Why don't voters 'put the Gini back in the bottle'? Inequality and economic preferences for redistribution

The classic democratic theory of redistribution claims that an increase in market income inequality causes an increase in the size of government through majority voter support for an offsetting expansion of redistribution. I argue that the predicted inequality-redistribution relationship can break down when voters face uninsurable idiosyncratic risk with respect to future labor income and a timing differential between tax collections and government outlays. This is formalized using an incomplete market heterogeneous-agent DSGE model with majority voting and 'time-to-build' policy, which suggests the collective demand for redistribution will not necessarily increase with growing income or wealth inequality. This result implies that even with equal political power among voters, democracies do not have a systematic mechanism to offset rising inequality as contrary to popular belief.