Should the penalty for murder vary with the life lost?

Farrar today argues for stiffer punishment for folks who shoot at or kill police officers.

I'm not opposed to the idea, in principle, that we might want penalties to vary somewhat with the type of murder victim. But I think David here has the sign wrong.

Recall again that we have optimal deterrence when the cost of deterring one more offense is equal to the net damage of the deterred offence. And, with a bit of algebraic manipulation, the expected penalty ought to be equal to the damage to the victim less the cost of deterring one more offence. (see the link above or Friedman for the derivation)

What's the expected penalty for an offence? The probability of being caught multiplied by the fine if caught. What's the likelihood of being caught if you murder someone in New Zealand? High. What's the likelihood of being caught if you murder a cop in New Zealand? I don't have the stats, but I'd be surprised if it weren't pretty close to certainty. The police do a reasonable job in investigating murders, and folks shooting another cop seem pretty likely to get priority treatment. So, the expected punishment for shooting a cop is already higher than the expected punishment for shooting anyone else, just because the probability of being caught and going to jail is rather higher. The damage to the victim isn't much different between police officers and other folks; perhaps since police officers have voluntarily taken on risky jobs, we could argue that the damage is somewhat less as they've revealed a preference for taking on risk relative to the median citizen (again, this is a revealed preference argument, not any assertion on my part about relative worth).

So it then has to be the case then that the cost of deterring one more police shooting is much much cheaper than the cost of deterring some other shooting for it to be optimal for the expected punishment for killing a police officer to be higher than the expected punishment for killing someone else. And I'm not convinced that that's the case. And the expected punishment for killing a police officer is already higher than that for killing a civilian because the probability of being caught is higher.

Higher penalties for shooting police officers consequently isn't likely to be efficient. You might salvage it by claiming that the damage to the victim is really higher than I'm thinking: that somehow the "victim" isn't just the officer but all of society. But my default has to be equal treatment absent some good empirical evidence that most folks care more - and really care more rather than just saying they do - about a police officer being shot than about a civilian being shot. And we'd have to weigh that against the revealed preference argument that the officer willingly chose a riskier occupation.

Stepping outside of economic arguments, I worry about setting the police as a caste apart from the citizenry. The United States has gone far too far down that road.