Let me tell you about a woman named Linda. Linda majored in sociology in college, and was also involved in a number of campus groups promoting social causes and political equality. Linda is a vegetarian and tries to ride her bicycle as much as possible. Now, given what you know about Linda, which of these statements is more likely to be true?
This particular puzzle is used to test people's ability to understand probability, and is often given as a way to show how people's common sense falls short of the logical process. It is a great piece of debunking of common wisdom.
That being said, it is somewhat dishonest, and quite possibly incorrect.
The logic behind the first answer being correct is that it presents less information, and therefore has more possibilities included in it. Even if, given what we know about Linda, it is 99% certain that she would wish to identify as a feminist, the first statement includes that possibility, as well as the 1% possibility that she goes against our stereotypes of crunchy granola girls, and is apathetic or antipathetic to feminism. Even if it requires a rather complex scenario to explain why this is so, it still is just one of many possible scenarios to describe what Linda is doing outside of her bank telling hours.
(Incidentally, the datedness of the question can be told both from the fact that at one time "feminist" was actually used as something other than a nexus for vague cultural conflict, and that banks used humans to give out money.)
To rephrase this as a mathematical question, which will show the logic more clearly,
- a is a number less than 1,000,000:
- a is less than 999,999:
- a is less than 500,000:
On a logical level, the answer that provides the least information is indeed correct. Perhaps this is a game of intellectual three card monte
, and perhaps it is an easy mistake for even a critically thinking person to make, but it is indeed more likely that Linda is a bank teller who may or may not identify as a feminist.
It is an important conclusion in some places and ways, for example if we consider Linda's slightly less chirpy brother Robert, who first went to juvenile hall at 16, and has been in and out of the Lincoln County jail ever since for a number of minor, stupid offenses involving fist fights, stolen cars and breaking windows. Is it more likely that Robert is
- A resident of Lincoln County
- A resident of Lincoln County who broke into a liquor store last Saturday night?
According to what we know about logic, and according to our legal systems presumption of innocence
, the answer is the first option.
And yet, there is a problem with the question that still makes me think the answer is not a matter of simple probabilities. Our mental faculties don't exist in a vacuum, and the use of the mind is to synthesize facts about the world. And specifically, figuring things out is a two-way street, and the narrator of the story is not excluded from the conclusions drawn. Which is what makes this not just a game of three card monte, but possibly a dishonest one.
Say that we were originally given a description of Linda's love of softball, needle point and her golden retriever, the question would be more obviously answered by the first answer. Or for that matter, if Linda wasn't mentioned at all, and instead we were presented with some data on the production of jute and pig iron in Brazil, followed by a query into Linda's occupation versus occupation and political views. In other words, the narration of the question is logically irrelevant to choosing an answer. And yet it is there. And since it is being there, we can reasonably (if not logically) assume that it is meant to convey information. The narrator is a partner with us, and if he is not acting in bad faith, we can assume that he is telling us this information for a reason, and that some information is supposed to be drawn from it. It can not strictly be logically inferred, but it can be reasonably inferred, that a Linda who has been drawn as a social activist would also be a feminist.
Once again, let me put this in a mathematical form:
- a is a number that is much less than 1,000,000
- a is a number less than 999,999
- a is a number less than 500,000
Which is more likely? On one hand, there is still a greater number of choices included in the "under 999,999" options, but the narrator went to the effort to put that word "much" in the first statement. The statement can now not be analyzed logically, especially given the vague meaning of the word "much". The narrator is hinting towards a conclusion, but has not given us all the information we need. It is now up to us to conjecture an answer based on all the information we are given.
So while the conclusion that Linda is more likely to be a bank teller than a bank teller and a feminist could be true if we pretend that human speech is mathematical, this is a pedantic and perhaps even wrong conclusion. Given that human discourse is (usually) likely to follow some rules of relevancy in the information presented, I think that a person who follows the hints that the narrator lays out is thinking totally reasonably.