Iâll stick to addressing the decision theory section; I havenât thought as much about the population ethics but probably have broadly similar objections there.
(1) What makes STOCHASTIC better than the strategy âtake exactly N tickets and then stopâ?
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 Iâd be pretty disappointed. This indicates to me that I didnât 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 ârecklessâ or âtimidâ strategies to meâat some point, youâre deliberately choosing the worse option, by your own lights! Thatâs at least weird, right?
âTake exactly Nâ 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 âŚ.???[1]
I get that youâre trying to avoid totalizing theoretical frameworks, but you also seem to be saying itâs better in some way that makes it worth choosing, at least for you. But why?
(2) In response to
But, well, you donât have to interpret my actions as expressing attitudes towards expected payoffs. I mean this literally. You can just ⌠not do that.
Iâm having trouble interpreting this more charitably than âwhen given a choice, you can just ⌠choose the option with the worse payoff.â Sure, you can do that. But surely youâd prefer not to? Especially if by âactionsâ here, weâre 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. Youâre writing as if this is a heavy theoretical assumption, but Iâm not sure itâs saying anything more than âyou prefer to do things that you prefer.â
(3) In addition to not finding your solution to the puzzle satisfactory,[2] Iâm not convinced by your claim that this isnât a puzzle for many other people:
Either youâre genuinely happy with recklessness (or timidity), or else you have antecedent commitments to the methodology of decision theory â 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, Iâd gloss âcommitment to viewing every action you take as expressing your attitude to expected consequencesâ here as âcommitment to viewing proposed solutions to decision-theory thought experiments as expressing ideas about what decisions are goodâ â which I take to be nearly a tautology.
So Iâm still having trouble imagining anyone the puzzles arenât supposed to apply to.
The only case I can make for STOCHASTIC is if you canât pre-commit to stopping at the N-th ticket, but can pre-commit to STOCHASTIC for some reason. But now weâre adding extra gerrymandered premises to the problem; it feels like weâve gone astray.
Although if you just intend for this to be solely your solution, and make no claims that itâs better for anyone else, or better in any objective sense then ⌠ok?
This is precisely why itâs a puzzleâthereâs no outcome (always refuse, always take, take N, stochastic) that I can see any consistent justification for.
Interesting comment! But Iâm also not convinced. :P
⌠or, more precisely, Iâm not convinced by all of your remarks. I actually think youâre right in many places, though Iâll start by focusing on points of disagreement.
(1) On Expected Payoffs.
You ask whether Iâm saying: âwhen given a choice, you can just ⌠choose the option with a worse payoff?â
Iâm saying âitâs sometimes better to choose an option with lower expected payoffâ. Still, you might ask: âwhy would I choose an option with lower expected payoff?â
First, I think the decision procedure âchoose the option with the highest expected payoffâ 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 âchoose the action with highest expected payoffâ 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: âyouâre recommending a certain course of action â why (or on what basis) do you recommend that course of action?â
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 âdo I recommend that all rational agents with my values in this decision context follow the decision procedure Iâm using to determine their action?
I think this criteria is independently justified, and indeed more foundational than purported justifications for EU maximization. Obviously, I donât 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 âchoose, at each point, the action with the highest expected payoffâ. Thatâs why I decide in the way I do.
In summary: Beckstead and Thomasâ 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 donât think Iâm 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.
Iâm saying, instead, that the assumption of âcontext-independent preferences over gamblesâ are not given for free, and are, at least, not explicitly provided in Beckstead and Thomasâ setup. I have preferences over fixed states of the world, or âdegenerateâ gambles. Given that I donât possess certainty over future states of the world, I use some decision procedure for navigating this uncertainty. This doesnât mean that I âreallyâ possess context-independent preferences over gambles, and then act in accordance with them.
âWait, are you really saying that you donât prefer a state of the world which delivers Utopia with probability (1âÎľ), and something marginally worse than the current world with the remaining probability?â
Yes, but I think thatâs 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 âbetterâ? Well, itâs better with some probability, and worse with some probability! I donât feel the need to construct some summary term which captures my âall-things-considered betterness ranking under uncertaintyâ.
(2) On STOCHASTIC More Specifically
I think youâre right that some alternative strategy to STOCHASTIC is preferable, and probably youâre right taking exactly N tickets is preferable. Iâll admit that I didnât 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 âdisappointmentâ term incorporated. In which case, youâll always be disappointed if you choose the option with the highest payoff for you. Does this mean that you didnât actually want the option with the highest payoff?
Thanks for the helpful pushback, and apologies for the late reply!
Interesting post! But Iâm not convinced.
Iâll stick to addressing the decision theory section; I havenât thought as much about the population ethics but probably have broadly similar objections there.
(1) What makes STOCHASTIC better than the strategy âtake exactly N tickets and then stopâ?
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 Iâd be pretty disappointed. This indicates to me that I didnât 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 ârecklessâ or âtimidâ strategies to meâat some point, youâre deliberately choosing the worse option, by your own lights! Thatâs at least weird, right?
âTake exactly Nâ 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 âŚ.???[1]
I get that youâre trying to avoid totalizing theoretical frameworks, but you also seem to be saying itâs better in some way that makes it worth choosing, at least for you. But why?
(2) In response to
Iâm having trouble interpreting this more charitably than âwhen given a choice, you can just ⌠choose the option with the worse payoff.â Sure, you can do that. But surely youâd prefer not to? Especially if by âactionsâ here, weâre 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. Youâre writing as if this is a heavy theoretical assumption, but Iâm not sure itâs saying anything more than âyou prefer to do things that you prefer.â
(3) In addition to not finding your solution to the puzzle satisfactory,[2] Iâm not convinced by your claim that this isnât 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, Iâd gloss âcommitment to viewing every action you take as expressing your attitude to expected consequencesâ here as âcommitment to viewing proposed solutions to decision-theory thought experiments as expressing ideas about what decisions are goodâ â which I take to be nearly a tautology.
So Iâm still having trouble imagining anyone the puzzles arenât supposed to apply to.
The only case I can make for STOCHASTIC is if you canât pre-commit to stopping at the N-th ticket, but can pre-commit to STOCHASTIC for some reason. But now weâre adding extra gerrymandered premises to the problem; it feels like weâve gone astray.
Although if you just intend for this to be solely your solution, and make no claims that itâs better for anyone else, or better in any objective sense then ⌠ok?
This is precisely why itâs a puzzleâthereâs no outcome (always refuse, always take, take N, stochastic) that I can see any consistent justification for.
Interesting comment! But Iâm also not convinced. :P
⌠or, more precisely, Iâm not convinced by all of your remarks. I actually think youâre right in many places, though Iâll start by focusing on points of disagreement.
(1) On Expected Payoffs.
You ask whether Iâm saying: âwhen given a choice, you can just ⌠choose the option with a worse payoff?â
Iâm saying âitâs sometimes better to choose an option with lower expected payoffâ. Still, you might ask: âwhy would I choose an option with lower expected payoff?â
First, I think the decision procedure âchoose the option with the highest expected payoffâ 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 âchoose the action with highest expected payoffâ 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: âyouâre recommending a certain course of action â why (or on what basis) do you recommend that course of action?â
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 âdo I recommend that all rational agents with my values in this decision context follow the decision procedure Iâm using to determine their action?
I think this criteria is independently justified, and indeed more foundational than purported justifications for EU maximization. Obviously, I donât 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 âchoose, at each point, the action with the highest expected payoffâ. Thatâs why I decide in the way I do.
In summary: Beckstead and Thomasâ 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 donât think Iâm 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.
Iâm saying, instead, that the assumption of âcontext-independent preferences over gamblesâ are not given for free, and are, at least, not explicitly provided in Beckstead and Thomasâ setup. I have preferences over fixed states of the world, or âdegenerateâ gambles. Given that I donât possess certainty over future states of the world, I use some decision procedure for navigating this uncertainty. This doesnât mean that I âreallyâ possess context-independent preferences over gambles, and then act in accordance with them.
âWait, are you really saying that you donât prefer a state of the world which delivers Utopia with probability (1âÎľ), and something marginally worse than the current world with the remaining probability?â
Yes, but I think thatâs 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 âbetterâ? Well, itâs better with some probability, and worse with some probability! I donât feel the need to construct some summary term which captures my âall-things-considered betterness ranking under uncertaintyâ.
(2) On STOCHASTIC More Specifically
I think youâre right that some alternative strategy to STOCHASTIC is preferable, and probably youâre right taking exactly N tickets is preferable. Iâll admit that I didnât 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 âdisappointmentâ term incorporated. In which case, youâll always be disappointed if you choose the option with the highest payoff for you. Does this mean that you didnât actually want the option with the highest payoff?
Thanks for the helpful pushback, and apologies for the late reply!