The idea is supposed to be that turning down the first sort of bet looks like ordinary risk aversion, the phenomenon that some people think concave utility functions explain; but that if the explanation is the shape of the utility function, then those same people who turn down the first sort of bet—which I think a lot of people do—should also turn down the second sort of bet, even though it seems clear that a lot of those people would not turn down a bet that gave them a 50% chance of losing $1k and a 50% chance of winning Jeff Bezos’s entire fortune.
(I personally would probably turn down a 50-50 bet between gaining $10.10 and losing $10.00. My consciously-accessible reasons aren’t about losing $10 feeling like a bigger deal than gaining $10.10, they’re about the “overhead” of making the bet, the possibility that my counterparty doesn’t pay up, and the like. And I would absolutely take a 50-50 bet between losing $1k and gaining, say, $1M, again assuming that it had been firmly enough established that no cheating was going on.)
But would you continue turning down such bets no matter how big your bankroll is? A serious investor can have a lot of automated systems in place to reduce the overhead of transactions. For example, running a casino can be seen as an automated system for accepting bets with a small edge.
(Similarly, you might not think of a millionaire as having time to sell you a ball point pen with a tiny profit margin. But a ball point pen company is a system for doing so, and a millionaire might own one.)
If you were playing some kind of stock/betting market, you would be wize to write a script to accept such bets up to the Kelly limit, if you could do so.
My bankroll is already enough bigger than $10.10 that shortage of money isn’t the reason why I would not take that bet.
I might well take a bet composed of 100 separate $10/$10.10 bets (I’d need to think a bit about the actual distribution of wins and losses before deciding) even though I wouldn’t take one of them in isolation, but that’s a different bet.
The idea is supposed to be that turning down the first sort of bet looks like ordinary risk aversion, the phenomenon that some people think concave utility functions explain; but that if the explanation is the shape of the utility function, then those same people who turn down the first sort of bet—which I think a lot of people do—should also turn down the second sort of bet, even though it seems clear that a lot of those people would not turn down a bet that gave them a 50% chance of losing $1k and a 50% chance of winning Jeff Bezos’s entire fortune.
(I personally would probably turn down a 50-50 bet between gaining $10.10 and losing $10.00. My consciously-accessible reasons aren’t about losing $10 feeling like a bigger deal than gaining $10.10, they’re about the “overhead” of making the bet, the possibility that my counterparty doesn’t pay up, and the like. And I would absolutely take a 50-50 bet between losing $1k and gaining, say, $1M, again assuming that it had been firmly enough established that no cheating was going on.)
But would you continue turning down such bets no matter how big your bankroll is? A serious investor can have a lot of automated systems in place to reduce the overhead of transactions. For example, running a casino can be seen as an automated system for accepting bets with a small edge.
(Similarly, you might not think of a millionaire as having time to sell you a ball point pen with a tiny profit margin. But a ball point pen company is a system for doing so, and a millionaire might own one.)
If you were playing some kind of stock/betting market, you would be wize to write a script to accept such bets up to the Kelly limit, if you could do so.
Also see my reply to koreindian.
My bankroll is already enough bigger than $10.10 that shortage of money isn’t the reason why I would not take that bet.
I might well take a bet composed of 100 separate $10/$10.10 bets (I’d need to think a bit about the actual distribution of wins and losses before deciding) even though I wouldn’t take one of them in isolation, but that’s a different bet.