Perhaps the most advanced topic that I cover every semester in my Principles of Microeconomics class at George Mason University is (Kenneth) Arrow ‘s Impossibility Theorem . (I do so in the context of a larger discussion featuring public-choice economics .) I do not go into the mathematics of the Theorem, but I do give some classic demonstrations of this important theory.
My takeaway understanding of this Theorem is that it – along with each of many other works in the broad category of the economics of collective decision-making – demonstrates the error, and the consequent danger, of anthropomorphizing any collective. It shows the mistake of presuming that a collective that “chooses” (say, through majoritarian voting) candidate A over candidates B and C, or policy X over policies Y and Z, can in any sensible way thought to be very much like an individual human being who chooses option A or course-of-action X.
Collectives are not sentient human beings. It is folly to suppose that just because each member of the collective has some voice in determining the actions of the collective, that the collective thereby is some sort of scaled-up human-like decision-maker. It is not, and it cannot be.
One feature of Arrow’s Impossibility Theorem is its insistence on the importance of the criterion called “independence of irrelevant alternatives .” This criterion came to mind in a discussion with some of my students on Tuesday night, after class, of the Virginia gubernatorial election. At the time of the discussion (10pm-ish) it was clear that Democratic candidate Terry McAuliffe had defeated GOP candidate Ken Cuccinelli, but by a margin smaller than many had predicted. At the time, a reasonable suspicion was that Libertarian Party candidate Robert Sarvis  (btw, boasting a graduate degree from GMU Econ!) cost Cuccinelli the election. The plausible assumption is that Sarvis pulled vastly more votes from Cuccinelli than from McAuliffe.
Let’s accept this assumption as being true and accept also that, had Sarvis not run, Virginia’s next governor would be not Terry McAuliffe but, instead, Ken Cuccinelli. (It’s not an unreasonable assumption, and we’ll go with it here – although it’s not necessarily correct .)
If Sarvis did swing the election from Cuccinelli to McAuliffe, this fact is further evidence that collective decision-making is not analogous to individual decision-making. To see why, consider the following hypothetical example (that I steal from a lecture that Alex Tabarrok sometimes gives).
You walk into an ice-cream store and ask what flavors are available today. The clerk says “We’ve got vanilla and strawberry.” You ponder for a moment and tell the clerk “I’ll have strawberry.” Just before the clerk starts to scoop out your strawberry ice cream, he turns to you and says, “Oh, I almost forgot. We also have pistachio.” In response, you ponder for another second and then tell the clerk, “Well, in that case, I’ll have vanilla.”
Obviously, such a response by you would be (for lack of a better term) irrational. It would certainly be odd and unexpected. If you prefer strawberry to vanilla, why in the world would your learning of the availability of pistachio change your preference between these two flavors (strawberry and vanilla) from strawberry to vanilla? Your learning of the availability of pistachio ice cream ought not – and, in reality, almost surely will not – prompt you to switch your order from strawberry to vanilla.
But such ‘switching’ is routine in democratic elections. If the voters collectively would have ‘chosen’ Ken Cuccinelli over Terry McAuliffe had Robert Sarvis not been on the ballot, but instead ‘chose’ McAuliffe over Cuccinelli because Sarvis was in fact on the ballot, these voters (as a collective) clearly do not act as a rational individual decision-maker acts. (If you don’t like the McAuliffe-Cuccinelli-Sarvis example, think Bush-Gore-Nader in 2000, or Clinton-Bush-Perot in 1992.)
Anthropomorphizing collectives – including collections of voters – is a mistaken and dangerous folly. Its romance is surely real for many people, but that doesn’t make the practice any less mistaken and foolish.