Fred Bookstein was at my talk in Seattle on voting power (the relevant articles are here and here) but didn’t get a chance to ask a question, so he’s asking it now:
Why is voting power considered a “good” in all those models? What is good about it? With what generally shared human desiderata, if any, is it associated?
It isn’t obvious to me [Bookstein] that the probability of the individual vote’s determining the outcome of a group choice is a meaningful quantity in any social-theoretic sense. You’re at the same school where C. Wright Mills taught, and my criterion of being meaningful is pretty much the same as Mills’s in The Sociological Imagination (the book that has the chapter “On Intellectual Craftsmanship” that my students adore). His criterion for a meaningful social analysis is one that (I think these are his words, my copy is at the office) turns ordinary human troubles into problems whose resolution has some effect on human freedom, broadly construed. Trouble is that this notion of “voting power” seems to have nothing whatever to do with Mills’s, etc., notion of “power” as in “power elite,” and it doesn’t seem to me to relate to anything having any effect on human freedom broadly construed. So why is voting power considered to be any kind of “power” at all, instead of an index of a certain pathology of process; and how does it relate, if it does at all, to the classic themes of social theory in which I was trained before I turned to statistics? In that classic context, it’s way more important to be able to set the issues put before the voters than to vote: what happens to that idea, the power to set the agenda, in the voting-power approach?
This can’t be a novel query, and may well correspond to some sort of other of Methodenstreit within the field of political science such as I have been managed to straddle for some decades in evolutionary biology now. So feel free just to point me to good articles or polemics or something. Mills has been dead for 47 years, and my teacher Talcott Parsons for 30 years; that might be part of my answer, I fear. And of course this question is aimed at Prof. Gelman of the Polit. Sci. department, not Prof. Gelman of the Statistics Department who gave such a delightful lecture. But, still, I’d like to know if the topic has anything to do with the sort of social theory I was taught when young.
My quick reply is that calculations of voting power is important because they are used to allocate votes in two-level voting systems, or at least to justify such allocations (such as the slight overrepresentation of small states in the U.S. Electoral College or the large overrepresentation of small countries in the EU Council of Ministers). This is what got me started in this area: annoyance that inappropriate mathematical calculations were used in order to justify unequal representation. (There’s lots more detail in our BJPS article linked to above; suffice it to say here that the classical voting power calculations are based on an implicit assumption that elections in large states or countries will be much closer, in percentage terms, than elections in small jurisdiction–an assumption that doesn’t happen to hold up in the actual elections we’ve looked at.) So, as long as voting power is used to allocate representation, I think it’s worth doing right.
Beyond this, yes, I’m starting to agree that “power” is a misleading term for what is actually the probability that your vote is decisive. “Decisiveness probability” is too long, though. Maybe “pivotality”?
Regarding Mills and Parsons: that’s out of my area of expertise. If there are any sociologists in the audience, maybe you have some comments?
Steven Lukes's Power: A Radical View, although old (first published in the early 1970s), still is a good discussion. He distinguishes three levels of power: (1) influence over decisions–getting the result you want in the face of opposition (2) agenda-setting (3) setting the limits of what's imaginable. It seems that voting power would certainly qualify as an example of the first level of power. Parsons made the same general argument–that there are different kinds of power–although he drew the distinction in a different way.
As I recall, Mills was also mainly concerned with power over decisions, although he thought the important decisions involved war and peace and that any differences between Democrats and Republicans on domestic policy were minor and would have little impact on human lives. That was an easier argument to make in the 1950s than it is today.