In a comment on an old blog post, a person called "D" brought up a nice puzzle for Causal Decision Theory. Here's (my version of) the scenario.
You have just taken over as one of three pilots on a spaceship that is on its way to Betelgeuse. The spaceship's flight operations are largely automatised. The only input needed from the pilots is the destination. At present, the only available destinations are Betelgeuse and a service station on a nearby moon. (Other destinations could not be safely reached with current fuel levels.)
Informal talk about de re necessity is sometimes "weak" and sometimes "strong", in Kripke's terminology. When I say, 'Elizabeth II could not have failed to be the daughter of George VI', I mean – roughly – that Elizabeth is George's daughter at every world at which she exists. By contrast, when I say, 'Elizabeth II could not have failed to exist', I don't just mean that Elizabeth exists at every world at which she exists. My claim is that she exists at every world whatsoever. The former usage is "weak", the latter "strong".
When people give a semantics for the language of Quantified Modal Logic (QML), they typically treat the box as strong. '\( \Box Fx \)' is assumed to say that x is F at every accessible world, not just at every accessible world at which x exists.
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:
Harsanyi (1955) famously showed that a few seemingly harmless assumptions, when combined, entail the utilitarian doctrine that the goodness of a state of the world is the sum of the state's goodness for each individual. In other words, moral value is additive across people.
Recently, I've argued that value is additive on the grounds that its components are "separable", in the sense that if two states s and s' differ only with respect to some components, then the betterness ranking of s and s' does not depend on the respects in which s and s' agree. Debreu (1960) showed that, under some modest further assumptions, separability entails additive representability. I've never had a close look at Debreu's theorem, since the result isn't surprising.
There are many conceptions of linguistic meaning. One approach, that I like, assumes that the semantic values we assign to sounds and scribbles function somewhat like the numbers we assign to certain pieces of paper and plastic when we say that they are a "5 pound note" or a "10 pound note": they are a compact summary of the kinds of activities people can perform with the relevant objects. With a 5 pound note you can buy certain kinds of goods. With the sounds 'it is raining' you can inform people that it is raining.
When people like Lewis (1975) spell out this use-based conception of semantics, they generally focus on assertion and information exchange. Roughly, the semantic value assigned to a declarative sentence is identified with the information that is conventionally conveyed by an utterance of the sentence.
Why should you maximize expected utility? A well-known answer – discussed, for example, in McClennen (1990), Cubitt (1996), and Gustafsson (2022) – goes as follows.
There are many alleged counterexamples to expected utility theory: Allais's Paradox, Ellsberg's Paradox, Sen (1993)'s polite agent who prefers the second-largest slice of cake, Machina (1989)'s mother who prefers fairness when giving a treat to her children, and so on. In all these cases, the preferences of seemingly reasonable people appear not to rank the options by their expected utility.
Those who make these claims generally assume that utility is a function of material goods. In Allais's Paradox, for example, the possible "outcomes" (of which utility is a function) are assumed to be amounts of money. As has often been pointed out, the apparent violations of expected utility theory all go away if the outcomes are individuated more finely – if, for example, we distinguish between an outcome of getting $1000 as the result of a risky gamble and an outcome of getting a sure $1000. See, for example, Weirich (1986), or Dreier (1996).
If some ideal is impossible to reach, should we get as close to the ideal as we can?
It's easy to come up with apparent counterexamples. Lipsey and Lancaster (1956) are sometimes said to have proved that getting as close to the ideal as we can is not the best option. Have they really?
Wiens (2020) helpfully summarizes the main result of Lipsey and Lancaster and explains how it applies outside economics. (The Lipsey and Lancaster paper is all about tariffs and taxes and Paretian conditions.)
A few thoughts on Brown (2014) and Brown (2020) and the composition of value.
Some propositions (or properties, but let's run with propositions) have value. They are reasons to act one way rather than another. We may ask how this kind of value distributes over the space of propositions.
Since logically equivalent propositions plausibly have the same value, we can picture the propositions as regions in logical space – sets of possible worlds. Now how is the value of a region related to the value of other regions – to its subregions, for example? This is the question Campbell Brown raises in Brown (2014) and Brown (2020).
When something is good, or desirable, or a reason, then this is usually because it has some good (desirable, etc.) features. The thing may also have bad features, but if the thing is good then the good features outweigh the bad features. How does this weighing work? I'd like to say that the total goodness of a thing is always the sum of the goodness of its features. This "additive" view seems to be unpopular in both ethics and economics. I'll try to defend it.
I first need to state the view more precisely.
To begin, I assume that there are ultimate bearers of value. If we're talking about personal desire, this means that there are some things an agent desires "intrinsically" or "non-derivatively". Being free from pain might be a common example. If you desire to be free from pain then this is typically not because you really desire something else, and you think being free from pain is either a means to the other thing or evidence for the other thing. You simply desire being free from pain, and that's the end of the story.