Persuasion II

Every once in a while, an apparently intelligent person writes something so gob-smackingly wierd and illogical that you know that they have to have a screw loose. Such people are frequently libertarians. Consider the case of Alex Tabarrok:

Intelligence Squared has held a series of debates in which they poll ayes and nayes before and after. How should we expect opinion to change with such debates? Let's assume that the debate teams are evenly matched on average (since any debate resolution can be written in either the affirmative or negative this seems a weak assumption). If so, then we ought to expect a random walk; that is, sometimes the aye team will be stronger and support for their position will grow (aye after - aye before will increase) and sometimes the nay team will be stronger and support for their position will grow. On average, however, we ought to expect that if it's 30% aye and 70% nay going in then it ought to be 30% aye and 70% nay going out, again, on average. Another way of saying this is that new information, by definition, should not swing your view systematically one way or the other.

Alas, the data refute this position. The graph shown below (click to enlarge) looks at the percentage of ayes and nayes among the decided before and after. The hypothesis says the data should lie around the 45 degree line. Yet, there is a clear tendency for the minority position to gain adherents - that is, there is an underdog advantage so positions with less than 50% of the ayes before tend to increase in adherents and positions with greater than 50% ayes tend to lose adherents. What could explain this?

Let's review. Alex sees some interesting data, forms a hypothesis about how it should behave, and finds hypothesis does not explain the facts. So far so good. It's what he says next that is completely nuts.

I see two plausible possibilities.

1) If the side with the larger numbers has weaker adherents they could be more likely to change their mind.

2) The undecided are key and the undecided are lying.

Notice that neither of these "explanations" is (1) compatible with his original hypothesis of randomness or (2) explains anything. There is also a serious element of innumeracy in his reasoning. Suppose, for example, that propensity to change one's mind was purely random. In that case, the proportion of majority and minority changing their minds would be the same for both groups, but the absolute numbers would be greater in the majority, leading to a change in just the direction seen. Oddly enough, Alex knows this, but rejects it for reasons incomprehensible to me.

I doubt that that is the full explanation however, and I find his starting hypothesis (of purely random changes) implausible. For one thing, I have read the debate topics. Essentially all of them are emotionally loaded, multi-faceted, and far from the primary concerns of the average citizen. I intend to consider this point further, but first let's give Alex a bit more rope:

Thus 2 is my best guess. Note first that the number of "undecided" swing massively in these debates and in every case the number of undecided goes down a lot, itself peculiar if people are rational Bayesians. A big swing in undecided votes is quite odd for two additional reasons. First, when Justice Roberts said he'd never really thought about the constitutionality of abortion people were incredulous. Similarly, could 30% of the audience (in a debate in which Tyler recently participated (pdf)) be truly undecided about whether "it is wrong to pay for sex"? Second, and even more doubtful, could it be that 30% of the people at the debate were undecided--thus had not heard arguments in let's say the previous 10 years that converted them one way or the other--but on that very night a majority of the undecided were at last pushed into the decided camp? I think not, thus I think lying best explains the data

Doh. Roberts was an appelate judge whose entire career was the interpretation of the law and the constitution, and the question of abortion is the most contentious constitutional issue of the past several decades. Most people don't frequent prostitutes, and even those who do have little motive to examine the morality of the question. I see no parallel here.

Tabarrok once more:

Some questions for readers. Can you think of another hypothesis to explain the data

How about this. When complex issues people have not thought much about are defended in debate, people replace prejudices with more informed choices. Because the issues are difficult, there is no clear cut right answer, and informed people are more likely to split half and half when the evidence on either side is approximately equal.

Can you think of a way of testing competing hypotheses

Ask people why they changed their minds.

And does anyone know of a larger database of debate decisions with ayes, nayes and undecided before and after.

Election debates and polls - though the debaters are rarely equal in those contests.

Shooting libertarian fish in a barrel.