Imagine you are given a pile of tokens, representing real money, and invited to donate to a common pot. There are other players but you can’t interact with them. The sum of collective contributions will be trebled, then shared equally among all players. What do you do?

If everyone submits all their money, all get richer. But if everyone except you pays in, you can enjoy the collective payout while retaining your original stash. The flaw in the selfish strategy is that other people might have the same idea. If no one pays in, there is no bounty to share.

This is the public goods game, an experiment that economists and psychologists use, with many rule variations, to test conditions under which people pool or hog resources.

It is a simple but useful tool for unravelling some of the mess in British politics. For example, it illuminates a link between two stories that do not, on the face of it, seem connected – the scandal of prisoners accidentally released from jail and a crisis in the BBC over alleged institutional bias. Both are case studies in the problem of coordinating public goods in a climate of mistrust.

The key is collective identity. A routine finding in the game is that participants’ willingness to share goes up when they feel part of a group. It doesn’t have to be a deep connection. Picking sides with a coin toss is sufficient to make team heads and team tails display heightened solidarity within their tribes.

The political implications are obvious. Taxpayers are happier to make higher contributions if they see the benefit to themselves or people like them. If they think the money goes to undeserving people – outsiders, cheats – they resent paying.

Convicted criminals are low on most people’s list of worthy beneficiaries. Politicians have little interest in making the case that more should be spent on jails. The public goods argument would be that a well-resourced criminal justice........

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