Hack 69. Cure Conjunctionitus
| The probability of two independent events both happening can never be more likely than either of the events happening alone. Surprisingly, this common sense truth is not commonly sensed. Imagine that you are introduced to John, a tall, pleasant, athletic-looking man at a dinner party. You chat with John for a few minutes and discover that he is friendly and quick to laugh, but not exactly bright. John is eager to talk about the currently ongoing World Series and also asks you about the car you drive. On your way home from the dinner party, your spouse asks you about the man you were chatting with before dinner. You share a little bit about John, but realize that you never learned what he does for a living. In fact, as you realize, you really don't know that much about him. Your spouse decides to play a little mind game with you and explains: I know a little about John. I'm going to provide a series of statements about him. They might be true or not true. All might be true. All might be untrue. There might be a mix. I want you to place the statements in order based on how confident you are that each statement is true. When we are done, I'm going to diagnose whether you suffer from a common brain ailment known as Conjunctionitus. Your spouse then asks you to rank the following statements, guessing which are most likely true about John:
You, like many other people, might have ranked statement 3 (former baseball player) as one of the most likely possibilities and 1 (computer scientist) as one of the least likely. So far, not so crazy; at least they are reasonable guesses based on the conversation you had. The symptom related to Conjunctionitus has to do with the position you assigned statement 5 in your rankings. I'm betting you ranked it as more likely than 1. If so, you might suffer from Conjunctionitus, a condition that results in people making poor probability judgments. The truth is that the probability of two events occurring together can never be greater than the probability of either one occurring alone. Thus, it cannot be more likely that John is a computer scientist who used to play baseball than it is that John is a computer scientist. Never fear, though; the first step in improving your ability to make likelihood judgments in these situations is to admit you have a problem. The next step is to understand the condition, so that healing can begin. The ProblemAlthough more information might make a description seem more similar or representative of someone or something, more information does not make something more likely. As mentioned earlier, the probability of two events occurring together cannot be more likely than one of them occurring alone. Consider all of the possible things a man can be in the world. How do you decide which things John is most likely to be? You could start by looking at base rates. There are probably more married men in the world than there are computer scientists, car salesman, former baseball players, Republicans, preachers, marathon runners, and clarinet players. Thus, it is most likely that John is married. Where did you rank that possibility? Because we probably don't really know the base rates of all the other possibilities, we can use the information we have about John to predict which of the other possibilities is most likely. We do know that if we consider the group of all former baseball players and the group of all computer scientists, there will probably only be a small number of men who belong to both groups. Thus, the likelihood of being in that group of computer scientists who used to play baseball must be smaller than the likelihood of being in the group of computer scientists or of being in the group of former baseball players. Most people, however, even though they are rational, intelligent decision makers, will be drawn toward sentences that are conjunctions (i.e., that list two separate "facts"), as if the listing of the "facts" together makes them more likely to be true. Even if, and maybe especially if, the second "fact" by itself seems unlikely. Conjunction Junction, What's Your Function?Why do our minds tend to work this way? In the 1970s, Nobel Prize winner Daniel Kahneman and his colleague Amos Tversky presented college students with several problems in which one option was highly representative of a given personality description, one option was incongruent with the description, and one option included both the highly similar and the incongruent options. Perhaps the most well-known problem that demonstrates the conjunction fallacy is the now-famous (at least in cognitive psychology circles) Linda Problem: Linda is 31 years old, single, outspoken, and very bright. She majored in Philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and she also participated in antinuclear demonstrations. Subjects were asked to rank these statements based on high likely they were to be true:
Kahneman and Tversky (and many others who have since replicated their work) found that people consistently ranked option 8 (a bank teller active in the feminist movement) as being more likely than option 6 (a bank teller). This is because option 8 provides more information, which seems to be more representative of Linda. Because we expect her to be politically active, but we don't expect her to be a bank teller, it seems as though the only way she could be a bank teller is if she is also politically active. However, we know that 8 can never be more likely than options 3 or 6, because if we imagine all people active in the feminist movement, a subset of them (perhaps a small subset) will be bank tellers. Likewise, if we imagine all of the bank tellers in the world, a subset (again, perhaps a small one) will be active in the feminist movement. Thus, the likelihood of being a bank teller must be greater than the likelihood of being a bank teller who is active in the feminist movement. Makes sense, right? But your mind doesn't want to work that way.
The CureTo stop thinking wrongly about these sorts of propositions, the cure is simple:
The conjunction fallacy can be seen at work in numerous places. Be aware of situations in which it might occur and analyze the situation. For example, you can ask a baseball fan about a favorite player who doesn't often hit home runs. Ask whether the player is more likely in the next game to do which of the following:
The fan probably believes that a home run with a strikeout in the game is more likely than just a home run. But it cannot be so.
Once you are aware of this common error in probability estimation, you can see it everywhere. For example, one place in which you can readily find the conjunction fallacy is in the political prediction arena. Is George W. Bush more likely to:
Of course, you know the answer now, but many political analysts might argue with you. But that's because they have the sickness. They have Conjunctionitus. You did too, once, but now you are cured. See Also
Jill Lohmeier |
EAN: 2147483647
Pages: 114