Thread by @FormalTheory

This paper by @ScottFAbramson, @Korhan_Kocak, and
@asyamagazinnik on conjoint analysis has been getting a lot of attention, and rightly so! We wanted to add a bit from a @formaltheory perspective. 1/ scholar.princeton.edu/sites/default/…

One influential strand of formal theory in political science is Social Choice Theory (SCT), which studies the aggregation of *individual preferences* to broader *group preferences*. 2/

For example, suppose we know whether a bunch of individuals prefer A or B. Majority rule is a way to aggregate these preferences into whether the group prefers A or B: just count how many prefer each go with the higher number. 3/

Sounds easy, but lots of classic SCT results show how things can go haywire. Perhaps the most famous example is that majority rule can lead to preference "cycles", where the group (strictly) prefers A to B, B to C, and C to A. Turns out aggregating preferences is complicated! 4/

Empirical political science also often studies individual and group preferences. One newly popular such method is conjoint experiments, which ask people to decide between pairs of choices (often candidates for office) that vary on several dimensions (age, party, gender, etc.) 5/

The idea: to figure out whether voters generally have a preference for, say, male and female candidates, we should give them lots of hypothetical choices that vary on this dimension and the others. This is plausibly more realistic than directly asking about M/F preference 6/

Then, comparing the probability of voting for the F vs M candidate (averaging over the other characteristics), we can uncover whether the electorate has a preference for one gender over the other. Right? 7/

WRONG! 8/

Abramson, Kocak, and Magazinnik show the deep connection between SCT and conjoints. By applying some classic ideas from SCT, they show that the estimates empirical papers use may be misleading about majority preferences. 9/

A key intuition is that majority rule -- for better or worse! -- does not depend on the intensity of preferences. Either a majority of voters prefer a female candidate or a majority do not. 10/

However, by adding in other characteristics and then averaging over candidate choices, estimates from conjoints are influenced by preference intensity. 11/

For example, suppose a small minority of voters will never vote for a female candidate, and the majority have a slight preference for females. The minority will always vote for M over F, but the majority will sometimes vote for Ms with other good attributes. 12/

Since the minority preference effectively gets weighted more, it can look like the majority holds their views when this isn't in fact true. 13/

SCT hasn't been the most active area in the last few decades, at least in mainstream political science. Some argue that this is because it is too abstract and theoretical to speak to real political institutions. This paper provides a strong counter to that view. 14/

In any case, it is a great example of how some ideas which were developed primarily for their theoretical interest can be hugely relevant to empirical research. 15/15