My attention has been drawn (thanks Paul) to an article which describes how one might find the optimal number of members of parliament in a representative democracy.
In a nutshell, a parliament with too few representatives is not “democratic” enough, possibly leading to an unstable political system, in which various undesirable forms of political expression, including of course violent ones, will develop. In contrast, too many representatives entail substantial direct and indirect social costs, they tend to vote too many acts, interfere too much with the operation of markets, increase red tape and create many opportunities for influence, rent-seeking activities and corruption.
In their paper the authors derive a formula in which the optimal number of representatives is approximately proportional to the square root of the population of the country.
They test their formula against the data and find that Israel, New Zealand, the Netherlands and the USA have far too few representatives. I’m not sure how this correlates with their predictions about the instability of under-represented democracies: all four countries are very stable, non-violent democracies as far as I’m aware. I don’t have access to the CEPR paper but I’d be curious as to whether they address this issue. Their model makes some predictions which are easily falsifiable and I’d like to know how it stacks up against the evidence.