Pragmatics and Statistics

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One of my Listservs led me to this interesting article by John Allen Paulos about the distinction between the "literary and scientific cultures". As part of the discussion, Paulos discusses some cases where knowing a narrative background affects how probability is assessed.

Consider the following two statements.

  1. Sarah is a bank teller.
  2. Sarah is a bank teller and has a philosophy degree.

The answer is that the first option is more probable because only one condition needs to be met. In order for the second to be true, two conditions are required - being a bank teller and having a degree in philosophy degree.

Now consider this version from Paulos in which the teller is given a brief bio:

Linda is single, in her early 30s, outspoken, and exceedingly smart. A philosophy major in college, she has devoted herself to issues such as nuclear non-proliferation. So which of the following is more likely?:

  1. Linda is a bank teller.
  2. Linda is a bank teller and is active in the feminist movement.

The finding is that more people will be that the second option is the most likely - i.e. that Linda is a bank teller and in the feminist movement, even though it requires the fulfillment of two conditions.

There are several philosophical tacks one can take to the problem, but I think one factor is that the story along with the presentation of the information affects the construction of the model used to evaluate the statements.

Someone reading first scenario without the narrative probably constructs the intended model where the probability of being a bank teller versus a bank teller with a philosophy degree is evaluated across all adult women. It's easy to see that fulfilling condition A is more probably than fulfilling condition A and B.

The second scenario with Linda though probably causes most people to build a model not across all adult women but across all adult women who have a philosophy degree and who were activists in their youth. It's NOT the same pool of candidates, and there is a legitimate reason to think probability judgments COULD be different. Interestingly, if you presented the two Linda options as

  1. Linda is a bank teller.
  2. Linda is active in the feminist movement.

then the conclusion would likely be that Linda being active in the feminist movement is more likely than her being a bank teller. In other words, readers could be using the narrative to build a stereotyped persona where someone who was politically active in college remains active. In the same vein, most people likely assume that someone with a philosophy degree becomes a teller only as a last resort and that most tellers have a degree in accounting or other related field. This is one possible source of the fallacy.

I would also argue that the presentation of the options causes the pragmatic engine to introduce another logical trap. Because both options allow that Linda is a bank teller, This could mean that readers assume the Linda ends up as a bank teller (even though that's not what the option says). Thus, readers could be interpreting the Linda options as:

  1. Linda is a bank teller who is not active in the feminist movement.
  2. Linda is a bank teller who is active in the feminist movement.

There is a further pragmatic interpretation that option a) "Linda is a bank teller" means that she is not politically active at all. That's not literally the case (for instance, option a) does allow that Linda could still be active in the anti nuclear proliferation movement, but not the feminist movement). In pragmatic land though, omitting information is interpreted as meaning it doesn't exist. That's why people often consider not saying something to be "lying."

So to summarize, I think the skewed probability judgments aren't just a result of people being sucked into a mini soap opera, but to two factors the narrative introduces - 1) narrowing the set of women to those with philosophy degrees, which leads to different stereotypes and 2) the options leading to misconstrued pragmatics which differ from what the literal meaning is.

The ability to reasonably construct a pragmatic meaning behind a literal statement is critical for social relations and reducing conversational length. But it can lead to some glitches like the narrative above.