How to bet on climate change

If a trusted expert advised you to do something or else face grave consequences, I imagine you'd probably listen. If that advice was backed up by hard evidence then it should be a done deal. But in the case of global warming, some people just don't want to listen.

The anti-science movement growing through the US and the rest of the western world denies that rising carbon dioxide levels in the atmosphere are changing the climate. The recent Republican debates in the US have brought to the fore some rightwing politicians' opinions on the threat posed by global warming. In short, Republican candidates claim to have cottoned on to the "hoax" of global warming and powerful lobby groups are not just denying the science behind climate change but aggressively rubbishing and discrediting it.

This is a risky hand to play. I'll explain why by equating the pros and cons of this position to a famous "wager" posed by the 17th century mathematician Blaise Pascal.

Pascal's Wager is to do with whether to believe in God or not. It says that since we can't prove or disprove the existence of God we should wager that he does exist, because there's a lot to gain if it turns out he does and not much lost if he doesn't.

Perhaps we could frame the arguments about global warming as a similar wager. If we wager that global warming is a serious problem and we need to act urgently then, in a similar way to Pascal's Wager, there would be relatively little lost if it turns out not to be such a problem and plenty to gain if it is.

In a more formal statistical way, we can say that our null hypothesis is that there is no God or that there is no serious danger from global warming.

We can classify the situation as one of four alternatives. The first two are the situations where our conclusions about the null hypothesis are spot-on. So, that is the null hypothesis is actually true and we think that it is true or the null hypothesis is false and we think that it's false too. So, we call it correctly in either situation.

The other two situations are when we call it wrongly whatever the truth is. So, that is when the null hypothesis is true and we think it is false or the null hypothesis is false and we think that it is true. In our global warming example this would be when we stock up on suntan lotion and think that global warming exists but it doesn't, or global warming exists but we back the wrong team and there's no problem.

These are called false positives and false negatives, respectively. In terms of Pascal's Wager, the false positive (thinking there's a problem when there isn't) is not so bad, but the false negative (thinking there's no problem when there is) could be catastrophic.

But of course, although we can think about the global warming issues in terms of a Pascal-type wager there is an important distinction. In the case of the existence of God this is more than a little tricky to prove, but the science and evidence behind the questions on global warming appear to be rather more conclusive. Unfortunately, it seems it'll take God himself to pipe up about the dangers of global warming to convince some Republicans.