Jeff at Cheap Talk reports on Andrew Caplin’s good point: making tests less informative can make people better off, because often they don’t want that much information, but may still want a bit.

This reminded me of a more basic question: what makes people want to avoid getting information?

That is, when would people prefer to believe P(X)=y% than to have a y% chance of believing X, and a (1-y)% chance of believing not X?

One such time is when thinking about the question at all would be disconcerting. For instance you may prefer whatever probability distribution you already have over the manners in which your parents may make love, than to consider the question.

Another time is when more uncertainty is useful in itself. A big category of this is when it lets you avoid responsibility. As in, ‘I would love to help, but I’m afraid I have no idea how to wash a cat’, or ‘How unfortunate that I had absolutely no idea that my chocolate comes from slaves, or I would have gone to lots of effort to find ethical chocolate’. If you can signal your ignorance, you might also avoid threats this way.

I’m more interested in situations like the one where you could call the doctor to get the results of your test for venereal disease, but you’d just rather not. Knowing would seem to mostly help you do things you would want to do in the case that you do have such a disease, and you are already thinking about the topic. It seems you actually prefer the uncertainty to the knowledge in themselves. The intuitive interpretation seems to be something like ‘you suspect that you do have such a disease, and knowing will make you unhappy, so you prefer not to find out’. But to the extent you suspect that you have the disease, why aren’t you already unhappy? So that doesn’t explain why you would rather definitely be somewhat unhappy than a chance of being unhappier with a chance of relief from your present unhappiness. And it doesn’t distinguish that sort of case from the more common cases where people like to have information.

A few cases where people often seek ignorance:

• academic test results which are expected to be bad
• medical test results
• especially genetic tendencies to disease
• whether a partner is cheating
• more?

Notice that these all involve emotionally charged situations – can you think of some that don’t?

Perhaps there aren’t really any cases where people much prefer belief in a y% chance of X over a y% chance of believing X, without external influences such as from other people expecting you to do something about your unethical chocolate habit.

Another theory based on external influences is this. Suppose you currently believe with 50% probability that you have disease X, and that does indeed fill you with 50% dread. However because it isn’t common knowledge, you are generally treated as if the chance were much lower. You are still officially well. If you actually discover that you have the disease, you are expected to tell people, and that will become much more than twice as unpleasant socially. Perhaps even beside the direct social effects, having others around you treat you as officially well makes you feel more confident in your good health.

This makes more sense in the case of a partner cheating. If you actually find out that they are cheating it is more likely to become public knowledge that you know, in which case you will be expected to react and to be humiliated or hurt. This is much worse than being treated as the official holder of a working relationship, regardless of your personal doubts.

This theory seems to predict less preference for ignorance in the academic test case, because until the test comes out students don’t have so much of an assumed status. But this theory predicts that a person who is generally expected to do well on tests will be more averse to finding out than a person who usually does less well, if they have the same expectation of how well they went. It also predicts that if you are already thought to be unwell, or failing school or in a failing marriage, you will usually be particularly keen to get more information. It can only improve your official status, even if your private appraisal is already hopeful in proportion to the information you expect to receive.

I have not much idea if this theory is right. What are other cases where people don’t want more information, all things equal? Does social perception play much part? What are other theories?