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OK, the media overwhelmingly mentions his activist achievements. But, can I point out it is the same Daniel Ellsberg as in "The Ellsberg paradox" [0]? I have a
by 317070 3y ago
OK, the media overwhelmingly mentions his activist achievements. But, can I point out it is the same Daniel Ellsberg as in "The Ellsberg paradox" [0]?
I have an urn with 30 red balls and 30 green balls. You can pick a color, and you get 10$ if you guessed the next ball I pull out of the urn correctly.
Alternatively, I have another urn with an unknown amount of red and green balls in them. You could also choose to use this urn with a color of your choice, if you want?
Which of these 4 options do you pick?
It turns out that people overwhelmingly prefer the first urn. They have an aversion to epistemic uncertainty, even though from utility theory, all 4 options are equivalent. Even weirder, if we would have played this game repeatedly, the second urn is clearly preferable. Then why do we have this intuition?
The experiment from his paper is slightly different and (in my opinion) harder to understand, but the sketch above illustrates the same paradox between what utility theory tells us is the best decision, and what we intuitively decide.
Do note that he was working at the RAND corporation at the time, where they were running probabilistic simulations of the cold war, the so called Cold War games. (People were literally throwing dice all day to run the simulations of the various nuclear war scenarios). His paradox was a critique to that method, as we don't actually know the probabilities involved in these nuclear scenarios, in the same way as we don't know the amount of red and green balls in one of the urns.
Therefore, we might want to discredit decisions based on scenarios where we don't have good estimates of the probabilities of the outcomes, in favour of scenarios where we do know them.
[0] https://en.wikipedia.org/wiki/Ellsberg_paradox https://en.wikipedia.org/wiki/Ellsberg_paradox
- cubefox 3y ago> Even weirder, if we would have played this game repeatedly, the second urn is clearly preferable. I don't think that's the case? Edit: I get it now, under repetition the probability distribution of the second urn could be inferred, and the gambler could use this information to bet on the more frequent color. However, the Ellsberg paradox only says we prefer known distributions to unknown ones, and under repetition the distributions of both urns would be known. So it doesn't say people would prefer betting on the first urn in the repetition case.
- michaelt 3y agoWhen the game is repeated, does the second urn always have the same distribution of balls?
- deleted 3y ago[deleted]
- 317070 3y agoIt is the case if the balls are being put back. As you play more games, you would figure out the proportion of red and green balls in the second urn. Therefore, you would figure out which is the better colour. Repeated games under epistemic uncertainty actually allows you to get an edge by extracting information and reducing that uncertainty, in comparison to a game which is guaranteed to have no edge for you.
- cubefox 3y agoYeah, but that would change an unknown distribution to a known distribution. Then the Ellsberg paradox does no longer apply.
- 317070 3y agoYes, but why do we intuitively avoid epistemic uncertainty, even though it is something which can only _give_ us an edge here? To make clear: playing this game with an urn which has an equal amount of red and green balls, is the worst case scenario when you get to pick the colour that wins. The second urn can only be the same or better, whether or not you can figure out any information about the balls in it.
- deleted 3y ago[deleted]
- gonehome 3y agoIn a one time game it’s a 50% known bet vs. an unknown bet. 50% is not bad odds?
- puika 3y agoI knew Ellsberg rang a bell. I got to know about him from Peter Norvigs awesome [jupyter] notebooks: https://github.com/norvig/pytudes/blob/main/ipynb/ProbabilityParadox.ipynb https://github.com/norvig/pytudes/blob/main/ipynb/Probabilit.... The probability ones are quite fun to go through and it's very expressive Python.
- furyofantares 3y agoThe first option makes sense to me. Both choices have the same expected value; I understand that, but I also feel it's more likely I have misunderstood something about the second option. I'm crystal clear on the first. Literally any tiebreaker for "which of these options with all the same value" seems fine, I do have to make a decision after all. And I think I'd be slightly skeptical that the experimenter is trying to trick me in some way with the second option in the unlikely case that I've misunderstood it.
- 6gvONxR4sf7o 3y agoI agree this seems to be the reason. The second urn has a more uncertain return in the same way that I'm uncertain about the 98th digit of pi. It's not a random event, but my certainty around it is related to the deductive effort I put in. It's immediately clear that they're the same-ish, and also immediately clear that the first urn doesn't have a gotcha. Still very interesting.
- p_j_w 3y agoThe experimenter can't trick you in the second option because you get to choose the color. Both options have the same expected value.
- furyofantares 3y agoI was clear that I understand that both options have the same expected value. I said so twice in the post.
- inimino 3y agoThis assumes the experimenter has zero ability to predict your choice.
- cubefox 3y agoBut presumably people would pick the first urn even if it had a bit worse expected utility than the second. Say, the green ball wins, and you can choose between either drawing from an urn with 29 green and 31 red balls, or drawing from an urn with an unknown number of red and green balls. The Wikipedia article says that people have active ambiguity aversion, not just that they use ambiguity as a tie breaker.
- corpMaverick 3y agoThe second option is better. To win you have to bet that the second ball is the same color as the first ball. The second option could have 30 and 30 (worst case) or it could have 59 and 1(best case), so almost any ball mix is better or equal than the first option when you only have about 50% chances of wining.
- gameman144 3y agoWhy would 30 and 30 be the worst case? You could have drawn a statistically improbable first ball, no? E.g. in your 59:1 example, you could have drawn the 1 rare ball.
- ajmurmann 3y agoOne draw isn't enough to establish a frequency anyways. You want to draw a few times and then pick a strategy. Of course it's important to differentiate with this between worst case urn composition and worst case draws.
- chirau 3y ago30:30 is not the worst case. You could have picked the only ball of a different color. i.e. 1:59. Best case is 60:0 Worst case is 1:59
- Hermitian909 3y agoLike many "thought experiment paradoxes" I think this makes perfect sense if you get out of the habit of thinking too abstractly. The mathematical assumption is that for the urn with the unknown number of red and green balls all distributions are equally likely and so P(red) = 0.5. But why should I assume they're all equally likely other than that it is part of the problem construction? The reason I prefer the known distribution is because this is a contrived game and my experience with contrived games has conditioned me to expect a "trick" such that I am somehow disadvantaged to lose in a way that is not clear to me. Perhaps whoever set up the game knows my favorite color is green. In probabilistic terms I have a Bayesian prior influencing my choice. In order to answer this paradox "correctly" I need to rely on my experience contrived problems like this to recognize I'm expected to abstract the problem and pretend that my prior does not exist. I find if you resist the urge to abstract in this way a stunningly large proportion of philosophical paradoxes cease to be paradoxes.
- cubefox 3y agoThis explanation (suspected deception/trickery) is mentioned in the Wikipedia article, after the "info-gap" explanation: https://en.wikipedia.org/wiki/Ellsberg_paradox#Possible_explanations https://en.wikipedia.org/wiki/Ellsberg_paradox#Possible_expl... However, it does seem plausible to me that people would prefer the first urn even if they didn't suspect any trickery.
- dash2 3y agoYou can't get away from the problem by assuming that my subjective P(red) ≠ 0.5. It only seems like this because the example was simplified. Look at the "one-urn paradox" version at https://en.wikipedia.org/wiki/Ellsberg_paradox https://en.wikipedia.org/wiki/Ellsberg_paradox. This clarifies that there is no subjective probability that can rationalise people's behaviour. If you prefer betting on red to betting on black, you should also prefer betting on red or yellow to betting on black or yellow.
- Hermitian909 3y agoIMO the one urn problem does nothing to get away from this. Recapping the one urn problem: 90 balls in one urn. 30 are red, 60 are black or yellow in unknown proportion. Users must pick a set of gambles called a scenario, then pick a particular gamble. All balls are equally likely to be pulled. I'll list out the possible probabilities based on possible ground state truth: Scenario 1: Gamble A: Receive $100 if you draw a red ball P(0.33~) Gamble B: Receive $100 if you draw a black ball P(0)-P(0.66~) Scenario 2: Gamble C: Receive $100 if you draw a red or yellow ball P(0.33~)-P(1) Gamble D: Receive $100 if you draw a black or yellow ball P(0.66~) Per my earlier argument, this scenario triggers my "someone is trying to trick and/or scam me" heuristic which creates an expectation that my choice of scenario will be predicted somehow, and that the color distribution will be chosen to maximally disadvantage me. I think most people would feel the same way and so I'd assume that most people would prefer gambles A and D respectively and that's exactly what happens.
- quickthrower2 3y agoBayes tells me … it depends. Is this on a backstreet near a tourist trap?
- Blahah 3y agoYeah, because utility theory is not how people think. Give most people a puzzle that allows for significant gain if you answer correctly, or simply not being harmed if you answer suboptimally, and most people try to escape what they correctly intuit as a trap. Not choosing the best answer is wrong, you don't assume you are smarter than the other person, so opt out.
- oefnak 3y agoThat's really strange, I immediately preferred the second urn, since another probability can't be worse than 50:50. The one other person I asked also chose the 2nd.