Posts on: 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:
In The Logic of Decision, Richard Jeffrey pointed out that
the desirability (or "news value") of a proposition can be usefully
understood as a weighted average of the desirability of different ways
in which the proposition can be true, weighted by their respective
probability. That is, if A and B are incompatible propositions,
then
(1) Des(AvB) = Des(A)P(A/AvB) + Des(B)P(B/AvB).
So desirabilities are affected by probabilities. If you prefer A
over B and just found out that conditional on their disjunction, A is
more likely then B, then the desirability of the disjunction goes
up. That seems right.
One of the novelties in Richard Jeffrey's "Logic of Decision"
(1965) was to unify the space over which probabilities and values are
defined: both probability and desirability are distributed over the
space of possible worlds, of ways things might be. By contrast, in
earlier theories like that of Savage, probabilities were defined over
states (or events) and utilities over
consequences, which were taken to be distinct kinds of
things. Technically, this difference between Savage and Jeffrey isn't
terribly important as long as anything an agent may care about can be
found in the set of 'consequences'. However, the distinction and the
labeling in Savage's treatment carries a danger to overlook the
complexity of human values. This has, I believe, led to a number of
serious mistakes.
Bas van Fraassen's Reflection Principle says that your current beliefs should be in line with your current beliefs about your future beliefs. More precisely,
PRB: P_1(A | P_2(A)=x) = x.
P_1 is your credence at time 1, P_2 your credence at time 2. PRB says that conditional on the assumption that at time 2 you believe A to degree x, you should already believe A to degree x at time 1. For agents who believe that they will (or might) change their beliefs in irrational ways between the two times, PRB is not a reasonable demand: if you know that you will be hit on the head tomorrow and consequently believe that the Earth is flat, you shouldn't believe that the Earth is flat now. On the other hand, if you're certain you will not change your beliefs in any such irrational way between now and tomorrow, then PRB is reasonable: suppose tomorrow you will believe that the Earth is flat by rationally responding to some very surprising new information; then you can infer that there exists some such information strongly supporting that the Earth is flat. But the fact that there is evidence for P is of course itself evidence for P. Hence you should already believe today that the Earth is probably flat.
Reinventing broken wheels is more fun than patching small punctures in functioning ones. So here are some thoughts on desires that are undistorted by knowing the relevant literature.
It seems that unlike for rational belief, there are very few formal constraints on rational desire. For instance, if you desire A & B, it doesn't follow that you should desire A: I'd like to be beaten up and get a billion dollars compensation for it, but I don't desire to be beaten up. By the same example, you may desire A without desiring the disjunction A v B. More generally, all these principles are invalid for rational desire:
Sometimes I wish I hadn't done something, and that I could undo what I did. That is a coherent desire. What I desire is after all not that the world be such that at time t1, I do X, and then at t2, I do something else to the effect that at t1, I didn't do X. That's nonsense (unless I wish to inhabit a branching universe, which, let's stipulate, I don't). Rather, I desire that at t2, I do something to the effect that at t1, I didn't do X in the first place.
A harder case: suppose I wish I had never existed, and wish to undo my existence. That still makes sense, I guess. It's like the wish to be somebody else: I wish to do be a person who does something such that by doing this, they make it the case that the person I in fact am never came into existence.