Voting Systems as Linear Transformation Models

In this paper, a new voting system model is introduced as a linear transformation model. The size of compartmental populations in each political group corresponding to every voted subject, the population weights, the weighted votes policy against each political group, the “Yes” and “No” rates, the “No” rejection policy and the “Yes” increase policy are the inputs / outputs of the introduced linear models. Some parametric studies have been achieved concerning the answer of some interesting questions, for example: the effect of unfair election policy, the critical population size of the opposite political group and others. The inverse problem and a stochastic case are also introduced.