An assumption that seems to be present in the betting framework here is that you frequently encounter bets which have positive EV.
I think in real life, that assumption is not particularly realistic. Most people do not encounter a lot of opportunities whose EV (in money) is significantly above ordinary things such as investing in the stock market.
Suppose you have $100k and are in the situation where you only win 10% of the time, but if you do you get paid out 10,000x your bet size. But after the bet you do not expect to find similarly opportunities again and you also plan to donate everything to GiveDirectly.
If you were to rank optimize, which, iiuc, mean maximizing the probability of being “the richest person in the room”, then you should bet nothing, because then you have a 90% probability of being richer than the counterfactual-you who bets a fraction of the wealth. But if you care a lot about the value your donations provide to the world, then you should probably bet $40k-$100k (depending on the diminishing returns of money to GiveDirectly, or maybe valuing having a bit of money for selfish reasons).edit: But if you care a lot about the value your donations provide to the world, then you should probably bet all $100k (there are likely diminishing returns of money given to GiveDirectly, but I think the high upside of the bet outweighs the diminishment by a big margin. Also, by assumption of this thought experiment, you were not planning to keep any money for selfish purposes.).
Is this 100k personal money or money budjeted for going to donation? Why being only able to give 60k because of lost 40k on the downturn is less important than being able to give 400 060 000 on the upturn?
If you calculate the bet size having your personal money as the reference level but evaluate impact how much you were going to give seems inconsistent. If you have 100k personal and bet 40k and only give the bet proceeds to donation then the reference level is 40k instead of 100k (assuming that without taking the oppportunity you would have just donated your ante directly).
Yes, good catch. I edited. I made two mistakes in the above:
confused personal money with “altruistic money”: In the beginning of the comment I assumed that all money would be donated, and none kept. By the end of my comment, my mental model has apparently shifted to also include personal money/”selfish money” (which would be justified for people to keep).
I included a range of numbers for the possible bet size, and thought that lower bet amounts would be justified due to diminishing returns. Checking the numbers again, the diminishing returns are not that significant (at the scale of $1B likely far below 10x), and my opinion is now that you should bet everything.
Yes, endorsed. That should probably be mentioned explicitly. (e: added to the post)
(Technically neither of the technical definitions I gave applies here. And this is a case where you can’t maximize every percentile simultaneously—maximizing your 11th percentile returns means betting nothing, and maximizing your 10th percentile means betting everything. But yes, for a single bet, maximizing “probability of ending up richer than I would have, if I had bet a different amount but the result was the same” is probably the natural way to extend the concept to cases like this, and it means betting nothing in this case.)
An assumption that seems to be present in the betting framework here is that you frequently encounter bets which have positive EV.
I think in real life, that assumption is not particularly realistic. Most people do not encounter a lot of opportunities whose EV (in money) is significantly above ordinary things such as investing in the stock market.
Suppose you have $100k and are in the situation where you only win 10% of the time, but if you do you get paid out 10,000x your bet size. But after the bet you do not expect to find similarly opportunities again and you also plan to donate everything to GiveDirectly. If you were to rank optimize, which, iiuc, mean maximizing the probability of being “the richest person in the room”, then you should bet nothing, because then you have a 90% probability of being richer than the counterfactual-you who bets a fraction of the wealth.
But if you care a lot about the value your donations provide to the world, then you should probably bet $40k-$100k (depending on the diminishing returns of money to GiveDirectly, or maybe valuing having a bit of money for selfish reasons).edit: But if you care a lot about the value your donations provide to the world, then you should probably bet all $100k (there are likely diminishing returns of money given to GiveDirectly, but I think the high upside of the bet outweighs the diminishment by a big margin. Also, by assumption of this thought experiment, you were not planning to keep any money for selfish purposes.).Is this 100k personal money or money budjeted for going to donation? Why being only able to give 60k because of lost 40k on the downturn is less important than being able to give 400 060 000 on the upturn?
If you calculate the bet size having your personal money as the reference level but evaluate impact how much you were going to give seems inconsistent. If you have 100k personal and bet 40k and only give the bet proceeds to donation then the reference level is 40k instead of 100k (assuming that without taking the oppportunity you would have just donated your ante directly).
Yes, good catch. I edited. I made two mistakes in the above:
confused personal money with “altruistic money”: In the beginning of the comment I assumed that all money would be donated, and none kept. By the end of my comment, my mental model has apparently shifted to also include personal money/”selfish money” (which would be justified for people to keep).
I included a range of numbers for the possible bet size, and thought that lower bet amounts would be justified due to diminishing returns. Checking the numbers again, the diminishing returns are not that significant (at the scale of $1B likely far below 10x), and my opinion is now that you should bet everything.
Yes, endorsed. That should probably be mentioned explicitly. (e: added to the post)
(Technically neither of the technical definitions I gave applies here. And this is a case where you can’t maximize every percentile simultaneously—maximizing your 11th percentile returns means betting nothing, and maximizing your 10th percentile means betting everything. But yes, for a single bet, maximizing “probability of ending up richer than I would have, if I had bet a different amount but the result was the same” is probably the natural way to extend the concept to cases like this, and it means betting nothing in this case.)