Measure and collapse of participatory democracy in a two-party system

Measure what is measurable, and make measurable what is not so (Galileo Galilei). According to the above sentence we do not ask why we need to measure democracy but if it is possible to measure something which is not unequivocally defined. Although, it is unlikely a final agreement on the definition of democracy, the idea that it is a form of governance based on collective decision making seems to be uncontested. On the premise that in the high-quality democracy citizens (agents) not only must have equal participation rights but must want to participate in shaping decision, as an effective measure of democracy in a two party political system we propose the percentage of the total population that actually voted in a given elections only for two major parties. Thus, we disregard not only nonvoters but also smaller parties voters whom votes will not have a substantial impact on the election and consequently they will not be in the loop, even theoretically. To describe such a system a sociophysics model based on the $S=1$ Ising model (Blume-Capel) is proposed. The measure of democracy, V_D index, as a function of inter-party conflict is analyzed.