Regarding decision theory: I responded to you on substack. I’ll stand by my thought that real-world decisions don’t allow accurate probabilities to be stated, particularly in some life-or-death decision. Even if some person offered to play a high-stakes dice game with me, I’d wonder if the dice are rigged, if someone were watching us play and helping the other player cheat, etc.
Separately, it occurred to me yesterday that a procedure to decide how many chances to take depends on how many will meet a pre-existing need of mine, and what costs are associated with not fulfilling that need. For example, if I only need to live 10 more years, or else something bad happens (other than my death), and the chances that I don’t live that extra 10 years are high unless I play your game (as you say, I only have 1 year to live and your game is the only game in town that could extend my life), then I will choose an N of 1. This argument can be extended to however many years. There are plausible futures in which I myself would need to live an extra 100 years, but not an extra 1000, etc. That allows me to select a particular N to play for in accordance with my needs.
Let’s say, though, for the sake of argument, that I need to live the entire 10^50000 years or something bad will happen. In that case, I’m committed to playing your game to the bitter end if I want to play at all. In which case, if I choose to play, it will only be because my current one year of life is essentially worthless to me. All that matters is preventing that bad thing from happening by living an extra 10^50000 years.
Alternatively, my only need for life extension is to live longer than 10^50,000. If I don’t, something bad will happen, or a need of mine won’t be met. In that case, I will reject your game, since it won’t meet my need at all.
This sort of thinking might be clearer in the case of money, instead of years of life. If I owed a debt of 10^50000 dollars, and I only have 1 dollar now, and if in fact, the collector will do something bad to me unless I pay the entire debt, well, then, the question becomes whether your game is the only game in town. If so, then the final question is whether I would rather risk a large chance of dying to try to pay my debt, or whether I would rather live through the collector’s punishment because the money I have already (or earned from playing your game to less than the end) is short of the full repayment amount. If death were preferable to the collector’s punishment and your game was the only game in town, then I would go with playing your game even though my chances of winning are so pitifully small.
Similar thinking applies to smaller amounts of debt owed, and commensurate choice of N sufficient to pay the debt if I win. I will only play your game out to high enough N to earn enough to pay the debt I owe.
Regardless of the payoff amount’s astronomically large size as the game progresses, there is either a size past which the amount is greater than my needs, or my needs are so great that I cannot play to meet my needs (so why play at all), or only playing to the end meets my needs. Then the decision comes down to comparing the cost of losing your game to the cost of not meeting my pre-existing needs.
Oh, you could say, “Well, what if you don’t have a need to fulfill with your earnings from playing the game? What if you just want the earnings but would be ok without them?” My response to that is, “In that case, what am I trying to accomplish by acquiring those earnings? What want (need) would those earnings fulfill, in what amount of earnings, and what is the cost of not acquiring them?”
Whether it’s money or years of life or something else, there’s some purpose(s) to its use that you have in mind, no? And that purpose requires a specific amount of money or years. There’s not an infinitude of purposes, or if there are, then you need to claim that as part of proposing your game. I think most people would disagree with that presumption.
Regarding decision theory: I responded to you on substack. I’ll stand by my thought that real-world decisions don’t allow accurate probabilities to be stated, particularly in some life-or-death decision. Even if some person offered to play a high-stakes dice game with me, I’d wonder if the dice are rigged, if someone were watching us play and helping the other player cheat, etc.
Separately, it occurred to me yesterday that a procedure to decide how many chances to take depends on how many will meet a pre-existing need of mine, and what costs are associated with not fulfilling that need. For example, if I only need to live 10 more years, or else something bad happens (other than my death), and the chances that I don’t live that extra 10 years are high unless I play your game (as you say, I only have 1 year to live and your game is the only game in town that could extend my life), then I will choose an N of 1. This argument can be extended to however many years. There are plausible futures in which I myself would need to live an extra 100 years, but not an extra 1000, etc. That allows me to select a particular N to play for in accordance with my needs.
Let’s say, though, for the sake of argument, that I need to live the entire 10^50000 years or something bad will happen. In that case, I’m committed to playing your game to the bitter end if I want to play at all. In which case, if I choose to play, it will only be because my current one year of life is essentially worthless to me. All that matters is preventing that bad thing from happening by living an extra 10^50000 years.
Alternatively, my only need for life extension is to live longer than 10^50,000. If I don’t, something bad will happen, or a need of mine won’t be met. In that case, I will reject your game, since it won’t meet my need at all.
This sort of thinking might be clearer in the case of money, instead of years of life. If I owed a debt of 10^50000 dollars, and I only have 1 dollar now, and if in fact, the collector will do something bad to me unless I pay the entire debt, well, then, the question becomes whether your game is the only game in town. If so, then the final question is whether I would rather risk a large chance of dying to try to pay my debt, or whether I would rather live through the collector’s punishment because the money I have already (or earned from playing your game to less than the end) is short of the full repayment amount. If death were preferable to the collector’s punishment and your game was the only game in town, then I would go with playing your game even though my chances of winning are so pitifully small.
Similar thinking applies to smaller amounts of debt owed, and commensurate choice of N sufficient to pay the debt if I win. I will only play your game out to high enough N to earn enough to pay the debt I owe.
Regardless of the payoff amount’s astronomically large size as the game progresses, there is either a size past which the amount is greater than my needs, or my needs are so great that I cannot play to meet my needs (so why play at all), or only playing to the end meets my needs. Then the decision comes down to comparing the cost of losing your game to the cost of not meeting my pre-existing needs.
Oh, you could say, “Well, what if you don’t have a need to fulfill with your earnings from playing the game? What if you just want the earnings but would be ok without them?” My response to that is, “In that case, what am I trying to accomplish by acquiring those earnings? What want (need) would those earnings fulfill, in what amount of earnings, and what is the cost of not acquiring them?”
Whether it’s money or years of life or something else, there’s some purpose(s) to its use that you have in mind, no? And that purpose requires a specific amount of money or years. There’s not an infinitude of purposes, or if there are, then you need to claim that as part of proposing your game. I think most people would disagree with that presumption.
What do you all think? Agree? Disagree?