Predictable polarization is everywhere: we can often predict how people’s opinions, including our own, will shift over time. Extant theories either neglect the fact that we can predict our own polarization, or explain it through irrational mechanisms. They needn’t. Empirical studies suggest that polarization is predictable when evidence is ambiguous, that is, when the rational response is not obvious. I show how Bayesians should model such ambiguity and then prove that—assuming rational updates are those which obey the value of evidence—ambiguity (...) is necessary and sufficient for the rationality of predictable polarization. The main theoretical result is that there can be a series of such updates, each of which is individually expected to make you more accurate, but which together will predictably polarize you. Polarization results from asymmetric increases in accuracy. This mechanism is not only theoretically possible, but empirically plausible. I argue that cognitive search—searching a cognitively accessible space for a particular item—often yields asymmetrically ambiguous evidence, I present an experiment supporting its polarizing effects, and I use simulations to show how it can explain two of the core causes of polarization: confirmation bias and the group polarization effect. (shrink)

The gambler’s fallacy is the tendency to expect random processes to switch more often than they actually do—for example, to think that after a string of tails, a heads is more likely. It’s often taken to be evidence for irrationality. It isn’t. Rather, it’s to be expected from a group of Bayesians who begin with causal uncertainty, and then observe unbiased data from an (in fact) statistically independent process. Although they converge toward the truth, they do so in an asymmetric (...) way—ruling out “streaky” hypotheses more quickly than “switchy” ones. As a result, the majority (and the average) exhibit the gambler’s fallacy. If they have limited memory, this tendency persists even with arbitrarily-large amounts of data. Indeed, such Bayesians exhibit a variety of the empirical trends found in studies of the gambler’s fallacy: they expect switches after short streaks but continuations after long ones; these nonlinear expectations vary with their familiarity with the causal system; their predictions depend on the sequence they’ve just seen; they produce sequences that are too switchy; and they exhibit greater rates of gambler’s reasoning when forming binary predictions than when forming probability estimates. In short: what’s been thought to be evidence for irrationality may instead be rational responses to limited data and memory. (shrink)