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comment by tailcalled · 2022-02-23T21:33:26.344Z · LW(p) · GW(p)

I doubt all of your ought claims.

Replies from: JBlack

↑ comment by JBlack · 2022-02-24T04:50:48.017Z · LW(p) · GW(p)

I doubt all of the claims, including the "is" claim.

Replies from: Richard_Kennaway

↑ comment by Richard_Kennaway · 2022-02-24T15:22:04.109Z · LW(p) · GW(p)

Me too. The claims are doing all the work, while the argument is a triviality.

Replies from: joshua-clymer

↑ comment by joshc (joshua-clymer) · 2022-02-24T17:35:18.774Z · LW(p) · GW(p)

I agree that the claims are doing all of the work and that this is not a convincing argument for utilitarianism. I often hear arguments for moral philosophies that make a ton of implicit assumptions. I think that once you make them explicit and actually try to be rigorous the argument always seems less impressive, and less convincing.

Replies from: tailcalled

↑ comment by tailcalled · 2022-02-24T18:49:11.915Z · LW(p) · GW(p)

I think a key principle involves selecting the right set of ought claims as assumptions. Some are more convincing than others. E.g. I believe "The fairness of an outcome ought to be irrelevant (this is probably the most interesting and contentious assumption)." can be replaced with something like "Frequencies and stochasticities are interchangable; X% chance of affecting everyone's utility is equivalent to 100% chance of affect X% of people's utility".

Replies from: joshua-clymer

↑ comment by joshc (joshua-clymer) · 2022-02-26T01:50:02.764Z · LW(p) · GW(p)

This is a much more agreeable assumption. When I get a chance, I'll make sure it can replace the fairness one and add it to the proof and give you credit.

comment by TLW · 2022-02-25T01:31:02.795Z · LW(p) · GW(p)

Another issue:

By the Von Neumann–Morgenstern utility theorem, this implies that there exists a function:

It implies that there exists some such function. It does not imply there exists a single unique function. And indeed the resulting function is not unique.

If I have two choices and $B$ , and I rank $A > B$ , $u (P_{A}) = 10 P_{A}$ might be one valid function (Effective value of $10$ for $A$ and $0$ for $B$ ). But $u (P_{A}) = 2 P_{A} + 1$ might be another (Effective value of $3$ for $A$ and $1$ for $B$ .)

Since for any two VNM-agents X and Y, their VNM-utility functions u_X and u_Y are only determined up to additive constants and multiplicative positive scalars, the theorem does not provide any canonical way to compare the two. Hence expressions like u_X(L) + u_Y(L) and u_X(L) − u_Y(L) are not canonically defined, nor are comparisons like u_X(L) < u_Y(L) canonically true or false. In particular, the aforementioned "total VNM-utility" and "average VNM-utility" of a population are not canonically meaningful without normalization assumptions^[1].

This, unfortunately, rather undermines the rest of your argument.

^{^}
https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Morgenstern_utility_theorem#Incomparability_between_agents

Replies from: joshua-clymer

↑ comment by joshc (joshua-clymer) · 2022-02-26T01:55:04.706Z · LW(p) · GW(p)

I don't think I agree that this undermines my argument. I showed that the utility function of person 1 is of the form h(x + y) where h is monotonic increasing. This respects the fact that the utility function is not unique. 2(x + y) + 1 would qualify, as would 3 log(x + y), etc.

Showing that the utility function must have this form is enough to prove total utilitarianism in this case since when you compare h(x + y) to h(x'+ y'), h becomes irrelevant. It is the same as comparing x + y to x' + y'.

Replies from: TLW

↑ comment by TLW · 2022-02-26T05:43:57.400Z · LW(p) · GW(p)

I have three agents $B$ and $C$ , each with the following preferences between two outcomes $a$ and $b$ :

Agents $A$ and $B$ prefers $a > b$
1. Agent $C$ prefers $b > a$
For any two lottos < $L$ , with an $x %$ chance of getting $a$ , otherwise $b$ > and < $M$ , with an $y %$ chance of getting $a$ , otherwise $b$ >:
1. if $X > Y$
  1. $A$ and $B$ prefer $L$
  2. $C$ prefers $M$ .
2. If $X = Y$ , all three agents are indifferent between $L$ and $M$
3. if $X < Y$ :
  1. $A$ and $B$ prefer $M$
  2. $C$ prefers $L$ .

(2 is redundant given 1, but I figured it was best to spell it out.)

This satisfies the axioms of the VNM theorem.

I'll give you a freebee here: I am declaring that agent $C$ 's utility function is: $u_{C} (P_{a}) = - 2 P_{a}$ as part of the problem. This is compatible with the definition of agent $C$ 's preferences, above.

As for agents $A$ and $B$ , I'll give you less of a freebee:
I am declaring as part of the problem that one of the two agents, agent [redacted alpha] has the following utility function: $u_{[Redacted Alpha]} (P_{a}) = 3 P_{a}$ . This is compatible with the definition of agent [redacted alpha]'s preferences, above.
I am declaring as part of the problem that the other of the two agents, agent [redacted beta] has the following utility function: : $u_{[Redacted Beta]} (P_{a}) = P_{a}$ . This is compatible with the definition of agent [redacted beta]'s preferences, above.

Now, consider the following scenarios:

Agent [redacted alpha] and agent $C$ are choosing between $a$ and $b$ :
1. The resulting utility function is $u_{[Redacted Alpha]} (P_{a}) + u_{C} (P_{a}) = 3 P_{a} - 2 P_{a} = P_{a}$
2. The resulting optimal outcome is outcome $a$ .
Agent [redacted beta] and agent $C$ are choosing between $a$ and $b$ :
1. The resulting utility function is $u_{[Redacted Beta]} (P_{a}) + u_{C} (P_{a}) = P_{a} - 2 P_{a} = - P_{a}$
2. The resulting optimal outcome is outcome $b$ .
Agent $A$ and agent $C$ are choosing between $a$ and $b$ :
1. Is this the same as scenario 1? Or scenario 2?
Agent $B$ and agent $C$ are choosing between $a$ and $b$ :
1. Is this the same as scenario 1? Or scenario 2?

Please tell me the optimal outcome for 3 and 4.

comment by TLW · 2022-02-24T04:40:16.327Z · LW(p) · GW(p)

This assumes that the act of evaluating a utility function has no utility cost.

I do not agree with this (implicit) assumption.

Replies from: joshua-clymer

↑ comment by joshc (joshua-clymer) · 2022-02-24T17:28:40.972Z · LW(p) · GW(p)

Good point, I overlooked this.