Yes, selfish agents are more problematic than average utilitarians. They have precommitment issues: what they decide before knowing who they are is not what they would decide after—this does, however, leave them open to money pumps, so you could argue that they should go the UDT or precommitment route.
If they don’t have access to precommitments, then the discontinuity that happens when they learn who they are means that they no longer behave the same way as average utilitarians would (whos utility function doesn’t change when they find out who they are).
Okay. So, going the UDT route, what are the prices people would pay? (also known as the “correct” route—done by choosing the optimal strategy, not just the best available action)
In the selfish non-anthropic problem, we evaluate the payoff of the strategies “always yea” and “always nay.” If heads (0.5), and if picked as decider (0.1), yea gives 100 and nay 700. If tails (0.5) and picked as decider (0.9), yea gives 1000 and nay 700. Adding these expected utilities gives an expected payoff of 455 from “always yea” and an expected payoff of 350 from “always nay.” (corrected)
However, in the “isomorphic” altruistic case, you don’t actually care about your personal reward—you simply care about the global result. Thus if heads (0.5), “always yea” always gives 100 and “always nay” always gives 700. And if tails, “always yea” always gives 1000 and “always nay” always gives 700. So in that case the payoffs are “yea” 550 and “nay” 700.
So this “isomorphic” stuff doesn’t look so isomorphic.
In the selfish case, you forgot the 0.5: the payoff is 455 for “always yea”, 350 for “always nay”.
And you seem to be comparing selfish with selfless, not with average utilitarian.
For an average utilitarian, under “always yea”, 100 is given out once in the heads world, and 1000 is given out 9 times in the tails world. These must be shared among 10 people, so the average is 0.5(100+1000x9)/10=455. For “always nay”, 700 is give out once in the heads world, and 9 times in the tails world, giving 0.5(700 + 9x700)/10=350, same as for the selfish agent.
The reason it doesn’t solve the problem is because the people who want to donate to charity aren’t doing it so that the other people also participating in the game will get utility—that is, they’re altrusits, but not average utilitarians towards the other players. So the formulation is a little more complicated.
They’re selfless, and have coordinated decisions with precommitments—ADT will then recreate the UDT formulation, since there are no anthropic issues to worry about. ADT + selflessness tends to SIA-like behaviour in the Sleeping beauty problem, which isn’t the same as saying ADT says selfless agents should follow SIA.
Well, yes, it recreates the UDT solution (or at least it does if it works correctly—I didn’t actually check or anything). But the problem was never about just recreating the UDT solution—it’s about understanding why the non-UDT solution doesn’t work.
Yes, selfish agents are more problematic than average utilitarians. They have precommitment issues: what they decide before knowing who they are is not what they would decide after—this does, however, leave them open to money pumps, so you could argue that they should go the UDT or precommitment route.
If they don’t have access to precommitments, then the discontinuity that happens when they learn who they are means that they no longer behave the same way as average utilitarians would (whos utility function doesn’t change when they find out who they are).
Okay. So, going the UDT route, what are the prices people would pay? (also known as the “correct” route—done by choosing the optimal strategy, not just the best available action)
In the selfish non-anthropic problem, we evaluate the payoff of the strategies “always yea” and “always nay.” If heads (0.5), and if picked as decider (0.1), yea gives 100 and nay 700. If tails (0.5) and picked as decider (0.9), yea gives 1000 and nay 700. Adding these expected utilities gives an expected payoff of 455 from “always yea” and an expected payoff of 350 from “always nay.” (corrected)
However, in the “isomorphic” altruistic case, you don’t actually care about your personal reward—you simply care about the global result. Thus if heads (0.5), “always yea” always gives 100 and “always nay” always gives 700. And if tails, “always yea” always gives 1000 and “always nay” always gives 700. So in that case the payoffs are “yea” 550 and “nay” 700.
So this “isomorphic” stuff doesn’t look so isomorphic.
In the selfish case, you forgot the 0.5: the payoff is 455 for “always yea”, 350 for “always nay”.
And you seem to be comparing selfish with selfless, not with average utilitarian.
For an average utilitarian, under “always yea”, 100 is given out once in the heads world, and 1000 is given out 9 times in the tails world. These must be shared among 10 people, so the average is 0.5(100+1000x9)/10=455. For “always nay”, 700 is give out once in the heads world, and 9 times in the tails world, giving 0.5(700 + 9x700)/10=350, same as for the selfish agent.
Ah, good point. I made a mistake in translating the problem into selfish terms. In fact, that might actually solve the non-anthropic problem...
EDIT: Nope.
Why nope? ADT (with precommitements) simplifies to a version of UDT in non-anthropic situations.
The reason it doesn’t solve the problem is because the people who want to donate to charity aren’t doing it so that the other people also participating in the game will get utility—that is, they’re altrusits, but not average utilitarians towards the other players. So the formulation is a little more complicated.
They’re selfless, and have coordinated decisions with precommitments—ADT will then recreate the UDT formulation, since there are no anthropic issues to worry about. ADT + selflessness tends to SIA-like behaviour in the Sleeping beauty problem, which isn’t the same as saying ADT says selfless agents should follow SIA.
Well, yes, it recreates the UDT solution (or at least it does if it works correctly—I didn’t actually check or anything). But the problem was never about just recreating the UDT solution—it’s about understanding why the non-UDT solution doesn’t work.
Because standard decision theory doesn’t know how to deal properly with identical agents and common policies?