There's a link between the question of whether John Terry should be England captain and what to do about Iran's possible development of nuclear weapons. Both raise the question: upon what level of probability should we act?

This level varies according to circumstance. At one extreme we have the criminal law, which requires that a defendant be proved guilty beyond reasonable doubt. This means we only act upon very high levels of probability - though how high is not (pdf) clear.

But in other cases, we apply the precautionary principle - a small probability of danger is sufficient to act to prevent harm. And in financial markets, a 1-2% probability suffices to trigger action - for example when the 'tail risk' of a default or financial crisis causes investors to dump a financial asset.

The fact that, depending on context, we use very different probabilities tells us that our choice of 'probability trigger' rests not upon epistemological grounds but rather upon cost-benefit ones.

For example, because we consider the cost of imprisoning an innocent man very high, we set the probability trigger high in criminal cases. Similarly, the cost of default might be so high that it is worth acting to avoid the small probability thereof, so we set the probability trigger low.

And the same might apply to Iran and nuclear weapons. Even if there is only a small probability of Iran getting a nuclear weapon, the cost of this might be so high as to justify military action now to prevent it.

All of this might seem trivial. It's just expected utility theory.

However, there are some non-trivial effects here.

One problem is that there's a trade-off here between efficiency and justice. In criminal justice cases, requiring proof beyond reasonable doubt allows some guilty people to go free. This is justified by Blackstone's formulation: 'better that ten guilty persons escape than that one innocent suffer'. The converse can also apply. Expected utility might justify a pre-emptive strike on Iran's nuclear facilities, even if this entails the injustice of killing some innocent people.

And here, two other complications enter.

One is that we often misapply probability triggers. It has become a clich'' to say that Terry is innocent until proven guilty. But this is wrong. There is no reason to apply the standard of criminal proof in this context. Stripping a man of the England captaincy is very different from depriving him of his liberty. We don't need proof that Terry is a racist to remove him from the captaincy. The mere possibility that a man is racist is - when combined with his other character flaws - sufficient to deny him the largely honorific position of England captain. Alan Green - a man I usually have no time for - sees this better than others.

A similar error sometimes happens in discussion of climate change policy. We don't need proof that man-made global warming is happening to justify reducing carbon emissions. All we need is for the cost of reducing emissions to be smaller than the probability-weighted cost of a climate disaster.

Secondly, our thinking about these issues is clouded by countless cognitive biases. One particular one here might be the zero-risk bias - our preference for reducing risk to zero. This might lead us to want 'proof' - such as in the Terry case - even where none is needed. It might also bias us towards acting against Iran - because we might want to over-pay for reducing to zero the risk of them obtaining a nuclear weapon.

All I'm saying here is that apparently minor cases such as John Terry and major ones such as Iran's weapons programme raise awkward issues of both probability and ethics - issues which we are not necessarily well-equipped to deal with.