I agree that it would be weird to accept the lottery with a positive EU only if you take it some specific number of times. In the normal, everyday decision making I wouldn’t argue for this. Indeed, I think the EU is the right approach to making decisions under uncertainty. I’m willing to follow it, even if chances of success are low, but the stakes are high enough to make the EU positive. What I argue for, is the justification why I’m willing to follow the EU. I don’t think that this is self-evident, that I should choose the option with the highest EU. I think that what makes following the EU the right choice is the law of large numbers. If I have to pay 10$ for a lottery where you have 99,9% chance that you will win nothing and 0,1% chance that you will win 100000000000 $ then I think I should pay. But the rationale why I should play, at least for me, is not that it is intrinsically worth it/rational. For me the reason why this is a good option , is that it finally will pay off, and in the end I will have a lot more money than I had at the start. Also, I think this holds also if I was able to buy only one ticket for that lottery, because even if I will gain nothing from this particular choice, still I will encounter low probability-high stakes choices many times in my life, so finally it would be worth it. My point is just that EU needs the law of large numbers or repeated decision making or series of choices, however we call it, to be the rational strategy. And I don’t mean necessarily ,,choices concerning playing this particular lottery”. I mean making any choices under uncertainty. In other words, in the end the EU is more probable than improbable, to produce the outcome with the highest upside. This is why I think that this first order approach, which I described earlier, in fact implies the EU when we look at our situation holistically. For this reason, I regard the EU as rational.
My whole point is basically that it won’t harm you, if you make the one exception from following the EU in the case of one particular low probability-high stake decision, that is Pascal’s wager. The condition is that you need to be able to reliably restrict yourself to making just one (or at least limited) number of exceptions, since finally you will encounter the case when despite of the low probability, consequences will occur to be real.
Sure, this addition may seem ad hoc an a bit theoretically inelegant. It’s also true that it demands that assumption of how much choices you will have occasion to make, but it doesn’t look very problematic for me. All things considered, it seems to me that the rationale standing behind it (derived from the way in which I think the EU is justified) is enough to justify it.
You’ve mentioned also those infinite possibilities of different Gods only slightly different form each other. Fair enough, in this case maybe the infinitesimals are the right representation of credence that one should have in such options. Nevertheless, if we are to follow the EU in literally every case, then it still seems to make sense to determine which God (or set of possible Gods similar to each other) has the highest probability and then to accept the wager. Maybe the acceptance of the wager would not look like the proponents of it usually imagine (i.e. accepting particular religion) but rather devoting yourself to doing research to find out which God is the most probable one (because of the information value). Nevertheless, it still would have a significant influence on the way we live. And maybe this is fine and we should just accept this conclusion, I’m not sure about it. However, the approach that I’ve proposed here for me seems to be rather more rational.
There is the issue whether one believes the stated chances are real or whether one is in error about it. If you believed that there was a 1/4th chance of heads when in fact the coin was fair then your betting will be lead astray. However if the odds are correct and the math says you end up with more money there is no way to argue that you can forgo the option and claim to be a money grabbing agent.
We could think of some agent wanting to not buy a payout biased lottery ticket where they think they wil save the cost of the ticket and get to keep to call themselfs as a good decision maker. If the odds are 10% of 1000$ for 1 $ ticket and the agent thinks they expect to lose on money they have made a math error. You don’t get to call yourself being able to calculate odds correctly if you make a limited amount of mistakes. And certainly you don’t end up going “over the limit” of “all accruable winnings” by the price of ticket. Either the ticket price is part of the accruable winnings, or the total is some subtotal that doesn’t actually represent everything achievable.
The usual worry about what would be the policy implication of accepting the pascal wager would be that you would be prone to be pascal mugged. Anyone can fabricate a very remote very low comfortability threat and ask for finite compensation to not do it. But a website saying you are the 1000000000th visitor to the website is not a very good evidence of those chances being real. And in a way very higly tuned chances need very much data to be well founded. That way almost anyone can make 50:50 claims but very few people can plausibly state any 0.00000001% odds. Thus in a finite aged universe none can have the inductive support for any infinidesimal chance.
There can be many dimensions of asking indecidably low odds of what could happen. An agent that systematically excused each of the questions to be a one-off exception could be totally prey to rare events.But one has to distinguish doing well in a the model and doing well in fact. You don’t get to not get victimised by supernovas if you lack the capacity to model supernovas. It can make sense to focus on what you can model and stay silent on what you can’t model but pushing the edge on what you can model can be critical.
Thanks for your comment. I’ve thought through the issue cerafully and I’m no longer so confident about this topic. Now I’m planning to read more about the Pascal’s wager and about the decision theory in general. I want to think about it more, and do my best to come up with a good enough solution for this problem.
Thank you for the whole disccusion and the time devoted for responding to my arguemnts.
I agree that it would be weird to accept the lottery with a positive EU only if you take it some specific number of times. In the normal, everyday decision making I wouldn’t argue for this. Indeed, I think the EU is the right approach to making decisions under uncertainty. I’m willing to follow it, even if chances of success are low, but the stakes are high enough to make the EU positive. What I argue for, is the justification why I’m willing to follow the EU. I don’t think that this is self-evident, that I should choose the option with the highest EU. I think that what makes following the EU the right choice is the law of large numbers. If I have to pay 10$ for a lottery where you have 99,9% chance that you will win nothing and 0,1% chance that you will win 100000000000 $ then I think I should pay. But the rationale why I should play, at least for me, is not that it is intrinsically worth it/rational. For me the reason why this is a good option , is that it finally will pay off, and in the end I will have a lot more money than I had at the start. Also, I think this holds also if I was able to buy only one ticket for that lottery, because even if I will gain nothing from this particular choice, still I will encounter low probability-high stakes choices many times in my life, so finally it would be worth it.
My point is just that EU needs the law of large numbers or repeated decision making or series of choices, however we call it, to be the rational strategy. And I don’t mean necessarily ,,choices concerning playing this particular lottery”. I mean making any choices under uncertainty. In other words, in the end the EU is more probable than improbable, to produce the outcome with the highest upside. This is why I think that this first order approach, which I described earlier, in fact implies the EU when we look at our situation holistically. For this reason, I regard the EU as rational.
My whole point is basically that it won’t harm you, if you make the one exception from following the EU in the case of one particular low probability-high stake decision, that is Pascal’s wager. The condition is that you need to be able to reliably restrict yourself to making just one (or at least limited) number of exceptions, since finally you will encounter the case when despite of the low probability, consequences will occur to be real.
Sure, this addition may seem ad hoc an a bit theoretically inelegant. It’s also true that it demands that assumption of how much choices you will have occasion to make, but it doesn’t look very problematic for me. All things considered, it seems to me that the rationale standing behind it (derived from the way in which I think the EU is justified) is enough to justify it.
You’ve mentioned also those infinite possibilities of different Gods only slightly different form each other. Fair enough, in this case maybe the infinitesimals are the right representation of credence that one should have in such options. Nevertheless, if we are to follow the EU in literally every case, then it still seems to make sense to determine which God (or set of possible Gods similar to each other) has the highest probability and then to accept the wager. Maybe the acceptance of the wager would not look like the proponents of it usually imagine (i.e. accepting particular religion) but rather devoting yourself to doing research to find out which God is the most probable one (because of the information value). Nevertheless, it still would have a significant influence on the way we live. And maybe this is fine and we should just accept this conclusion, I’m not sure about it. However, the approach that I’ve proposed here for me seems to be rather more rational.
There is the issue whether one believes the stated chances are real or whether one is in error about it. If you believed that there was a 1/4th chance of heads when in fact the coin was fair then your betting will be lead astray. However if the odds are correct and the math says you end up with more money there is no way to argue that you can forgo the option and claim to be a money grabbing agent.
We could think of some agent wanting to not buy a payout biased lottery ticket where they think they wil save the cost of the ticket and get to keep to call themselfs as a good decision maker. If the odds are 10% of 1000$ for 1 $ ticket and the agent thinks they expect to lose on money they have made a math error. You don’t get to call yourself being able to calculate odds correctly if you make a limited amount of mistakes. And certainly you don’t end up going “over the limit” of “all accruable winnings” by the price of ticket. Either the ticket price is part of the accruable winnings, or the total is some subtotal that doesn’t actually represent everything achievable.
The usual worry about what would be the policy implication of accepting the pascal wager would be that you would be prone to be pascal mugged. Anyone can fabricate a very remote very low comfortability threat and ask for finite compensation to not do it. But a website saying you are the 1000000000th visitor to the website is not a very good evidence of those chances being real. And in a way very higly tuned chances need very much data to be well founded. That way almost anyone can make 50:50 claims but very few people can plausibly state any 0.00000001% odds. Thus in a finite aged universe none can have the inductive support for any infinidesimal chance.
There can be many dimensions of asking indecidably low odds of what could happen. An agent that systematically excused each of the questions to be a one-off exception could be totally prey to rare events.But one has to distinguish doing well in a the model and doing well in fact. You don’t get to not get victimised by supernovas if you lack the capacity to model supernovas. It can make sense to focus on what you can model and stay silent on what you can’t model but pushing the edge on what you can model can be critical.
Thanks for your comment. I’ve thought through the issue cerafully and I’m no longer so confident about this topic. Now I’m planning to read more about the Pascal’s wager and about the decision theory in general. I want to think about it more, and do my best to come up with a good enough solution for this problem.
Thank you for the whole disccusion and the time devoted for responding to my arguemnts.