Information flows both ways (Martian conspiracy theory edition)

March 7, 2018

(This article was originally published at Statistical Modeling, Causal Inference, and Social Science, and syndicated at StatsBlogs.)

A topic that arises from time to time in Bayesian statistics is the desire of analysts to propagate information in one direction, with no backwash, as it were. But the logic of Bayesian inference doesn’t work that way. If A and B are two uncertain statements, and A tells you something about B, then learning more about B also tells you something about A (except in some special cases of conditional independence). Here’s an example from applied statistics in drug development.

The same principle applies in other areas of life. For example, a couple years ago I discussed how journal reputation is a two-way street: prestigious outlets such as the Lancet or PNAS lend their reputations to the articles they publish—but when it turns out they’re publishing low-quality work, the negative reputation rebounds on the journal. It has to be that way.

And Mark Palko has discussed a related phenomenon in politics, in which groups that use disinformation to their political advantage can get overwhelmed by it. Here’s Palko:

If you want to have a functional institution that makes extensive use of internal misinformation, you have to make sure things move in the right direction.

With misinformation systems as with plumbing, when the flow starts going the wrong way, the results are seldom pretty.

As Palko put it more recently, “contradictory beliefs often mask similar, or at least compatible, personalities. It is remarkably difficult to reconcile flat earth and alien invasion theories, but adherents of both can frequently find common ground in their sense of isolation and, more to the point, persecution by society in general and the scientific and academic establishment in particular.”

I’ve felt the same way about various goofy social priming theories that we’ve discussed over the years. For example, it’s remarkably difficult to reconcile the theories that votes and political attitudes are determined by shark attacks and college football games and ovulation and subliminal smiley faces and chance encounters with strangers on the street. It’s the piranha problem. But all these theories, inconsistent with each other as they are, all feel the same in that they’re all based on an attitude that voters are capricious and easily manipulated.

The thing that the researchers who favor these theories don’t realize is that if you can be consistently manipulated 100 different ways, then you can’t be consistently manipulated at all—because in any given setting, the manipulator have no control over the 99 other possible manipulations. Al these theories kind of feel like they’re allies of each other, but hey’re actually competing. In that way it’s similar to the idea that the flat earth and alien invasion theories feel like allies—and I wouldn’t be surprised if supporters of one of these theories have warm feelings about the other one—even thought either of these theories would pretty much rule out the other.

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