Wednesday, January 14, 2009


Consider the following ordinary form of argument. Risk R1 is less than risk R0. Risk R0 is a reasonable risk to take. Therefore, risk R1 is as well. Typically, R0 is a risk that reasonable people routinely take, without worrying about it. Thus, we might be told that flying is safer than driving, and since (this premise is usually implicit) it is reasonable to risk driving, it is reasonable to risk flying.

This is a bad form of argument as it stands, for two reasons. The first is that it needs to be established that the benefits associated with taking risk R1 are no less than those of risk R0. The second is that even if the benefit claim is true, this only shows that it would be rational to take R1 instead of of R0. It does not show that it would be rational to take R1 in addition to R0. (Thus, it would be reasonable to fly regularly instead of driving regularly. But given that one is driving regularly, it does not follow from the risk-comparison alone that it is reasonable also to fly.)

Here's an example to show the second failure. The fatality rate for Mount Everest climbs is apparently about 9%. Let us suppose that Kenya is a single woman, with no family, and who does not do any job for which she is essential (e.g., she is not an irreplaceable top cancer researcher). It might (I actually doubt it) be reasonable for Kenya to climb Mount Everest, for the sake of the various goods instantiated by the climb, despite the 9% risk of death. But if the above argument-form were sound, it would be likewise reasonable for her to additionally engage in another activity that carries an 8.9% risk of death and has similar benefits. But the argument could then be iterated. If there was some third activity that carried an 8.8% risk of death, it would be reasonable to additionally do that. Therefore, by repeated application of the argument form, we would conclude that if it is reasonable for Kenya to climb Mount Everest, it would be reasonable for her to do climb Mount Everest and do A, B, C, D, E, F, G, H and I, each of which has a slightly lower risk of death than the previous. Let's say the risks are 9.0, 8.9, 8.8 and so on. Assuming independence (not quite right), her chance of surving all ten activities is less than 47%. But it seems that it is only reasonable to engage in a series of actions that one is less likely to survive than not for the gravest of reasons (such as saving someone's life). The sorts of reasons involved in the climb of Mount Everest are not like that, and even having the benefits ten times over is not worth it.

A related, but I think not identical, issue is that benefits need not be additive. The benefit of both A and B need not be the sum of the benefits of A and of B in isolation. It might be more, or it might be less.


Heath White said...

I am not in a position to do the math right now, but suppose that activities A-I are sequential. (Kenya climbs Everest, then climbs McKinley, then climbs Kilimanjaro, etc.) The risk of doing all the climbs, say, is different before and after completion of the first climb. Before the first climb, your risk of surviving is less than 47%. But after the first climb, your risk of surviving all ten is somewhat higher. And the more you survive, the higher your chances of surviving all the climbs get.

To my mind this is paradoxical. Let's say (just for simplicity; it isn't true!) it is rational to take risks where your chances of death are less than 50% and irrational otherwise. Then it is rational to climb Everest, rational to climb McKinley, rational to climb Kilimanjaro, etc., but irrational to embark on the sequence as a whole. Peculiar.

Alexander R Pruss said...

Or even more paradoxically, if it's rational to play Russian roulette once if the payoff is ten million dollars (I don't think it is rational, but the case could be made), then it's rational to play it ten times. But if you do that, you'll be dead, almost for sure.

I think we do need to think in terms of policies when making prudential decisions, in part for reasons like this one. Perhaps a part of a prudent life is ensuring that one does not take too many risks--having a policy of not taking more than a certain total amount of risk. E.g., one might set oneself a limit of five engagements in a hazardous recreational activity in any given year. And then one will have to say: "I've done hang-gliding three times and I've done cliff-diving twice this year. So I'll have to wait until next year until I climb McKinley." This is paradoxical, because of course the risk of climbing McKinley is not bigger for one's having done hang-gliding and cliff-diving. (On the contrary, these activities increase one's physical fitness, and hence making climbing McKinley less hazardous.) But unless one has some risk-limiting policies, one will be like the person who played Russian roulette ten times (i.e., dead).

Maybe there is a Kantian lesson from all this, that prudence, and not just morality, requires a generalizability of maxims within a life. Thus, the maxim: "Climb a mountain if you're alive, because you'll likely survive" is a prudentially bad maxim, because if we generalize it--i.e., act on it whenever it is applicable--we will be climbing mountains all the time, and pretty soon we'll be dead (supposing, contrary to fact, independence between tries), which is contrary to prudence. But the maxim "Climb exactly three high mountains in your lifetime, and avoid other high-risk activities" is much better. After having climbed the three mountains, if someone suggests hang-gliding, you say: "Sorry, I've done my lifetime's worth of high-risk activities." (Of course, in practice, the sort of person who would claim three high mountains is unlikely to think in this way!)

This is all somewhat related to the stuff Parfit discusses in Reasons and Persons in connection with small probabilities.

Tim Lacy said...

You mention the goods obtained from climbing Mount Everest. But if the other activities (B-I) are also climbs, then there are diminishing returns and less and less incentive for Kenya to take part in those activities. You must posit different goods for the subsequent activities to cause Kenya to embark on your fictional series of risky behaviors. - Tim

Alexander R Pruss said...

True. And even if the other things are not climbs, but are valuable for the same kind of reason for which a climb is (excitement, effort, teamwork, etc.), there will probably be some diminishment in value.