Diagnostic Expectations vs Anchoring

For 4 decades I have been trying to deal with, what seems to me to be a contradiction between empirical results. Kahneman and Twersky note two things. One is diagnostic expectations – people over react to useful signals of membership in a group – diagnostic symptoms.  One example is that red hair is diagnostic of being Irish – a larger fraction of Irish people have read hair. In fact the vast majority of red heads are not Irish because the vast vast majority of people are not Irish. People also overestimate the probability that someone is Irish conditional on the person having red hair. So they over-react to the diagnostic information that someone has red hair. Another way of putting it is they under-react to the fact that 99.95% of people are not citizens of the Irish Republic and 99.5% are not ethnically Irish.

One way of interpreting this is that numbers bore and irritate people while stereotypes are interesting and salient.  Words beat number. When asked the question it is natural (irresistible) to imagine a red headed Irish person and a picture is worth a thousand words.  Another way is that people tend to put to little weight on unconditional probabilities, in this case the baseline frequency.

Behavioral economists interpret it as over-reaction to new information and use “diagnostic expectations” to refer to any over-reaction to new information and then to any excessive adjustment of expectations over time.  I quibble with the semantics, but also actually disagree.  I think they key issue is not that people are told “red haired” after they are told “a person” but that images and stereotypes beat numbers in our brains.

The  point is that there is an apparently contradictory empirical observation called “anchoring” if people are asked to state a probability and then given new information and ask to state the probability conditional on the new information we adjust *less* than we should. In fact, pretty robustly half as much as we should. This totally contradicts the behavioral economists interpretation of “diagnostic expectations.” Do we adjust too little or too much ? 

One serious concern is that the empirical results obtained by psychologists are so complicated that they do not impose intellectual discipline. A simple selective glance at the literature includes apparently opposite results and, if one is allowed to select the one which fits an anomoly in economic data, one can fit anything without really explaining it.

More interestingly the apparent contradiction must have an explanation. This is really psychology not pscyhology applied to economicsm. I think the key is that the experiments which show over-reaction to new information, show over reaction to stereotypes compared to numbers – to words and evoked images compared to numbers. To reasoning not based on arithmetic which requires concentration and bores and irritates us.

This means that the patterns in economic behavior, which involved numbers and other numbers, need an explanation. I will try some guesses in a later post.