A recent NBC/YouGov opinion survey shows that nearly two-thirds of American adults agree with a pullout from Afghanistan (see question 4). Can we infer that the electorate prefers a pullout to maintaining a small military in Afghanistan or even to a “forever war”? Not at all, as the “Condorcet paradox” (also called the “paradox of voting”) demonstrates. Here is an example.

I am not taking sides on the substantive issues in the Afghan war, but only pointing out that the electorate does not know what “it” wants. In general, we can expect it to prefer both A and non-A; in this case, pullout and non-pullout.

Imagine that the American voters are (or have been or will be) facing three alternatives:

  • M: providing Moderate support to an Afghan government keeping the Taliban at bay
  • F: waging a Forever war in Afghanistan
  • R: Retreating or pulling out from, or never intervening in, Afghanistan

Assume that the preferences of American voters among these three alternatives divide them into three equal groups:

  • Vgroup (1/3 of voters) where each voter prefers M to F and F to R. Being rational in the sense of having transitive preferences, each voter in this group also prefers M to R. (In the table below, this is symbolically represented by M>F>R, where “>” only means “preferred to.”)
  • Vgroup (1/3 of voters) where each voter prefers F to R and R to M and, therefore, F to M. (In the table, this is symbolically represented by F>R>M.)
  • V3 group (1/3 of voters) where each voter prefers R to M and M to F and, therefore, R to F. (In the table, this is symbolically represented by R>M>F.)
Condorcet Paradox Illustrated
M>F>R>M>F>R>M …

Suppose the electorate is asked to choose between M and F. Members of V1 and V3, will vote for M, making it the winning alternative with two-thirds of the votes. If the voters are asked instead to choose between F and R, the result of the vote would be F because V1 and V2 vote for F; the winner is F. The electorate thus prefers the moderate solution in Afghanistan (M) to a forever war (F) and a forever war (F) to a retreat (R). If the electorate is rational, it must prefer a moderate solution (M) to a retreat (R).

Now, if the same voters are asked, perhaps at a later election (or opinion poll), to choose between R and M, the majority, V2 and V3, votes for R. Without any voter changing his mind, the majority that preferred a moderate solution (M) to a retreat (R) also prefers the contrary: a retreat (R) to a moderate solution (M). The last line of the table describes the electorate’s intransitive and cycling preferences.

Don’t be surprised if that happens in the real world.

This does not mean that majority votes are never useful, only that we can’t count on the electorate to be rational even if no voter changes his mind. The aggregation of voters’ preferences may give incoherent results and will generally do so as the number of voters or issues increases. For a more thorough discussion of the irrationality of voting and its political implications, see my review of a classic book by William Riker, “Populist Choices Are Meaningless,” Regulation 44:1 (Spring 2021), pp. 54-57; and my article on “The Impossibility of Populism,” The Independent Review 26:1 (Summer 2021), pp. 15-25. Teaser: the equivalent of the Condorcet paradox affects any voting system respecting some basic axioms related to rationality.