Basic Model of Belief Formation

I've been thinking a bit about how people form beliefs. I'll spell out my model here and then look at a few implications. For the time being I'm using "belief" to mean beliefs about factual matters, but I think values can be added in without changing the basic logic. Also please bear in mind that this post is just meant to lay out a basic model. In future posts I will or now I just want to frame my thoughts.

The idea is that people form beliefs in a kind of Bayesian process, incorporating new information as they absorb it. Ideally they modulate their level of confidence to match the amount of information available to them. I've included a numerical example below, but I think the intuition is pretty easy without bogging down in the numbers. When you come to a topic you are unfamiliar with, the initial facts that are presented to you will give you a general sense of what the issue is. But you should recognize that there are other facts out there that may change your view, and so at first your beliefs are highly provisional. As you become more confident that you've gathered enough relevant information, you shift toward a higher degree of confidence in your conclusions. This is clearly visible in the numerical example below.

Another key aspect of this is its path dependency. There are a lot of relevant facts that might bear on a particular issue, and at various points in the learning process you might be leaning pretty far in one direction or another. (In my numerical example below, you can see that after round 2, Player A sees a 33% chance that x is 3 and a 0% chance that x is 8, while Player B sees a 0% chance that x is 3 and a 50% chance that x is 8.) So although fully formed individuals should come to the same conclusion, they get there by different paths, and at any given moment partially-informed individuals may have very different outlooks.

Finally, note that the pieces of information could be categorized by the conclusions they tend to promote. This is not necessarily easy—for instance, the fact that x is greater than 6 boosts the probability that x = 8 for Player B but not for Player A, as a result of the information they had already learned—but in theory it's possible to select facts that tend to support a desired conclusion (whether or not it is true), and in practice it seems likely this is a feasible thing to do.

That's enough for now, I'll write another post later applying this model in a somewhat less theoretical way.



Here's the illustration. Let's say there are two "players" in a game where the point is to guess x, where x is an integer between 1 and 10 (inclusive). Each player learns a new piece of information each round. Note that I am making an implicit assumption about the way the information is generated, but I'm going to ignore that nuance. Here are Player A's thoughts:

Round 1
information: x is odd
conclusion:

20% chance x is 1
20% chance x is 3
20% chance x is 5
20% chance x is 7
20% chance x is 9

Round 2
information: x is a factor of 72
conclusion:

33.3% chance x is 1
33.3% chance x is 3
33.3% chance x is 9

Round 3
information: x is greater than 6
conclusion:

100% chance x is 9



Now here are Player B's thoughts:

Round 1
information: x is a factor of 72
conclusion:
14.3% chance x is 1
14.3% chance x is 2
14.3% chance x is 3
14.3% chance x is 4
14.3% chance x is 6
14.3% chance x is 8
14.3% chance x is 9

Round 2
information: x is greater than 6
conclusion:
50% chance x is 8
50% chance x is 9

Round 3
information: x is odd
conclusion:
100% chance x is 9