Offered a bet that pays $X if I pick a color and then see if a random ball matches that color, you’ll pay more
I’m not sure I follow. If I were to take this bet, it seems that the prior according to which my utility would be lowest is: you’ll pick a color to match that gives me a 0% chance of winning. So if I’m ambiguity averse in this way, wouldn’t I think this bet is worthless?
(The second point you bring up would make sense to me if this first point did, although then I’d also be confused about the papers’ emphasis on commitment.)
Sorry—you’re right that this doesn’t work. To clarify, I was thinking that the method of picking the color should be fixed ex-ante (e.g. “I pick red as the color with 50% probability”), but that doesn’t do the trick because you need to pool the colors for ambiguity to arise.
The issue is that the problem the paper identifies does not come up in your example. If I’m offered the two bets simultaneously, then an ambiguity averse decision maker, like an EU decision maker, will take both bets. If I’m offered the bets sequentially without knowing I’ll be offered both when I’m offered the first one, then neither an ambiguity-averse nor a risk-averse EU decision-maker will take them. The reason is that the first one offers the EU decision-maker a 50% chance of winning, so given risk-aversion its value is less than 50% of $1. So your example doesn’t distinguish a risk-averse EU decision-maker from an ambiguity-averse one.
So I think unfortunately we need to go with the more complicated examples in the paper. They are obviously very theoretical. I think it could be a valuable project for someone to translate these into more practical settings to show how these problems can come up in a real-world sense.
Thanks!
I’m not sure I follow. If I were to take this bet, it seems that the prior according to which my utility would be lowest is: you’ll pick a color to match that gives me a 0% chance of winning. So if I’m ambiguity averse in this way, wouldn’t I think this bet is worthless?
(The second point you bring up would make sense to me if this first point did, although then I’d also be confused about the papers’ emphasis on commitment.)
Sorry—you’re right that this doesn’t work. To clarify, I was thinking that the method of picking the color should be fixed ex-ante (e.g. “I pick red as the color with 50% probability”), but that doesn’t do the trick because you need to pool the colors for ambiguity to arise.
The issue is that the problem the paper identifies does not come up in your example. If I’m offered the two bets simultaneously, then an ambiguity averse decision maker, like an EU decision maker, will take both bets. If I’m offered the bets sequentially without knowing I’ll be offered both when I’m offered the first one, then neither an ambiguity-averse nor a risk-averse EU decision-maker will take them. The reason is that the first one offers the EU decision-maker a 50% chance of winning, so given risk-aversion its value is less than 50% of $1. So your example doesn’t distinguish a risk-averse EU decision-maker from an ambiguity-averse one.
So I think unfortunately we need to go with the more complicated examples in the paper. They are obviously very theoretical. I think it could be a valuable project for someone to translate these into more practical settings to show how these problems can come up in a real-world sense.