Hare's Clever Argument For Completeness

Applies to both preferences and value

Edit: I’m apparently unable to read. Hare doesn’t endorse this argument. He thinks that the belief in comparability commits one to one of two weird results, and explains the implications, but he think that we can just accept one of the weird results.

I’m currently reading Hare’s book “The Limits of Kindness.” I suspect it’s something in the water, but something keeps making the best books turned out by consequentialists begin with “The Limits of”—see Kagan’s book for another example. This is a super clever book—it churns out brilliant arguments with alarming speed. One argument, though not explicitly packaged as one, is for the requirement of complete preferences.

One’s preferences are complete if they, for any two things, have some preference ordering between the two of them. Suppose that one, when deciding between Harvard and Yale, says “I just can’t decide.” This would be an example of incomplete preferences. Note, this is not valuing them equally—they’d still be undecided if someone offered them an extra dollar to go to Yale, even though they’d prefer Yale plus a dollar to regular Yale, they have no preference between Yale plus a dollar and Harvard or Yale without the extra dollar and Harvard.

Hare has a persuasive argument that this is irrational. Suppose that there is a fair coin that will if heads send you to Yale and if tails send you to Harvard. Someone offers you that instead, if it’s heads they’ll send you Harvard and if it’s tails they’ll send you to Yale with an extra dollar. This seems like a good deal—after all, it replaces a 50% chance of Yale and 50% chance of Harvard with a 50% chance of Yale with an extra dollar and a 50% chance of Harvard. You prefer having the extra dollar.

That this is good follows from the following obvious principle.

If one gamble offers the same outcomes with the same probability as another, except that instead of one worse event with some probability it gives a better event with the same probability, it is better than the other gamble.

But completeness has to deny this if one accepts the following plausible principle.

If there are two coinflips and whether one gets heads or tails, they are indifferent between the actual outcomes of the two gambles, then they are actually indifferent between the two gambles.

Indifferent here means one doesn’t prefer either to the other, not that they’re precisely equal.

If one gets heads, then they are indifferent between the gambles, because the options if they get heads are Yale or Harvard and if they get tails then the choice is between Harvard and Yale plus a dollar. In both cases, they’re indifferent.

Now, here’s where I think this argument is important and broaches new ground. It’s old news that having incomplete preferences is irrational. But I think this paper is pretty important in advancing the dialectic for a few reasons.

First, a lot of people don’t think it’s irrational to have incomplete preferences. Thus, more arguments are useful here.

Second, most of the arguments for the irrationality of complete preferences are money pumps. But money pumps are only about preferences not value. But Hare’s argument can be repurposed to apply to value. Suppose that, as a matter of axiology, A+>A, while they’re both incomparable with B. Then, as a matter of axiology, if a coin has a 50% chance of getting A+, a 50% chance of B, versus another with a 50% chance of A and a 50% chance of B, which is better. One gets the same problem.

This may not seem significant. I think that, if one wants to reject the repugnant conclusion, maybe the best way to do it is to adopt the view sketched out here. This view is compatible with rationally permitting incomplete preferences, but not incompleteness in value. Thus, if value is complete, one way to reject the repugnant conclusion is not successful.