Robin Varghese points to this paper by James Galbraith and Travis Hale, “State Income Inequality and Presidential Election Turnout and Outcomes.” At a technical level, they offer a new state-level inequality measure that they claim is better than the measures usually used. I haven’t read this part of the paper carefully enough to evaluate these claims. They then run some regressions of state election outcomes on state-level inequality, and find that “high state inequality is negatively correlated with turnout and positively correlated with the Democratic vote share, after controlling for race and other factors.” So far, so good, I suppose (although I recommend that they talk with a statistician or quantitative political scientist about making their results more interpretable–I’d recommend they use the secret weapon, but at the very least they could do things like transform income into percentage of the national median, so they don’t have coefficients like “4.58E-06”).
But then they write:
We [Galbraith and Hale] can, however, infer that the Democratic Party has engaged in campaigns that have resonated with both the elite rich and the comparatively poor.
Well, no, you can’t infer that from aggregate results! To state it in two steps:
1. Just because state-level inequality is correlated with statewide vote for the Democrats, this does not imply that individual rich and poor voters are supporting the Democrats more than the Republicans. To make this claim is to make the ecological fallacy.
2. The Democrats do much better than the Republicans among poor voters, and much worse among the rich voters. (There’s lots of poll data on this; for example, see here.) So, not only are Galbraith and Hale making a logically false inference, they are also reaching a false conclusion.
To conclude on a more polite note
I don’t want to be too hard on Galbraith on Hale. The essence of a “fallacy,” after all, is not merely that it’s a mistake, but that it’s a tempting mistake–that it seems right at the time. (Otherwise we wouldn’t have to warn people about these things.) Through the wonders of the www, the paper reached me, I noticed the mistake, I’ll notify the authors, and they can fix this part of the paper and focus it more on the inequality measure itself, which is presumably where their paper started in the first place.
P.S. I certainly don’t see my role in life as policing the web, looking for statistical errors. I just happened to notice this one, and the topic is something we’ve been researching for awhile. (And, of course, maybe I missed something important myself here…)
P.P.S. Galbraith and Hale have revised their paper to remove the implication about individual voters. I agree with them that this is an interesting topic to study–the key is, I think, to be able to work in the individual-level poll data to address questions of interest.