To explain, Part I of the paper, "The Political Economy of Progressive Rates," does an excellent job of explaining basic optimal tax models that underlie thinking about progressive and other tax rates, along with rational choice-based political economy models that can be used to predict legislative outcomes in a majoritarian framework. But that's just the set-up or background. The real work of the paper is done in Part II, "The Instability of Rate Schedules." Here, given the fact that, in the set-up, for any current set of rate schedules there is a majority that would prefer something else - leading to cycling, and making agenda control important - the paper "uses a set of Markov chain Monte Carlo simulations [to] explore what rate schedules are most likely under majoritarian voting." This takes the form of "heat maps" showing what rate structures emerge most frequently, among the assumed possibilities, under different sets of assumptions, e.g., regarding agenda control and the influence of the rich. "The simulations suggest that (1) rate progressivity becomes more likely as political power is concentrated in the hands of the rich, and (2) progressive rate structures are predominant even if there are relatively more rich than poor."
Under the rational choice model, the voters perfectly understand all the possible tax systems and everyone else's preferences. They are rational utility-maximizers, whose utility depends solely on own consumption and leisure. Disregarding changes to leisure (from adjustments to labor supply) to simplify the exposition, all they care about is having more money rather than less, from how a given tax change affects (a) their own tax liabilities, plus (b) the demogrant that they get given the overall revenue raised. (The demogrant functions as a proxy for positing uniform benefit from government spending.)
I myself tend to be somewhat of a skeptic regarding rational choice models of this kind. First there are the issues about rational choice generally, secondly about assuming that utility depends solely on own consumption and leisure, but also thirdly about applying it to voting in particular.
Last November 8 - before it had become clear to me what political outcomes would become known several hours later on that dark day - I posted the following, in the course of discussing a paper presented by Ilyana Kuziemko the day before at the Colloquium on High-End Inequality:
"The paper notes that, under the “workhorse political economy model” in which voters simply follow their own narrow economic self-interest, it would be paradoxical to find that rising inequality didn’t trigger increased support for redistribution. The model – which, happily, the authors, no less than I, regard as a useful strawman rather than something that is actually credible – posits that each voter’s support or opposition for addressing income inequality is simply a function of mean income minus own income, as this would determine whether symmetrically compressing income inequality would yield one a gain or a loss.
"This is not a convincing model for numerous reasons. Let’s even posit that people didn’t care about anything other than the effect on own income under the above setup. The model would still founder on the paradox of voting – i.e., the fact that, since I cannot have any statistically significant effect on the outcome, my voting (and even informing myself about the economic stakes to me) are a total waste of time when modeled in such a framework. People “shouldn’t” vote, and if rational “wouldn’t” vote, unless something else was going on....
"What’s a better basic account of how voters generally make choices? I rather like this quote from the newly published Christopher Achen and Larry Bartels, Democracy for Realists:
“'[M]ost residents of democratic countries have little interest in politics and do not follow news of public affairs beyond browsing the headlines. They do not know the details of even salient policy debates, they do not have a firm understanding of what the political parties stand for, and they often vote for parties whose longstanding issue positions are at odds with their own. Mostly, they identify with ethnic, racial, occupational, or other sorts of groups and often – whether through group ties or hereditary loyalties – with a political party. Even the more attentive citizens mostly adopt the political positions of the parties as their own: they are mirrors of the parties, not masters. For most citizens most of the time, party and group loyalty are the primary drivers of vote choices.'”
Oh's paper does not, however, make unsupported claims about the model's degree of descriptive accuracy. Instead, in its Part III, "Moving to the Real World," it discusses the issue of what we actually learn from the model. I agree that these models can provide an interesting perspective to add to other perspectives, and hence are worth doing.
BTW, the paper's current title doesn't do a perfect job of conveying what we learn from Part II. In essence, what the simulations show is that, in the model, the rich are more successful in gaining allies when they agree to a plan in which rates below the top income level are lowered. E.g., suppose that there initially were a flat 40% rate throughout. Lowering the tax rate to, say, 20% for the first $100,000 of income would reduce taxes by $20,000 for each individual with more than $100,000 of income. This would exceed the reduction in the demogrant, so they'd be better off. While they would also benefit for lowering the tax rate that applied to income above $100,000, they wouldn't have as many allies if they proposed that. Everyone who was earning $100,000 or less would be opposed, whereas people in the upper ranges of that group would also benefit (despite the reduced demogrant) from lowering tax rates for the first $100,000.
Another way of thinking about the paper is that it illustrates the benefit to people in the upper rate brackets from lowering what are, for them, inframarginal rates. This indeed is a point that may have helped, say, the designers of the 2001 Bush tax cuts - not to mention the current Republican Congressional leadership - in creating false impressions among voters regarding the overall distributional slant of their tax proposals.