Risky Business
This question came up in a discussion recently:
Suppose there were a global pandemic with a 100% mortality rate. Two drug options were available, but there were only enough resources to produce one of the two. Both drugs yield a mean (arithmetic average) survival rate of 75%, but they achieve it differently.
One drug guarantees the survival of 75% of the people taking it at any given time (but also guarantees the death of 25% of the people taking it at any given time). To put it another way, if this situation were faced 100 times, then you'd have 75% survival/25% mortality each of those 100 times. Or differently still: 25% of the people will die each time.
The other drug is all or nothing: either everyone lives, or everyone dies — but the "everyone lives" result happens 75% of the time, and the "everyone dies" result happens 25% of the time. To put it another way, if this situation were faced 100 times, then you'd have 100% survival 75 times, and 100% mortality 25 times. Or to put it differently still: there is a 25% chance each time that 100% of the people may die — and, of course, a 75% chance that 100% of the people may survive.
In both cases, each individual has the same chance of survival: 75%. The difference between the two is in how the risk is distributed through the population. In the first case, there will always be survivors, but at the cost of some always dying. In the second, everyone is in the same boat — everyone makes it or no-one does.
So, what would you do? Take the risk that your life will be sacrificed so that the rest may live, or (if you live) accept that others were sacrificed for you? Or would you have everyone face a common fate? And, if you would choose the first (25% die so that 75% live), how much less risky would the all-or-nothing option have to be before you'd choose it over the first (assuming that the risk of the first stays at 75%/25%): 85% chance that all would make it? 95%? 99%?
I'm definitely in the all-or-nothing camp. I simply could not ask a random 25% of the population to die for the other 75%. I don't think I could ask even 10% to die for 90%. But I don't know about 1% for 99%.
Suppose there were a global pandemic with a 100% mortality rate. Two drug options were available, but there were only enough resources to produce one of the two. Both drugs yield a mean (arithmetic average) survival rate of 75%, but they achieve it differently.
One drug guarantees the survival of 75% of the people taking it at any given time (but also guarantees the death of 25% of the people taking it at any given time). To put it another way, if this situation were faced 100 times, then you'd have 75% survival/25% mortality each of those 100 times. Or differently still: 25% of the people will die each time.
The other drug is all or nothing: either everyone lives, or everyone dies — but the "everyone lives" result happens 75% of the time, and the "everyone dies" result happens 25% of the time. To put it another way, if this situation were faced 100 times, then you'd have 100% survival 75 times, and 100% mortality 25 times. Or to put it differently still: there is a 25% chance each time that 100% of the people may die — and, of course, a 75% chance that 100% of the people may survive.
In both cases, each individual has the same chance of survival: 75%. The difference between the two is in how the risk is distributed through the population. In the first case, there will always be survivors, but at the cost of some always dying. In the second, everyone is in the same boat — everyone makes it or no-one does.
So, what would you do? Take the risk that your life will be sacrificed so that the rest may live, or (if you live) accept that others were sacrificed for you? Or would you have everyone face a common fate? And, if you would choose the first (25% die so that 75% live), how much less risky would the all-or-nothing option have to be before you'd choose it over the first (assuming that the risk of the first stays at 75%/25%): 85% chance that all would make it? 95%? 99%?
I'm definitely in the all-or-nothing camp. I simply could not ask a random 25% of the population to die for the other 75%. I don't think I could ask even 10% to die for 90%. But I don't know about 1% for 99%.
posted by Dr. Bubbles at 09:57
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