A Note on Expected Outcomes

(Potentially trivial for those well versed in philosophy or economics.)

I've noticed that in discussions of global warming, people sometimes claim that their choices make no difference, because whether they fly or not, that plane will still be in the air.

Similar arguments can be advanced on various other issues, such as the effects of buying less meat from the supermarket.

The argument is unsound. For whilst it is true that the chances of my action having an effect is low, the magnitude of the outcome is high. In fact, in such cases, the more unlikely my action is to have an effect, the greater the magnitude of the possible impact. (Only in these cases: Of other cases this will be false.)

So, imagine that this plane will still fly even without me on it. But perhaps the airline won't bother running this flight in future weeks if the passenger levels drop below a certain number this week. So my action might lead to numerous fewer flights, not just one fewer.

But perhaps this isn't how airlines run: perhaps once they have a plane, it's more cost efficient for them to fly it regardless. But then the effect of my action is this different one: To change how many planes they decide to buy next time they purchase planes, since the expected profit from each plane will be lower than it was before my decision to abstain, and there is some number below which there's no profit at all. Sure, the chances of my action having an effect on this are amazingly small, but just think: I could prevent truly enormous amounts of carbon emissions if I don't fly today.

[Update:
Or perhaps airlines are constrained by runway space more than by planes. So I won't affect how many planes they buy. But someone must make a decision on how many runways/airports to build, and there is some number of passengers lower than which they change their decision on these matters. My chances of affecting this are vanishingly small, but just think: I could stop a whole airport from running.]

Emissions are quoted in per-person terms for good reason, despite the low chances of my abstaining having an effect.