Caspian comments on Updating, part 1: When can you change your mind? The binary model - Less Wrong
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I don't build a model by looking at the observed results of a phenomena, and building in a special component to produce each observed result. You wouldn't learn anything from your models if you did that; they would produce what you built them to produce. I build a model by enumerating the inputs, modeling each input, and seeing how much of the observed results the output matches.
When I run the simulation, people do in fact align into different groups. So far, always 2 groups. But the alignment process doesn't give either group better overall accuracy. This shows that you don't need any internal coherence or problem understanding for people to align into groups. Attributing accuracy to people who tend to agree with you, and inaccuracy to those who disagree with you, produces saddle-point dynamics. Once the initial random distribution gets off the saddle point, the groups on the opposite sides each rapidly converge to their own attractor.
What's especially interesting is that this way of judging people's accuracy doesn't just cause different groups to converge to different points; it causes the groups to disagree with each other on every point. There isn't one "right" group and one "wrong" group; there are two groups that are right about different things. Their agreement within a group on some topics indirectly causes them to take the opposite opinion on any topic on which other groups have strong opinions. In other words: My enemy's belief P is evidence against P.
(Sleeping Beauty isn't the subject of this post.)
Does the 2-group split stay even if you continue the simulation until all answers have been revealed?
If you increase the standard deviation of p[i] so there are more very right and very wrong guessers, do they tend to split more into right and wrong groups? I expect they would.
Good question - no; revelation of answers eventually causes convergence into 1 group.
It makes the splitting happen faster.