instruere...inlustrare...delectare Disputations

Wednesday, December 09, 2009

Bernoulli's Wager

In a comment below, Rodak proposes thinking of the problem of anthropogenic global warming as a "classic Pascal's Wager situation," with a 2-by-2 payoff matrix something like this::

AGW is realAGW isn't real
Take action against AGWBillions of lives savedcleaner environment; sustainable energy
Don't take action against AGWBillions die; civilization collapsesA lot of bother avoided

I see two fundamental problems with this proposal.

First, neither "whether AGW is real" nor "whether to take action against AGW" is a binary variable. AGW can be "real" in an infinite variety of ways, and action against it can also be as varied as you like. Even if we discretize the variables over regions of small variability, we will wind up with far more than four possible outcomes. The above 2-by-2 matrix is merely an extract from a much larger (arguably infinite) table of possibilities. [1]

And how they are extracted brings me to the other problem: The payoffs are unknown.

Climate and society are both chaotic systems -- in fact, since they affect each other, they're chaotic subsystems of a larger chaotic system with a vast number of variables. The best climate models in the world have not been validated, the uncertainty of economic models is empirically established and recognized in law... and these models all produce input for the even sketchier models of what we really care about, which is the common good (of which I won't attempt a definition here).

On top of which, whatever is done will affect the system, and whatever is left undone will leave resources free to affect the system in yet other ways.

In brief, we don't have much of a handle on the real costs of any particular plan to combat AGW, nor do we have a handle on the real benefits. ("Real" here meaning "net effect on the common good," rather than "units of emissions" or "tax dollars over the next five years.") This makes casting the problem as a cost-benefit game a far thornier matter than living a moral life in the hope of an eternal reward.

1. Note that this criticism is also often, and validly, levelled at the classic Pascal's Wager. The variables there -- "whether God exists" and "whether to live as though God exists" -- are only binary when there's only a single authority defining what "God exists" and "live as though God exists" entail. In a religiously pluralistic society, you have a number of different "possible Gods," so to speak, and an even greater variety in living. (And even within, say, confessional Christianity, what is required for salvation varies depending on whom you ask.)