called the paradox of not voting).

There has been many kinds of models proposed by the way of modifying the Downs model. It seems, however, that most of them couldn't give solutions to what makes voters lead to polls yet.

At first, this paper surveys some typical attempts to the paradox, and indicates their difficulties to resolve it. Secondly, the paper gives an framework on voter models where the electrate would be supposed to be sufficiently large such as general elections. The framework here is based on the model proposed by Schwartz T. (1987) who proposed an additive utility model on some sub-electrates, and enables us to analyse when an incentive of an eligible voter becomes maximized with respect to his subjective expectation and certainty on the number of votes that would be obtained.