What I call prior indifference is commonly referred to as representativeness, defined as a probability judgement based on the similarity between the evidence and the object under investigation. For instance, Linda is judged to be more likely a Greenpeace supporter than a bank employee because her description is more representative of the former than of the latter. In simpler words, Linda looks more like a typical Greenpeace supporter than a typical bank employee. Such evidence obfuscates the prevalence of bank employees over Greenpeace supporters in the general population which, in the absence of a description, would naturally imply the opposite probability ranking.
I prefer the term prior indifference because it gets to the crux of the matter: the Inverse Fallacy. People confuse the probability of the hypothesis, given the evidence, with the probability of the evidence, given the hypothesis, because they assume the hypothesis to be equally likely true or false.
Prior indifference also explains probability judgements in response to neutral, unconfirmative evidence. For instance, faced with a totally unrepresentative description of Linda (e.g. “Linda is blonde and likes chocolate”), the right conclusion, according to Bayes’ Theorem, would be to stick to the Base Rate. In odds form, LR=1 implies PO=BO: neutral evidence is the same as no evidence. But this is not what happens empirically. Given an irrelevant description, people tend to assign the same probability to Linda being a bank employee or a Greenpeace supporter, just as they assign 50% support to the predictions of a useless coin-tossing expert. They are prey to the Prior Indifference Fallacy.
Prior indifference uncovers underlying connections among different cognitive heuristics. We have seen Representativeness. Another well-documented heuristics is Anchoring.
One of the experiments discussed in Thinking, Fast and Slow to illustrate anchoring (Chapter 11) involved two groups of visitors at the San Francisco Exploratorium. Members of the first group were asked:
Is the height of the tallest redwood more or less than 1,200 feet?
while members of the second group were asked:
Is the height of the tallest redwood more or less than 180 feet?
Subsequently, members of both groups were asked the same question:
What is your best guess about the height of the tallest redwood?
As it turned out, the mean estimate was 844 feet for the first group and 282 feet for the second group. People were anchored to the value specified in the first, priming question. The anchoring index was (844-282)/(1200-180)=55%, roughly in the middle between no anchoring and full anchoring. This index level is typical of other similar experiments.
Why is judgement influenced by irrelevant information? It is for the same reason – it seems to me – why, in Linda’s experiment, an unconfirmative description is not equivalent to no description. Evidence can blind us not only when it is relevant and purposefully sought, but also when it is irrelevant and incidentally assimilated. Among visitors, there will be people who have quite a good sense of the height of the tallest redwood (it is called Hyperion and it is 379 feet high), some people who have only a vague sense and some who have no idea. The less one knows about redwoods, the closer he is to the state of perfect ignorance that characterizes prior indifference. Under perfect ignorance, the number in the priming question acts as a neutral reference point, around which the probability that the tallest redwood is higher/shorter is deemed to be 50/50. Asked to give a number, people with little or no knowledge of redwoods will choose one around the reference point, thus skewing the group average towards it.
In the redwoods experiment the priming question may be thought to contain a modicum of information – uninformed people may take the number as an indication of the average height of redwoods. But anchoring works even when priming information is unequivocally insignificant. Kahneman describes an experiment where a wheel of fortune with numbers from 0 to 100 was rigged to stop only at 10 or 65. Participants were asked to spin the wheel and annotate their number, and then were asked:
What is your best guess of the percentage of African nations in the UN?
The average answer of those who saw 10 was 25%, while the average of those who saw 65 was 45%. Prior indifference is seen here in its clearest and most disturbing capacity.
We crave for and absorb information without necessarily being aware of it. Bayesian updates on unconfirmative evidence should be inconsequential: LR=1. But inconsequential evidence may influence our thoughts, estimates, choices and decisions much more than we would like to think. To protect against such danger, we should not only try to focus on relevant evidence, but also actively shield ourselves against irrelevant evidence – an increasingly arduous task in our age of information superabundance.
Pick a number between 0 and 1000.
What is the boiling point of beryllium?
Don’t be silly. Google it up. It is 2970 C°.
