Michael Huemer is a fan of weak deontology, the view that you should avoid committing rights violations merely to produce greater but comparable benefits (though you might be required to violate rights to produce much better consequences). But he acknowledges that while utilitarianism often contradicts our intuitions, the best reason to support it is to conclude that all other theories have more severe flaws.

The most severe flaw with weak deontology is what he in Knowledge, Reality, and Value calls the Aggregation Problem:

Say there are two people, A and B, who each have money in a bank. You want to give money to A, but, for whatever reason, you are unable to do so directly. What you can do is to hack into the bank’s computer and run a program which will steal $1 from B’s bank account, then give $2 to A. (The extra dollar comes from your own account, and you’re happy to give it, as A needs the money and you don’t.) The moderate deontologist says this is impermissible: Stealing is a rights-violation, which cannot be justified merely by producing slightly greater benefits for others. So far, so good – that’s not an implausible view on its face.

Now, it happens that you also would like to give some money to B, but again you can’t do so directly. You can only run a computer program which will steal $1 from A and then give $2 to B. (This is a separate program from the one that would steal from B to give to A.) Just as before, the moderate deontologist will presumably declare this impermissible.

However, if you do both actions, A and B are both better off. Intuitively, there’s nothing wrong with that. Money is fungible, so the net effect on A and B will be exactly as if you had simply transferred $1 to each of them, which would surely have been permissible. The fact that you carry out the transfer in this odd way, taking $1 away and giving $2 back, seems morally irrelevant.

So this would suggest that two wrongs make a right, that two individually unacceptable actions become acceptable in combination. Huemer elaborates in “A Paradox for Weak Deontology”:

Individuation Independence: Whether some behavior is morally permissible cannot depend upon whether that behavior constitutes a single action or more than one action.

Two Wrongs: If it is wrong to do A, and it is wrong to do B given that one does A, then it is wrong to do both A and B.

You would expect these two rules to hold for any correct moral theory, but this runs into the Aggregation Problem.

(-1 is a small harm, while +2 is a marginally larger gain)

He gives a specific example but you could think of others easily:

Torture Transfer: Mary works at a prison where prisoners are being unjustly tortured. She finds two prisoners, A and B, each strapped to a device that inflicts pain on them by passing an electric current through their bodies. Mary cannot stop the torture completely; however, there are two dials, each connected to both of the machines, used to control the electric current and hence the level of pain inflicted on the prisoners. Oddly enough, the first dial functions like this: if it is turned up, prisoner A’s electric current will be increased, but this will cause prisoner B’s current to be reduced by twice as much. The second dial has the opposite effect: if turned up, it will increase B’s torture level while lowering A’s torture level by twice as much. Knowing all this, Mary turns the first dial, immediately followed by the second, bringing about a net reduction in both prisoners’ suffering.

The contradiction between Individuation Independence and the Two Wrongs principle on the one hand and cases like Torture Transfer on the other imply that weak deontology must be false.

Possible objections have to claim that turning the first dial somehow justifies turning the second dial:

1. Turning the second dial doesn’t add to Prisoner B’s net suffering given that you turned the first dial. This doesn’t stand up to deontological scrutiny, since the first dial was causally independent of the decision to turn the second dial afterward. Huemer gives the example of a prisoner whose current is weakening due to machine malfunction, which wouldn’t justify turning up the current just because it merely slowed the pain reduction rather than increasing the pain.
2. Turning the second dial is justified because it compensates Prisoner A for your having turned the first dial. But this is the exact kind of tradeoff that’s fatal to deontology, whose principles demand that you not, for example, steal from one person to compensate the losses of some other person.
3. Turning the second dial is justified merely because it’s part of a set of actions that’s acceptable in aggregate. This solves the contradiction, but is also just an arbitrary principle. It would also suggest that if you woke up from a head injury to find Prisoner A at a slightly increased current and Prisoner’s B current cut in half, but weren’t sure whether you just found them like this or whether you did it yourself pre-amnesia, that you would have to investigate this question before deciding whether to turn the second dial.

This last objection brings to mind the funny question to ask people who wouldn’t turn the lever in the Trolley Problem: If you trip and turn the lever by accident, do you have to turn it back toward the five people after you dust yourself off?

Consequentialism solves the Aggregation Problem but suffers its own problems. Virtue is subtle.