putting it mildly, i can't get anyone even to want to understand this, much less publish it, which kind of makes the point again. it could be framed in many ways, and i will perhaps try a less directly attacking mode, because at its heart this is a plea for tolerance of diverse opinions and independent thinking. also i will say this: it is not some kind of gratuitous argument; it expresses systematicallly intuitions that i have always had.
At Last! A Mathematical Proof of Cynicism
By Crispin Sartwell
It may be that you, like me, doubt anything that any politician or political spokesman says. And if you're like me, it doesn't matter whether the politician is on the left or the right: you and I just don't think that any politician has any credibility. But unlike me you do not know that this can literally be proven mathematically, once and for all, beyond quibble or refutation. Follow this carefully.
To make my proof clear to laymen such as yourselves I am going to run through some hypothetical scenarios. Consider a factual question, say whether there is extra-terrestrial intelligent life (etil). And in our little scenario, let's say that the jury is out on that and that the evidence is evenly split, as far as we know. People in our society are trying to make up their minds one way or another, and when they do, we find that within different groups of us there are different distributions of opinion: the Star Trek fans are more likely to believe that there is etil than the non-Star-Trek fans, or opinions might be clustered within groups by education level, and so on.
On the other hand, if most of the green-eyed people believed it and most of the blue-eyed people didn't, or if most of the gardeners believed it and most of non-gardeners didn't, or if most of the people who lived within 17,237 yards of a major river believed and if not not, we would be surprised. We'd grope for an explanation. That's because whether you're a gardener or not doesn't seem to have any connection to anything that might make someone believe either way. We'd have thought that eye-color couldn't possibly determine or be correlated to people's take on aliens.
But if we find that there is this correlation, one thing we could immediately, though provisionally, conclude is that something is going on that isn't related to the evidence of whether there is etil: maybe their tendency to believe different things about this is in the genes in some bizarre way, or maybe there are more interesting social distinctions between these groups than we thought. But the difference between the two groups cannot be connected to the actual evidence that there is etil: the aliens are just as visible to blue as to green eyes. That is, the difference in the distribution of opinions has no rational basis, though of course there may be many people in each group whose belief is rational or who believe what they believe after an honest attempt to assess the evidence.
Now consider the question of whether the healthcare bill will increase the deficit, or the question of whether Sarah Palin influenced Jared Loughner, and just stipulate in our still fictional world that the evidence is perfectly 50/50. And suppose that opinion on those questions broke down by whether people were gardeners or non-gardeners. We'd be surprised in just the same way. The differences between the groups cannot be the result of the evidence, because there is absolutely no reason to think that the evidence is available to one of these groups and not to the other.
Let's make our invented world a math problem. Every single gardener believes that the healthcare bill will increase the deficit, and every non-gardener believes not. If the evidence were equal on both sides, and the gardeners and the non-gardeners had equal access to the evidence, and everyone was sensitive to the evidence, then we'd expect a 50/50 split within each group on this question among people forming an opinion. In this case we should infer provisionally that at least half the people in each group believe what they believe because of factors that have nothing to do with the evidence, or that they believe for no reason connected to the truth of what they believe. The probability that any given person in either group believes because of factors that are relevant to the truth of the claim is at most .5.
I will express this by saying that a person in either group who takes the view of the consensus of the members of that group has a Credibility Index of .5.
This decimates the credibility of all gardeners and of all anti-gardeners. They are from the outset, all things being equal, only half likely to be sensitive to evidence or to be reliable guides to the truth. In fact, we can imagine people who are, provisionally, twice as credible on average. Let's say that in each group there is one dissenter: a gardener who believes that the healthcare bill will increase the deficit, and a non-gardener who believes it won't. We can estimate the probability that the dissenter's opinion is based on evidence as twice that of the person who has the consensus position of his own group. That is, the person who takes the anti-consensus view can't be discredited on these grounds. Other things being equal, people who take up the consensus position of their group, where group membership does not bear on access to evidence, are only half as likely to be basing their belief on the evidence as people who don't. Quite a surprising result, I believe. And yet the argument is entirely obvious and decisive.
Now on the question of whether healthcare will increase the deficit or whether Palin influenced Loughner, leftists and rightists, liberals and conservatives, Democrats and Republicans are exactly like gardeners and non-gardeners. Membership in such groups just is not correlated with availability of the evidence. That is obvious. Either the healthcare bill will increase the deficit or it won't. That we should help struggling families, or that we need foreclosure relief, or that we should get tough with Iran has absolutely no pertinence. If all the other assertions of American liberalism were true, that wouldn't provide a shred of evidence that the healthcare bill won't increase the deficit, and if all those of conservatism were true that wouldn't be any evidence that it will.
What counts in trying to figure out whether Palin influenced Loughner would be things like whether Loughner tivoed Sarah Palin's Alaska, or subscribed to her Twitter feed, or had her crosshairs map blown up and tacked to his wall, or left a note saying "I did it because I'm trying to do what Sarah Palin wants." Your posture on tax policy or whether the children of illegal immigrants should be citizens is neither here nor there. What counts on the healthcare bill is actual calculations made with good data. That semi-automatic guns should be banned or that Israel is our best friend in the region is obviously just irrelevant.
And yet out there on Capitol Hill and among the political consultants appearing on television there has been something close to unanimity on these issues: more or less all the left's op-ed columnists who appeared the Monday after the Saturday shooting blamed the 'atmosphere' of 'extreme rhetoric' and connected the shootings to Palin and Glenn Beck. On Tuesday all the right's op-ed columnist denied that completely. One hundred percent of the Republican caucus and the rest of the people embroiled from the official right in the debate insist that the healthcare bill will increase the deficit. And one hundred percent of the Democrats say it will decrease it. If you yourself aren't sure who to believe or which way the evidence really leans, you ought to start by dismissing all these people entirely. Or think of it this way, with no math: You could predict their position from their ideological affiliation. But that ideological affiliation is obviously and entirely irrelevant to whether or not their position is true. Believe people like that and, as we professors of pure mathematics like to put it, you are a "chump."
Now let us consider Keith Olbermann's belief that Palin influenced Loughner and that the healthcare bill will decrease the deficit. Olbermann's CI with regard to Palin is .5. His CI with regard to healthcare is .5. Thus his CI with regard to Palin and healthcare is .25. Conjoin the belief that global warming will put New York underwater by 2025 or whatever it may be and you're at .125. At ten factual beliefs his CI is less that .0005. And Olbermann has dozens or hundreds of beliefs about factual matters which are the consensus of his group. His credibility is vanishingly small. Infinitesimal. And even if it were the case that the evidence is usually on Olbermann's side - which believe me I am not asserting, and which would be an almost inconceivable coincidence - suitable adjustments to the calculations will yield a somewhat higher but a still less than negligible CI. "Olbermann," of course, could be Sean Hannity or John Boehner, Eugene Robinson or Joe Biden, David Axelrod or Mitt Romney.
Of all the human subjects my team studied, the only group whose members on average had a Credibility Index comparable to cable television pundits or Supreme Court justices was actively delusional schizophrenics. Of course, people in any of these categories should be treated with the utmost compassion, kindness, and condescension. It's just that you should definitely not take the fact that they're saying it to have any bearing on whether or not it's true.
The person who inconsistently but continuously rejects the consensus of her own group is, all things being equal, almost infinitely likelier to be basing what she says on the evidence, whatever partisans say or believe about themselves, not because the position of the dissenters is so good but because the position of the partisans is so bad. Indeed if a political hack believes that his own beliefs are grounded in evidence or are reality-based, that belief is itself only infinitesimally likely to be true. Q.E.D.
Crispin Sartwell teaches philosophy at Dickinson College in Carlisle, PA. His most recent book is Political Aesthetics (Cornell,2010).