Thanks for this—the summary is very useful and means I read a paper I would otherwise not known of! I’ve got a question which might be really obvious/stupid, but I’m no moral philosopher so apologies if it is.
I don’t quite follow the example with the choices about A & B, and the probabilities p & q. I looked at the original paper and they formulated it differently (with the addition of C) so I was wondering if you could clear up this question:
I don’t fully understand how you’ve structured the table. What I think you mean from the text is:
Option A means there is a probability of p+q of saving n lives, and a (1-p-q) probability of saving 0 lives
Option B means there is a probability p of saving N+n lives, otherwise saving 0 lives
However, from the table, under choice A it looks like you have a probability p of saving n lives, and a probability q of saving n lives, so surely a probability of p+q means you save 2n lives?
Thanks for reading James! It’s a good question, let me get to it.
It’s probably easier to see what’s going on if we set some concrete numbers down. So let’s say n is ten, and the states of nature are decided by rolling a six-sided die. The state with probability p (= 2⁄6) is where the die rolls 1 or 2, and the state with probability q (= 1⁄6) is where the die rolls 3. The last state with probability 1 - p—q (= 1⁄2) is where the die rolls anything else, so 4-6.
The table’s then supposed to mean that on A, you save 10 lives if the die rolls 1 or 2, you also save 10 lives if the die rolls 3, and you save nobody if it rolls 4-6. Or, putting it another way, you save 10 lives if the die rolls between 1 and 3 (with probability 1⁄6 + 2⁄6 = 1⁄2) and save nobody otherwise.
I think something that maybe wasn’t clear is that the probabilities in the tables are supposed to be attached to mutually exclusive events. That is, if you rolled a 1, you can’t also have rolled a 3. So there’s no way of saving 10 + 10 lives, because if you save 10 lives in one way (by rolling a 1), that means you didn’t save 10 lives in another way (by rolling a 3).
Thanks for this—the summary is very useful and means I read a paper I would otherwise not known of! I’ve got a question which might be really obvious/stupid, but I’m no moral philosopher so apologies if it is.
I don’t quite follow the example with the choices about A & B, and the probabilities p & q. I looked at the original paper and they formulated it differently (with the addition of C) so I was wondering if you could clear up this question:
I don’t fully understand how you’ve structured the table. What I think you mean from the text is:
Option A means there is a probability of p+q of saving n lives, and a (1-p-q) probability of saving 0 lives
Option B means there is a probability p of saving N+n lives, otherwise saving 0 lives
However, from the table, under choice A it looks like you have a probability p of saving n lives, and a probability q of saving n lives, so surely a probability of p+q means you save 2n lives?
Thanks for reading James! It’s a good question, let me get to it.
It’s probably easier to see what’s going on if we set some concrete numbers down. So let’s say n is ten, and the states of nature are decided by rolling a six-sided die. The state with probability p (= 2⁄6) is where the die rolls 1 or 2, and the state with probability q (= 1⁄6) is where the die rolls 3. The last state with probability 1 - p—q (= 1⁄2) is where the die rolls anything else, so 4-6.
The table’s then supposed to mean that on A, you save 10 lives if the die rolls 1 or 2, you also save 10 lives if the die rolls 3, and you save nobody if it rolls 4-6. Or, putting it another way, you save 10 lives if the die rolls between 1 and 3 (with probability 1⁄6 + 2⁄6 = 1⁄2) and save nobody otherwise.
I think something that maybe wasn’t clear is that the probabilities in the tables are supposed to be attached to mutually exclusive events. That is, if you rolled a 1, you can’t also have rolled a 3. So there’s no way of saving 10 + 10 lives, because if you save 10 lives in one way (by rolling a 1), that means you didn’t save 10 lives in another way (by rolling a 3).