An argument of Parfit's reconsidered with logical decision theory

A logical decision theory recommends that you choose as if deciding the output of your decision algorithm. The main difficulty in formulating a logical decision theory is how to define statements like: "If my algorithm outputs this, the result will be that". These look like counterfactual implications, but counterfactuals describe possible worlds with different contingent facts. What our decision algorithm outputs (with given input) is a logical fact, and it is not clear what it means to say what would happen if a logical fact were different. Much theoretical work has gone into elaborating this kind of counterpossible implication, without, in my opinion, satisfactory results. But what's the point of this theoretical work? Do we really need LDT? What's the difference between choosing the output of your decision algorithm and just making a choice? There is no difference, as long as your choice is the only thing in the world that depends on your decision algorithm. The only substantial applications of LDT are games where the player's environment contains some other implementation of the algorithm. The central example is Newcomb's problem. But Newcomb's problem sounds like a science fiction story, and I'm not convinced by the case that analogous problems are part of our ordinary social lives. But leaving aside the prospect of applying LDT to real life, I do think it's important in philosophy. In this post I'm going to share an example that came up when I was reading Derek Parfit's Reasons and Persons. It's an argument that Parfit makes where LDT seems conspicuously missing. Like, if you were familiar with LDT, you would have gone in a different direction. Derek Parfit's book introduces a zoo of theories of morality and rationality, which he refers to by single-letter acronyms. In the first part of the book (all I've read to be honest), he describes how these theories can be self-defeating, introducing a taxonomy of the varieties of self-defeat. The basic principle of LDT becomes applicable when Parfit introduces "collective self-defeat". This variety of self-defeat depends on the outcome of a game in which multiple players decide according to the same theory. Because you know the other players are deriving their decisions from the same theory as you are, a philosophical move inspired by LDT yields interesting results. Parfit's claim: S is collectively self-defeating I'm going to use a single argument of Parfit's as an example. The subject of the argument is the self-interest theory ( mjx-math { display: inline-block; text-align: left; line-height: 0; text-indent: 0; font-style: normal; font-weight: normal; font-size: 100%; font-size-adjust: none; letter-spacing: normal; border-collapse: collapse; word-wrap: normal; word-spacing: normal; white-space: nowrap; direction: ltr; padding: 1px 0; } mjx-container[jax="CHTML"][display="true"] { display: block; text-align: center; margin: 1em 0; } mjx-container[jax="CHTML"][display="true"][width="full"] { display: flex; } mjx-container[jax="CHTML"][display="true"] mjx-math { padding: 0; } mjx-container[jax="CHTML"][justify="left"] { text-align: left; } mjx-container[jax="CHTML"][justify="right"] { text-align: right; } mjx-mi { display: inline-block; text-align: left; } mjx-c { display: inline-block; } mjx-utext { display: inline-block; padding: .75em 0 .2em 0; } mjx-msup { display: inline-block; text-align: left; } mjx-mn { display: inline-block; text-align: left; } mjx-c.mjx-c1D446.TEX-I::before { padding: 0.705em 0.645em 0.022em 0; content: "S"; } mjx-c.mjx-c32::before { padding: 0.666em 0.5em 0 0; content: "2"; } mjx-c.mjx-c1D434.TEX-I::before { padding: 0.716em 0.75em 0 0; content: "A"; } mjx-c.mjx-c1D435.TEX-I::before { padding: 0.683em 0.759em 0 0; content: "B"; } mjx-container[jax="CHTML"] { line-height: 0; } mjx-container [space="1"] { margin-left: .111em; } mjx-container [space="2"] { margin-left: .167em; } mjx-container [space="3"] { margin-left: .222em; } mjx-container [space="4"] { margin-left: .278em; } mjx-container [space="5"] { margin-left: .333em; } mjx-container [rspace="1"] { margin-right: .111em; } mjx-container [rspace="2"] { margin-right: .167em; } mjx-container [rspace="3"] { margin-right: .222em; } mjx-container [rspace="4"] { margin-right: .278em; } mjx-container [rspace="5"] { margin-right: .333em; } mjx-container [size="s"] { font-size: 70.7%; } mjx-container [size="ss"] { font-size: 50%; } mjx-container [size="Tn"] { font-size: 60%; } mjx-container [size="sm"] { font-size: 85%; } mjx-container [size="lg"] { font-size: 120%; } mjx-container [size="Lg"] { font-size: 144%; } mjx-container [size="LG"] { font-size: 173%; } mjx-container [size="hg"] { font-size: 207%; } mjx-container [size="HG"] { font-size: 249%; } mjx-container [width="full"] { width: 100%; } mjx-box { display: inline-