Understanding Probability: Pascal’s Wager and Catastrophic Global Warming

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I love it when someone issues a well-constructed argument that supports my position on an issue. (It happens often, of course.) The latest case in point is a post by Robert Tracinski, “Pascal’s Wager for the Global Warming Religion” (The Federalist, May 3, 2016). Tracinski address this claim by some global-warming zealots:

Across the span of their lives, the average American is more than five times likelier to die during a human-extinction event than in a car crash.

There’s a lot more wrong with that statement than the egregious use of plural (“their lives”) and singular (“is”) constructions with respect to “the average American” (singular). Here’s what’s really wrong, in Tracinski’s words:

There is something that sounded familiar to me about this argument, and I realized that it borrows the basic form of Pascal’s Wager, an old and spectacularly unconvincing argument for belief in God. (Go here if you want to give the idea more thought than it probably deserves.) Blaise Pascal’s argument was that even if the existence of God is only a very small probability, the consequences are so spectacularly huge — eternal life if you follow the rules, eternal punishment if you don’t — that it makes even a very small probability seem overwhelmingly important. In effect, Pascal realized that you can make anything look big if you multiply it by infinity. Similarly, this new environmentalist argument assumes that you can make anything look big if you multiply it by extinction….

If Pascal’s probabilistic argument works for Christianity, then it also works for Islam, or for secular versions like Roko’s Basilisk. (And yes, an “all-seeing artificial intelligence” is included in this report as a catastrophic possibility, which gives you an idea of how seriously you should take it.) Or it works for global warming, which is exactly how it’s being used here.

Pascal was a great mathematician, but this was an awful abuse of the nascent science of probabilities. (I suspect it’s no great shakes from a religious perspective, either.) First of all, a “probability” is not just anything that you sort of think might happen. Imagination and speculation are not probability. In any mathematical or scientific sense of the word, a probability is something for which you have a real basis to measure its likelihood. Saying you are “95 percent certain” about a scientific theory, as global warming alarmists are apt to do, might make for an eye-catching turn of phrase in press headlines. But it is not an actual number that measures something.

Indeed.

Tracinski later hits a verbal home run with this:

This kind of Pascal’s-Wager-for-global-warming is part of a larger environmentalist program: a perverse attempt to take our sense of the actual risks and benefits for human life and turn it upside down.

If we’re concerned about the actual dangers to human life, we don’t have to assume a bunch of bizarre probabilities. The big dangers are known quantities: poverty, squalor, disease, famine, dictatorship, war. And the solutions are also known quantities: technology, industrialization, economic growth, freedom.

Repeat after me:

A probability is a statement about a very large number of like events, each of which has an unpredictable (random) outcome. Probability, properly understood, says nothing about the outcome of an individual event. It certainly says nothing about what will happen next.

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Related posts:

Pascal’s Wager, Morality, and the State

Some Thoughts about Probability

My War on the Misuse of Probability

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My War on the Misuse of Probability

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In the preceding post I say that “the problem with history is that the future isn’t part of it.” That is subtle criticism of the too-frequent practice of attributing a probability to the occurrence of a future event — especially a unique event, such as a war here or a terrorist attack there.

A probability is a statement about a very large number of like events, each of which has an unpredictable (random) outcome. Probability, properly understood, says nothing about the outcome of an individual event. It certainly says nothing about what will happen next.

A fair coin comes up heads with a probability of 0.5, and comes up tails with the same probability. But those aren’t statements about the outcome of the next coin toss. No, they’re statements about the approximate frequencies of the occurrence of heads and tails in a large number of tosses. The next coin toss will eventuate in heads or tails, but not 0.5 heads and 0.5 tails (except in the rare and unpredictable case of a coin landing on edge and staying there).

There’s a vast gap between routine processes of the kind to which probabilities attach — coin tosses, for example — and the complexities of human activity. Human activity is too complex and dependent on intentions and willful actions to be characterized (properly) by statements about the probability of this or that action.

It is fatuous to say, for example, that a war on the scale of World War II is improbable because such a war has occurred only once in human history. By that reasoning, one could have said confidently in 1938 that a war on the scale of World War II could never occur because there had been no such war in human history.

(Inspired by Bryan Caplan’s fatuous post, “So Far.”)