I came close to committing it. When I guessed the order I ignored the description almost completely. I first estimated how many school teachers there were compared to bank tellers. I thought there were mor school teachers. And how many psychiatric social workers? More bank tellers. Lots of insurance salesmen, more than bank tellers. And so on. I pretty much ignored Linda’s description and just looked at my guesses about the numbers of people. Lisa could have fallen into any of those categories entirely apart from those little scraps of information about her.
I did it wrong—I didn’t consider that more women than men tend to be schoolteachers, feminists, and members of the League of Women Voters and bank tellers, but not insurance salesmen. But my guesses about how many there were of each type were probably way off anyway.
I remembered from a college summer job—when people know a few random facts about somebody else they tend to put too much emphasis on those facts. Like, if you are asked to guess whether somebody is going to be a suicide bomber and what’s important is being right, then the answer is almost always no. Hardly any arabs are suicide bombers. Hardly any Wahabi arabs are suicide bombers. Hardly any young male wahabi arabs whose girlfriends have jilted them are suicide bombers. The way to bet is almost always no.
But by completely ignoring the information about Linda instead of ignoring the (guessed at) statistics about numbers of each category, haven’t I made the opposite mistake? There ought to be some best amount of weight to give that information. I assumed none of it was worth anything, and actually I even ignored that Linda was a woman though I obviously shouldn’t have. To do it right, wouldn’t you know the actual relative numbers of each category (instead of guessing) and also know how much weight to put on the individual information about Linda?
If you knew everything you could answer the question without bias.
The key mistake was not the probability numbers (though that certainly could be a mistake in real life), it was ranking bank-teller/feminist higher than bank-teller.
I think the point to bear in mind on this is that any time you add two criteria together the probabilities plummet.
When you did it yourself, you should have evaluated the bank teller and feminist part of the BT/F question separately (however you chose to evaluate it), and then examined the likelihood that both would be true. That way you should clearly see that the combination could not possibly have higher probabilities than either individual criteria.
It’s certainly a hard thing to do, I’m going to have to look out for this one because I’d wager I do it a ton.
What would be the opposite mistake?
I came close to committing it. When I guessed the order I ignored the description almost completely. I first estimated how many school teachers there were compared to bank tellers. I thought there were mor school teachers. And how many psychiatric social workers? More bank tellers. Lots of insurance salesmen, more than bank tellers. And so on. I pretty much ignored Linda’s description and just looked at my guesses about the numbers of people. Lisa could have fallen into any of those categories entirely apart from those little scraps of information about her.
I did it wrong—I didn’t consider that more women than men tend to be schoolteachers, feminists, and members of the League of Women Voters and bank tellers, but not insurance salesmen. But my guesses about how many there were of each type were probably way off anyway.
I remembered from a college summer job—when people know a few random facts about somebody else they tend to put too much emphasis on those facts. Like, if you are asked to guess whether somebody is going to be a suicide bomber and what’s important is being right, then the answer is almost always no. Hardly any arabs are suicide bombers. Hardly any Wahabi arabs are suicide bombers. Hardly any young male wahabi arabs whose girlfriends have jilted them are suicide bombers. The way to bet is almost always no.
But by completely ignoring the information about Linda instead of ignoring the (guessed at) statistics about numbers of each category, haven’t I made the opposite mistake? There ought to be some best amount of weight to give that information. I assumed none of it was worth anything, and actually I even ignored that Linda was a woman though I obviously shouldn’t have. To do it right, wouldn’t you know the actual relative numbers of each category (instead of guessing) and also know how much weight to put on the individual information about Linda?
If you knew everything you could answer the question without bias.
Being confused by the Gettier problem.
The key mistake was not the probability numbers (though that certainly could be a mistake in real life), it was ranking bank-teller/feminist higher than bank-teller.
I think the point to bear in mind on this is that any time you add two criteria together the probabilities plummet.
When you did it yourself, you should have evaluated the bank teller and feminist part of the BT/F question separately (however you chose to evaluate it), and then examined the likelihood that both would be true. That way you should clearly see that the combination could not possibly have higher probabilities than either individual criteria.
It’s certainly a hard thing to do, I’m going to have to look out for this one because I’d wager I do it a ton.