I’ll stick to addressing the decision theory section; I haven’t thought as much about the population ethics but probably have broadly similar objections there.
(1) What makes STOCHASTIC better than the strategy “take exactly N tickets and then stop”?
Both avoid near-certain death (good!)
Both involve, at some point, turning down what looks like a strictly better option
To me, STOCHASTIC seems to do this at the very first round, and all subsequent rounds. (If I played STOCHASTIC and drew a non-black ball first, I think I’d be pretty disappointed. This indicates to me that I didn’t actually want to randomize on that round.) Or you could just view STOCHASTIC as doing this on the round when you stop accepting tickets.
This very fact makes these strategies about as puzzling as the “reckless” or “timid” strategies to me—at some point, you’re deliberately choosing the worse option, by your own lights! That’s at least weird, right?
“Take exactly N” has the advantage of letting you decide the exact level of risk you want to take on, while STOCHASTIC involves an additional layer of uncertainty, which gets you ….???[1]
I get that you’re trying to avoid totalizing theoretical frameworks, but you also seem to be saying it’s better in some way that makes it worth choosing, at least for you. But why?
(2) In response to
But, well, you don’t have to interpret my actions as expressing attitudes towards expected payoffs. I mean this literally. You can just … not do that.
I’m having trouble interpreting this more charitably than “when given a choice, you can just … choose the option with the worse payoff.” Sure, you can do that. But surely you’d prefer not to? Especially if by “actions” here, we’re not actually referring to what you literally do in your day-to-day life, but a strategy you endorse in a thought-experiment decision problem. You’re writing as if this is a heavy theoretical assumption, but I’m not sure it’s saying anything more than “you prefer to do things that you prefer.”
(3) In addition to not finding your solution to the puzzle satisfactory,[2] I’m not convinced by your claim that this isn’t a puzzle for many other people:
Either you’re genuinely happy with recklessness (or timidity), or else you have antecedent commitments to the methodology of decision theory — such as, for example, a commitment to viewing every action you take as expressing your attitude to expected consequences.
To me, the point of the thought experiment is that roughly nobody is genuinely happy with extreme recklessness or timidity.[3] And as I laid out above, I’d gloss “commitment to viewing every action you take as expressing your attitude to expected consequences” here as “commitment to viewing proposed solutions to decision-theory thought experiments as expressing ideas about what decisions are good” — which I take to be nearly a tautology.
So I’m still having trouble imagining anyone the puzzles aren’t supposed to apply to.
The only case I can make for STOCHASTIC is if you can’t pre-commit to stopping at the N-th ticket, but can pre-commit to STOCHASTIC for some reason. But now we’re adding extra gerrymandered premises to the problem; it feels like we’ve gone astray.
Although if you just intend for this to be solely your solution, and make no claims that it’s better for anyone else, or better in any objective sense then … ok?
This is precisely why it’s a puzzle—there’s no outcome (always refuse, always take, take N, stochastic) that I can see any consistent justification for.
Interesting comment! But I’m also not convinced. :P
… or, more precisely, I’m not convinced by all of your remarks. I actually think you’re right in many places, though I’ll start by focusing on points of disagreement.
(1) On Expected Payoffs.
You ask whether I’m saying: “when given a choice, you can just … choose the option with a worse payoff?”
I’m saying ‘it’s sometimes better to choose an option with lower expected payoff’. Still, you might ask: “why would I choose an option with lower expected payoff?”
First, I think the decision procedure “choose the option with the highest expected payoff” requires external justification. I take it that people appeal to (e.g.) long-run arguments for maximizing expected utility because they acknowledge that the decision procedure “choose the action with highest expected payoff” requires external justification.
Arguments for EU maximization are meant to show you how to do better by your own values. If I can come up with an alternative decision procedure which does better by my values, this is an argument for not choosing the action with the highest expected payoff. And I take myself to be appealing to the same standards which (doing better by your lights) which are appealed to in defense of EU maximization.
I intepret you as also asking a separate question, of the form: “you’re recommending a certain course of action — why (or on what basis) do you recommend that course of action?”
Trying to justify my more foundational reasons will probably take us a bit too far afield, but in short: when I decide upon some action, I ask myself the question “do I recommend that all rational agents with my values in this decision context follow the decision procedure I’m using to determine their action?
I think this criteria is independently justified, and indeed more foundational than purported justifications for EU maximization. Obviously, I don’t expect you (or anyone else) to be convinced by this short snippet, but I do take myself to have reasons for action. I just think those reasons provide more foundational justifications than the use of EUM as a decision-procedure, and in certain cases license rejecting EUM (qua decision procedure).
In the case offered by Beckstead and Thomas, I think STOCHASTIC does better by my values than the decision procedure “choose, at each point, the action with the highest expected payoff”. That’s why I decide in the way I do.
In summary: Beckstead and Thomas’ case provides me with exogenously given payoffs, and then invites me to choose, in line with my preferences over payoffs, on a given course of action. I don’t think I’m deciding to act in a way which, by my lights, is worse than some other act. My guess is that you interpret me as choosing an option which is worse by my own lights because you interpret me as having context-independent preferences over gambles, and choosing an option I disprefer.
I’m saying, instead, that the assumption of ‘context-independent preferences over gambles’ are not given for free, and are, at least, not explicitly provided in Beckstead and Thomas’ setup. I have preferences over fixed states of the world, or ‘degenerate’ gambles. Given that I don’t possess certainty over future states of the world, I use some decision procedure for navigating this uncertainty. This doesn’t mean that I ‘really’ possess context-independent preferences over gambles, and then act in accordance with them.
“Wait, are you really saying that you don’t prefer a state of the world which delivers Utopia with probability (1−ε), and something marginally worse than the current world with the remaining probability?”
Yes, but I think that’s less weird than it sounds. The gamble I mentioned is better than the status quo with some probability, and worse with some probability. Is that state of the world ‘better’? Well, it’s better with some probability, and worse with some probability! I don’t feel the need to construct some summary term which captures my “all-things-considered betterness ranking under uncertainty”.
(2) On STOCHASTIC More Specifically
I think you’re right that some alternative strategy to STOCHASTIC is preferable, and probably you’re right taking exactly N tickets is preferable. I’ll admit that I didn’t think through a variety of other procedures, STOCHASTIC was just the first thought that came to mind.
One final critical response.
I would also be disappointed if I drew a black ball first. But I think I would be similarly disappointed if I drew a black ball at a later time. I think this is just a consequence of the fact that you can design decision-environments in which people will always be disappointed.
For example, you can always (trivially) design an environment in which the option with highest payoff includes a “disappointment” term incorporated. In which case, you’ll always be disappointed if you choose the option with the highest payoff for you. Does this mean that you didn’t actually want the option with the highest payoff?
Thanks for the helpful pushback, and apologies for the late reply!
Interesting post! But I’m not convinced.
I’ll stick to addressing the decision theory section; I haven’t thought as much about the population ethics but probably have broadly similar objections there.
(1) What makes STOCHASTIC better than the strategy “take exactly N tickets and then stop”?
Both avoid near-certain death (good!)
Both involve, at some point, turning down what looks like a strictly better option
To me, STOCHASTIC seems to do this at the very first round, and all subsequent rounds. (If I played STOCHASTIC and drew a non-black ball first, I think I’d be pretty disappointed. This indicates to me that I didn’t actually want to randomize on that round.) Or you could just view STOCHASTIC as doing this on the round when you stop accepting tickets.
This very fact makes these strategies about as puzzling as the “reckless” or “timid” strategies to me—at some point, you’re deliberately choosing the worse option, by your own lights! That’s at least weird, right?
“Take exactly N” has the advantage of letting you decide the exact level of risk you want to take on, while STOCHASTIC involves an additional layer of uncertainty, which gets you ….???[1]
I get that you’re trying to avoid totalizing theoretical frameworks, but you also seem to be saying it’s better in some way that makes it worth choosing, at least for you. But why?
(2) In response to
I’m having trouble interpreting this more charitably than “when given a choice, you can just … choose the option with the worse payoff.” Sure, you can do that. But surely you’d prefer not to? Especially if by “actions” here, we’re not actually referring to what you literally do in your day-to-day life, but a strategy you endorse in a thought-experiment decision problem. You’re writing as if this is a heavy theoretical assumption, but I’m not sure it’s saying anything more than “you prefer to do things that you prefer.”
(3) In addition to not finding your solution to the puzzle satisfactory,[2] I’m not convinced by your claim that this isn’t a puzzle for many other people:
To me, the point of the thought experiment is that roughly nobody is genuinely happy with extreme recklessness or timidity.[3] And as I laid out above, I’d gloss “commitment to viewing every action you take as expressing your attitude to expected consequences” here as “commitment to viewing proposed solutions to decision-theory thought experiments as expressing ideas about what decisions are good” — which I take to be nearly a tautology.
So I’m still having trouble imagining anyone the puzzles aren’t supposed to apply to.
The only case I can make for STOCHASTIC is if you can’t pre-commit to stopping at the N-th ticket, but can pre-commit to STOCHASTIC for some reason. But now we’re adding extra gerrymandered premises to the problem; it feels like we’ve gone astray.
Although if you just intend for this to be solely your solution, and make no claims that it’s better for anyone else, or better in any objective sense then … ok?
This is precisely why it’s a puzzle—there’s no outcome (always refuse, always take, take N, stochastic) that I can see any consistent justification for.
Interesting comment! But I’m also not convinced. :P
… or, more precisely, I’m not convinced by all of your remarks. I actually think you’re right in many places, though I’ll start by focusing on points of disagreement.
(1) On Expected Payoffs.
You ask whether I’m saying: “when given a choice, you can just … choose the option with a worse payoff?”
I’m saying ‘it’s sometimes better to choose an option with lower expected payoff’. Still, you might ask: “why would I choose an option with lower expected payoff?”
First, I think the decision procedure “choose the option with the highest expected payoff” requires external justification. I take it that people appeal to (e.g.) long-run arguments for maximizing expected utility because they acknowledge that the decision procedure “choose the action with highest expected payoff” requires external justification.
Arguments for EU maximization are meant to show you how to do better by your own values. If I can come up with an alternative decision procedure which does better by my values, this is an argument for not choosing the action with the highest expected payoff. And I take myself to be appealing to the same standards which (doing better by your lights) which are appealed to in defense of EU maximization.
I intepret you as also asking a separate question, of the form: “you’re recommending a certain course of action — why (or on what basis) do you recommend that course of action?”
Trying to justify my more foundational reasons will probably take us a bit too far afield, but in short: when I decide upon some action, I ask myself the question “do I recommend that all rational agents with my values in this decision context follow the decision procedure I’m using to determine their action?
I think this criteria is independently justified, and indeed more foundational than purported justifications for EU maximization. Obviously, I don’t expect you (or anyone else) to be convinced by this short snippet, but I do take myself to have reasons for action. I just think those reasons provide more foundational justifications than the use of EUM as a decision-procedure, and in certain cases license rejecting EUM (qua decision procedure).
In the case offered by Beckstead and Thomas, I think STOCHASTIC does better by my values than the decision procedure “choose, at each point, the action with the highest expected payoff”. That’s why I decide in the way I do.
In summary: Beckstead and Thomas’ case provides me with exogenously given payoffs, and then invites me to choose, in line with my preferences over payoffs, on a given course of action. I don’t think I’m deciding to act in a way which, by my lights, is worse than some other act. My guess is that you interpret me as choosing an option which is worse by my own lights because you interpret me as having context-independent preferences over gambles, and choosing an option I disprefer.
I’m saying, instead, that the assumption of ‘context-independent preferences over gambles’ are not given for free, and are, at least, not explicitly provided in Beckstead and Thomas’ setup. I have preferences over fixed states of the world, or ‘degenerate’ gambles. Given that I don’t possess certainty over future states of the world, I use some decision procedure for navigating this uncertainty. This doesn’t mean that I ‘really’ possess context-independent preferences over gambles, and then act in accordance with them.
“Wait, are you really saying that you don’t prefer a state of the world which delivers Utopia with probability (1−ε), and something marginally worse than the current world with the remaining probability?”
Yes, but I think that’s less weird than it sounds. The gamble I mentioned is better than the status quo with some probability, and worse with some probability. Is that state of the world ‘better’? Well, it’s better with some probability, and worse with some probability! I don’t feel the need to construct some summary term which captures my “all-things-considered betterness ranking under uncertainty”.
(2) On STOCHASTIC More Specifically
I think you’re right that some alternative strategy to STOCHASTIC is preferable, and probably you’re right taking exactly N tickets is preferable. I’ll admit that I didn’t think through a variety of other procedures, STOCHASTIC was just the first thought that came to mind.
One final critical response.
I would also be disappointed if I drew a black ball first. But I think I would be similarly disappointed if I drew a black ball at a later time. I think this is just a consequence of the fact that you can design decision-environments in which people will always be disappointed.
For example, you can always (trivially) design an environment in which the option with highest payoff includes a “disappointment” term incorporated. In which case, you’ll always be disappointed if you choose the option with the highest payoff for you. Does this mean that you didn’t actually want the option with the highest payoff?
Thanks for the helpful pushback, and apologies for the late reply!