Riker and the Mathematician's Fallacy
By Bryan Caplan
The last chapter of William Riker’s classic work, Liberalism Against Populism, contains some of the strangest statements I have read in quite a while. Background: Riker is deeply impressed by the literature on social intransitivity. As Arrow and others showed, sometimes a majority will vote for A rather than B, B rather than C, and C rather than A. If so, what is the “will of the people”? It doesn’t seem to have one, does it?
If you’re anything like me, you’re now asking “What major real-world issues does this apply to, if any?” Is it possible, contrary to appearances, that the minimum wage and drug prohibition are not really popular?
But Riker seems to have almost no interest in empirical public opinion research (much of which has subsequently found that, contrary to Riker’s fears, political opinion is roughly one-dimensional). Instead, he makes a series of bizarre theoretical arguments to somehow equate mere hypothetical possibility with reality.
It is possible, even probable, that strategic vote-trading is commonplace in the real world… If so, then all voting is rendered uninterpretable and meaningless. Manipulated outcomes are meaningless because they are manipulated, and unmanipulated outcomes are meaningless because they cannot be distinguished from manipulated ones.
Since [political] manipulation is frequent but unidentified, again all outcomes of voting are rendered meaningless and uninterpretable.
Populism as a moral imperative depends on the existence of a popular will discovered by voting. But if voting does not discover or reveal a will, then the moral imperative evaporates because there is nothing to be commanded. If the people speak in meaningless tongues, they cannot utter the law that makes them free. Populism fails, therefore, not because it is morally wrong, but merely because it is empty.
I’d like to interpret Riker charitably, but I just can’t. None of these arguments does much more than restate the obvious: It’s logically possible that the policy status quo exists because someone manipulated social intransitivities. Therefore, we “can’t know” if they’ve been manipulated. Therefore we can’t infer anything about what is popular from what exists. Therefore it’s meaningless to say that any policy is truly popular.
Riker’s problem: He suffers from what I call “the Mathematician’s Fallacy.” For the mathematician, you have either proved your result or you haven’t. There is no middle ground; either you have absolute certainty, or no business speaking. And that’s crazy. Every day all of us makes insightful, useful, intelligent observations about the world that fall short of absolute certainty. More certainty would be good, but what we now have is a lot more than zero.
I wish it were meaningless to say “Social Security is an extremely popular program.” But my best guess, unfortunately, is that Social Security really is extremely popular.