Disclaimer. Don't rely on these old notes in lieu of reading the literature, but they can jog your memory. As a grad student long ago, my peers and I collaborated to write and exchange summaries of political science research. I posted them to a wiki-style website. "Wikisum" is now dead but archived here. I cannot vouch for these notes' accuracy, nor can I even say who wrote them. If you have more recent summaries to add to this collection, send them my way I guess. Sorry for the ads; they cover the costs of keeping this online.
Meltzer and Richards. 1981. A rational theory of the size of government. Journal of Political Economy 89 (5): 914-927.
Although the model is more complex than this, here's the basic idea:
IN SUM: See Fig. 1, page 922
X = the difference between the decision maker's income and the income per capita. So the franchise, the median voter's income, and changes in relative productivity matter.
(a) The authors don't talk much about dictatorship, but if they did, it would probably sound a lot like the extractive "stationary bandit" that sets tax rates just high enough to maximize receipts without decreasing total economic output too much.
(b) In a democracy, the decision maker is the median voter.
(c) If the median voter does not work (is on welfare), he will set tax rates at exactly the point that a stationary bandit would (see above).
(d) If the median voter earns less than the mean income, he will set tax rates at the point that maximizes his personal income (the combination of his reduced wages (since he'll work less when there are higher taxes) and his increased welfare payments.
(e) If the median voter earns exactly the mean income (or more), he will set tax rates at zero. Why can't reverse redistribution (extraction) occur? Because if there are more rich people than poor people, they can do better by working harder than extracting.
Y = the "size of the government," but not really. Y is only the amount of redistribution.
Research on similar subjects