From The Oxford Handbook of Political Economy (2006):
Two of the more influential papers that examine inequality within a median voter context are Persson and Tabellini (1994) and Alesina and Rodrik (1994), which both argue that greater inequality will lead to greater preferences for redistribution, and show a negative empirical connection between inequality and growth.
The open question with these papers is whether inequality actually increases redistribution. Empirically there is a strong negative relationship between inequality and social welfare spending, which seems to contradict. While this negative correlation might reflect that more redistribution reduces inequality, it is also possible that more inequality leads to less redistribution rather than more because in unequal societies the poor lack the resources to push their political agenda.
Are there models that account for the disproportionate amount of power of a minority?
That is, how has the median-voter model been adapted to allow for different degrees of influence, and given such a model, is equality inherently unstable? Under what assumptions (of redistribution) would equality be stable? In particular, I'm interested in the dynamics of the system: if equality and inequality are both stable equilibria, what determines to which equilibrium the system converges?
For example, if the rich can influence political outcomes through lobbying activities or membership in special interest groups, then more inequality could lead to less redistribution rather than more. According to this view, as the rich become richer, they acquire a greater ability to influence policy and achieve the policy goals that they want.
Under a great variety of conditions the distribution of wealth on the sugarscape is highly skewed, with most agents having little wealth. Highly skewed distributions of income and wealth are also characteristic of actual human societies, a fact first described quantitatively by Vilfredo Pareto.
Although I imagine there are an infinite number of ways to model such a system, I'm asking for one that restrains itself to the rational agent model, could be explained mathematically (or as an algorithm), has been compared to empirical evidence (despite its limitations), and has been published in a journal or presented at a conference.
I recognize there are cultural, and especially ethnic, aspects to inequality, but I am asking for a mathematical model.