Naively (?), I’d say that if you invest your resources in an action with a 1 in a million chance of saving a billion lives, and a 999,999 in a million chance of having no effect, then (the overwhelming majority of the time) you haven’t done anything at all.
I think the idea you are getting at here is you’d rather have a 10% chance of saving 10 people than a 1/million chance of saving a billion lives. I can definitely see why you would feel this way (and there are prudential reasons for it—e.g. worrying about being tricked), but if you were sure this was actually the maths, I think you should definitely go for the 1/million shot of saving the billion.
To see why, imagine yourself in the shoes of one of the 1,000,000,010 people whose lives are at risk in this scenario. If you go for the ‘safe’ option, you have a 10%*1/1,000,000,010 ~= one in a billion chance of being saved. In contrast, if you go for the ‘riskier’ option, you actually have a one in a million chance—over a thousand times better!
Hi Larks. Thanks for raising this way of re-framing the point. I think I still disagree, but it’s helpful to see this way of looking at it which I really hadn’t thought of. I still disagree because I am assuming I only get one chance at doing the action and personally I don’t value a 1 in a million chance of being saved higher than zero. I think if I know I’m not going to be faced with the same choice many times, it is better to save 10 people, than to let everyone die and then go around telling people I chose the higher expected value!
I still disagree because I am assuming I only get one chance at doing the action and personally I don’t value a 1 in a million chance of being saved higher than zero.
Would you be interested in selling me a lottery ticket? We can use an online random number generator. I will win with a one-in-a-million chance, in which case you will give me all your worldly possessions, including all your future income, and you swear to do my wishes in all things. I will pay you $0.01 for this lottery ticket.
If you really believed that one-in-a-million was the same as zero, this should be an attractive deal for you. But my guess is that actually you would not want to take it!
So here is something which sometimes breaks people: You’re saying that you prefer A = 10% chance of saving 10 people over B = 1 in a million chance of saving a billion lives. Do you still prefer a 10% chance of A over a 10% chance of B?
Here is one answer to one part of your question.
I think the idea you are getting at here is you’d rather have a 10% chance of saving 10 people than a 1/million chance of saving a billion lives. I can definitely see why you would feel this way (and there are prudential reasons for it—e.g. worrying about being tricked), but if you were sure this was actually the maths, I think you should definitely go for the 1/million shot of saving the billion.
To see why, imagine yourself in the shoes of one of the 1,000,000,010 people whose lives are at risk in this scenario. If you go for the ‘safe’ option, you have a 10%*1/1,000,000,010 ~= one in a billion chance of being saved. In contrast, if you go for the ‘riskier’ option, you actually have a one in a million chance—over a thousand times better!
Hi Larks. Thanks for raising this way of re-framing the point. I think I still disagree, but it’s helpful to see this way of looking at it which I really hadn’t thought of. I still disagree because I am assuming I only get one chance at doing the action and personally I don’t value a 1 in a million chance of being saved higher than zero. I think if I know I’m not going to be faced with the same choice many times, it is better to save 10 people, than to let everyone die and then go around telling people I chose the higher expected value!
Would you be interested in selling me a lottery ticket? We can use an online random number generator. I will win with a one-in-a-million chance, in which case you will give me all your worldly possessions, including all your future income, and you swear to do my wishes in all things. I will pay you $0.01 for this lottery ticket.
If you really believed that one-in-a-million was the same as zero, this should be an attractive deal for you. But my guess is that actually you would not want to take it!
So here is something which sometimes breaks people: You’re saying that you prefer A = 10% chance of saving 10 people over B = 1 in a million chance of saving a billion lives. Do you still prefer a 10% chance of A over a 10% chance of B?
If you are, note how you can be Dutch-booked.