Blumberg and Hawthorne on weakening desire
Long ago, in 2007, I expressed sympathy for the idea that desire can be analysed in terms of expected value: 'S desires p' is true iff p worlds are on average better, by S's standards, than not-p worlds, where the "average" is computed with S's credence function. As I mentioned at the time, this has the interesting consequence that 'S desires p' and 'S desires q' does not entail 'S desires p and q'.
Blumberg and Hawthorne (2022) make the same observation, and argue that it is a serious problem for the expected-value analysis. Intuitively, they say, 'Bill wants Ann to attend' and 'Bill wants Carol to attend' entail 'Bill wants Ann or Carol to attend'. In general, they claim, the following principle of Weakening is valid:
S wants p, S wants q \( \models \) S wants p or q.
But consider the following scenario.
There are two lotteries. Lottery 1 has ten thousand tickets, one of which wins $1M and the others $0. Lottery 2 has a million tickets, one of which wins $1M and the others $0. Someone has given you a ticket as a present. You don't know from which lottery. Intuitively, (1) is true and (2) is false:
(1) You want your ticket to come from lottery 1.
(2) You want your ticket to come from lottery 2.
Let S1 be the set containing the winning ticket in lottery 2 and the lowest-numbered losing ticket in lottery 2. You haven't looked at the number of your ticket. Do you want your ticket to be in S1 (under this description)? Surely the answer is yes. (Imagine I say, "I have written down the numbers of the winning ticket and the lowest-numbered losing ticket in lottery 2. I am now going to reveal whether your ticket number is among these two numbers." Do you want the answer to be positive or negative?)
(3) You want your ticket to be in S1.
You see where this is going. Let S2 be the set containing the winning ticket in lottery 2 and the second-lowest-numbered losing ticket in lottery 2. As before:
(4) You want your ticket to be in S2.
And so on, until S999999.
Evidently, your ticket is in S1 or S2 or … or S999999 iff your ticket comes from lottery 2. The Weakening principle (together with the assumption that wanting is closed under logical equivalence) therefore entails that if (3) and (4) etc. are all true, then so is (2). But (2) is false.
A friend of Weakening might be able to account for this observation by suggesting that there's a subtle context switch between (2) and (3). I suspect this is what Blumberg and Hawthorne would say. If the two sentences are evaluated in the same context, they would say, the sentences have the same truth-value. This isn't crazy. But it is also not obvious.
At any rate, the dialectic has reversed. Blumberg and Hawthorne use the apparent validity of Weakening as an argument against a decision-theoretic analysis of 'want'. But Weakening isn't "apparently valid". On the contrary. There appear to be counterexamples.
At another point in their paper, Blumberg and Hawthorne complain that the decision-theoretic analysis makes desire reports too sensitive to credences and utilities.
Imagine, they say, that you won a trip abroad. You will be flown either to Paris, or to Berlin, or to Rio. You prefer Paris to the other locations. According to Blumberg and Hawthorne, (13b) is then clearly true.
(13b) You want to be flown to Europe.
The decision-theoretic analysis, however, says that the truth of (13b) depends on your preferences between Berlin and Rio and on your credences about the respective likelihood of Berlin and Paris.
Let's compare two cases.
In Case 1, you like Berlin almost as much as Paris, and Rio less. (Your credences don't matter, but let's say you give equal credence to getting to Paris and getting to Berlin.)
In Case 2, going to Berlin would be terrible. You have powerful enemies in Berlin who would kill you if you go there. You also know that your destination is chosen on the basis of a coin flip: if the coin lands heads, you go to Rio; if it land tails, you go to Berlin; if it lands on its edge, you go to Paris.
The decision-theoretic account says that (13b) is true in Case 1 and false in Case 2. Blumberg and Hawthorne claim that there is no difference between the two cases. In particular, they hold that (13b) is true in Case 2. You want to be flown to Europe, they say, despite the fact that you would be devastated to learn that you'll be flown to Europe and that you would pay everything you have to ensure that you'll be flown to Rio.
Without further context, I'd say (13b) is clearly true in Case 1, false in Case 2, and odd in intermediate cases. It's not a neutral datum that (13b) is true in both Cases.
I'm not saying that the simple decision-theoretic analysis is right, or that Blumberg and Hawthorne's analysis is wrong. (I haven't even explained what their analysis is.) I'm only saying that these arguments aren't great.