Occasional reflections on Life, the World, and Mathematics

There’s no knowledge like secret knowledge… Prominent in today’s news is Labour’s contention that

leaked Home Office documents suggesting government cuts are linked to the rise in violent crime, and demanded the home secretary explain herself to parliament.

It’s a bizarre accusation, not because it is implausible, but because it could not be otherwise, and the suggestion that this has been “revealed” by a secret report is part of implicitly accepting an inane pattern of government — and not just government — obfuscation that I am choosing to call the magical zero marginal. The way it works is, the government (let us say) feels an urge to reduce expenditures on (let us say) policing. It’s a problem, because the voters rather like police, by and large, and feel that they derive benefit. Not to worry, says the government press release (possibly produced by a dedicated key on the Whitehall keyboard), there will be no reduction in service. The costs will be made up with efficiency gains. The claim is that there is a significant portion of the current budget that is bringing zero marginal benefit, and whose elimination will therefore cause no harm. Perhaps this portion doesn’t exist as a budget line item now, but will after a “reorganisation” — but then the implicit claim is that the costs of the reorganisation as well will be covered by the savings.

The obvious question, which is almost never asked, is, why were you wasting all this money that was bringing zero net benefit? Why should efficiency gains be coupled to budget cuts one-to-one, rather than applying them earlier, when budgets are not being cut, to provide better service? It’s not as though a government service like policing has a natural level; you increase it to the point where the marginal value of additional expenditure either doesn’t justify the cost, or starts to create other negative effects (for example, on civil liberties). If “the same” policing benefit could have been had more cheaply, than almost certainly you should have had more policing.

Of course, the real answer is, the political leadership is appealing to loss aversion: People suffer far more from losing something (e.g., police protection) that they already have, than from not getting a benefit (e.g., additional crime reduction) that they don’t yet have.

But how, then, are we to explain today’s argument over police budget cuts? Call the budget reduction B, the efficiency saving and restructuring R, and the rise in violent crime V. Labour (and now the secret report) say that B+R caused V. But what could the Conservatives response be? V is caused by an unknown other cause X that happened around the same time as B+R. But if that is true, it still must be the case that B+R+X causes more additional crime than R+X alone, unless somehow, even after the reorganisation and restructuring and efficiency savings, the marginal value of a pound of extra police spending is still exactly zero. But if the marginal value of current spending is zero, then it must be the case that we are actually spending too much.

And the loss aversion argument doesn’t make sense here: The government is trying to argue that B+R together should have had no effect, but they failed to anticipate X. But the loss has actually occurred, and would not have occurred (or would have been less) if the government had not committed B, but only R. And the losses could be reversed by reversing R. It’s hard to imagine how an unanticipated new cause of crime would not increase the marginal value of additional police spending. And yet, the marginal value remains stubbornly zero — or, more realistically, but in terms that they would not publicly use, net value remains zero, so the marginal value of a pound of spending remains one pound.

If you leave your friend’s window open, and the rain spoils his antique carpet, he will not be satisfied to hear that you took precautions by moving the ladder that would have permitted a burglar to gain entry, and you really didn’t expect that it would rain. You could have moved the ladder and closed the window.

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