Bryan Caplan  

Riker and the Mathematician's Fallacy

Bleg: Terminal Health Care Sp... Social Security and Intransiti...

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.

Exhibit 1:

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.

Exhibit 2:

Since [political] manipulation is frequent but unidentified, again all outcomes of voting are rendered meaningless and uninterpretable.

Exhibit 3:

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.

Comments and Sharing

COMMENTS (3 to date)
Lawrance George Lux writes:

Study of Riker's take on Popular votes comes up with: the Popular vote is meaningless because Voters vote in support of their Self-Interest; or Voters are mislead in what their true Self-Interest is by clever device. I am an advocate of One can't fool even very many of the People very long.

Social Security is very popular, as it has worked effectively for Sixty years thereabouts. It would still be an effective program, if the Politicians had not spend the Trust Fund, throwing funding again back on the Taxpayers. The Public knows the Trust Fund was fixed previously by a incremental Tax hike, and the Public also knows George W. cut Taxes far more, especially for Upper-Income levels, than would be needed for an additional incremental Tax hike to bring Solvency to the SS Trust Fund. I don't think Republicans stand a chance on this one. lgl

Hol Onomy writes:
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.

Speaking as a mathematician, I am quite surprised to learn of this. Thank you for your insight into this matter Bryan.

David writes:

I disagree with your characterization of Riker's argument. social choice Theory assumes by its very nature more than binomial choice. It is not that social security is an indistinguishably popular or unpopular program, but rather if I were designing a social secutiry program, I could design it in many ways. I could make private accounts, full public funding via a special tax, funding from general tax revenue, etc. The possible range of benefits given out from my social security system is only limited by the amount of resources I am able to take in to feed it, from 0% of employment income up to and exceeding (the absurd) 500% of employed income. Here, we have a situation where people ant a policy, or agree on it's objective, but in no way do they agree how to run it, make it work, fund it, and how muhc of the problem should be allieviated by government. When we (political scientists) envision a legislature or other descision making body we assume that bargaining goes on and that each legislator has a single-peaked and symmetrical preference order around a given point on a line or plane (this is a big assumption, granted, but it is the least assuming way to arrange preference structures that might leave an equilibrium). On a unidimansional range, (i.e. social security or not, or any single dimension of the problem such as fundign or benefits levels) a majority may be discovered rather easily (see Downs, An Economic Theory of Democracy). However, all of these issues are multidimensional. When setting SS policy, one must decide both the benefit level and how to fund it. This problem is inherently multidimensional which leads to the Arrow problem. there is no point on the plane (without intitutional restriction - parties are an institutions) which can not be beaten under majoritarina rules. Riker, by addressing the social choice problem, is implying multidimensionality, which does make intentions impossible to determine. in the final vote. do my preferences change because I sincerely believe in them and have found out more information, or do they change because the legislator next seat over promised me that if I voted for the bill, I could get a highway project in my district? bith can change the preference point in the exact same way and be indistinguishable.

As to your assertion that it has been shown that people's preferences are unidimensional, not so. Political elites are overwhelmingly unidimensional- this coul dbe due to elite indoctrinization (Chong McKlosky, and Zaller) or that party forces their perpectives to polarize (Miller and Stokes). The People, on the other hand, are not nearly so polarized, nor so knowledgable . While there is overwhelming consensus among elites on the simple and basic components of the classic American doctrine, Capitalism and Democracy, the plebs do not share that consensus, nor the variation with in it. Scholars like Campbell as far back as 1964 have been unable to find individuals with coherent policy preferences in more than about 8.5% of the population. Recent poll data and experimental work does not give any more confidence in the american people to form coherent views about politics. The most charitable interpretation of poll numbers comes from Page and Shapiro's the Rational Public. Individuals, when we can concieve of them as rational (and we go out of our way to do so) most often look to their short term interests, determine if their and their family's situation is good or bad, and say yea or nea to the status quo. Riker is absolutely right to state that the people speak with meaningless tongues. It is quite clear, to me (a ph.d. candidate in political science that works on political psychology), that they are not even trying to utter a law that would make them truly free.


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