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November 28, 2008


Could it be simply mistrust of whomever will flip the coin (and pay the money)?

I had the same reaction the first time I heard of Ellsberg's paradox: if I am told that there are as many white balls as black balls, I might be able check ex-post whether that's true; if I am not told anything about the distribution of balls, I may fear that if I choose to bet on white you'll SOMEHOW manage to present me with a box of black balls only.

In other words:

"One of these days in your travels, a guy is going to show you a brand-new deck of cards on which the seal is not yet broken. Then this guy is going to offer to bet you that he can make the jack of spades jump out of this brand-new deck of cards and squirt cider in your ear. But, son, do not accept this bet, because as sure as you stand there, you're going to wind up with an ear full of cider." (Guys and Dolls)

Every now and then you run across a piece of research that, even after everything else you've read, still makes you sit up and say AAAARRRRRRRGGGHHHH!

Maybe they're interpreting the question as "how many cents should you count on" for some budgeting purpose, and somehow trying to maximize the expected utility of their estimate. (Subconsciously of course)

I'm guilty of this, at least somewhat. I might expect to win, on average, 1/2 of the coin flips, but I'll make plans based on the assumption that I'll win 1/3, because at least some of the time, I'm going to be unlucky, and I want things to be okay even when I am unlucky.

The Pokemon Trading Card Game has lots of cards that are good when you win coin flips and are bad when you don't. For example, a Baby Pokemon can't be attacked unless your opponent wins a coin flip. When evaluating abilities that depend on coin flips, I make the approximation that I'll win the coin flip 1/3 of the time, and not 1/2, because I'm not satisfied with winning the game only half of the time.

In the trivial case, suppose that I have two choices: either risk the game on a single coin flip, or make a play that will extend the game several more turns, giving both players more decisions to make. Unless I'm already in a poor position, a 50% chance of an immediate win immediately isn't worth the risk of a 50% chance of an immediate loss, because, if I'm better than my opponent (and I'd better be, because I want to win an entire tournament), I should be able to win more than 50% of the games that don't come down to lucky coin flips. However, I might as well bet the game on winning at least one out of three flips under most circumstances (because I'm not that good), and betting the game on winning one out of two flips will depend strongly on how good my position looks.

This is definitely a heuristic with a built-in bias of some kind; is it an unusually stupid one, given that winning only half my games isn't good enough?

I think the answer to this conundrum might lie in the very first line of your post.

"While we tend to be optimistic about our abilities, we are pessimistic about our luck"

In most 'successful' outcomes in life, the contributing factors are some combination of aptitude and randomness the relative proportions of which are ambiguous. We like to ascribe success to the former and failure to the latter.

It makes sense that if people systematically overrate their own aptitudes they will have to systematically under-rate their own luck as well, in order to square their self-image with the actual outcomes they observe in their lives.

Show people a situation they are obviously unable to influence through the exercise of skill and they will assume (on average) that their (imagined) misfortune will be still be present, while also noting their inability to balance it out with the application of their (equally imagined)talent

Exagerated pessimism is the logical outcome.

That's a good point, Doug S. I imagine that a lot of people interpret the question as, "How many wins would you think it reasonable to count on getting." Even though the game doesn't mention any cost to losing, the players are somehow imagining themselves as on the hook for making a wrong prediction of a win. So a risk-aversion bias is kicking in, even though the rules of the game don't really justify it.

It kind of makes sense if you think about life in the real world instead of the laboratory. In the environment in which we evolved, for example, it wouldn't be reasonable to just take someone's word for it if he said that a false prediction of a win would have no cost. I mean, how often does that really happen?

But I expect that this and other possibilities are addressed in the paper, if only I had the time to read it :).

Despair is so tempting! One interesting feature of the modern intarweb is that most mainstream news sites now allow ordinary citizens to comment on the stories of the day. Sometimes I go to these sites (like cnn, msnbc, or fox) and read the comment threads on political or economic stories.

People are certainly much different than the "striving to be objective, rational, kind, and honest" creatures I want them to be. I'm not even sure whether I can really be that different... perhaps I just fool myself.

If Eliezer is unable to convince Robin and most onlookers here (among the most rational people you'll find, all answering 5 to the topic question) of his probability vs time distribution estimate for AI hard takeoff, what chance does he have with the bulk of humanity? Surely rhetorical tricks, "ai-baiting", or religious fervor will be more likely to succeed. Would the ends justify such means?

Maybe even trying is fruitless and a recruitment + organization + implementation effort for building Friendly AI should just proceed without worrying about what most people think.

Note that

- Robin's "10C" means 10 euros;

- The study consisted of face-to-face interviews in the field by "professional interviewers experienced for in-person surveys" (p.4);

- The question was hypothetical;

- "The participant is then asked for his/her own estimation, according to his/her experience and his/her luck, of the number of times heads will occur" (p.4, emph mine);

- On a sample of thirty, if there is no gain associated to the coin tossing, the average is 4.9, and 90% answer 5 (p.3).

It does sound to me as if the way the question was framed would have given the impression that the interviewer wanted to hear an answer based on an (in Carrier's terms) supernatural concept of personal luck. Of course I don't expect that Eliezer would have been swayed :-) but it seems likely to me that there was a degree of please-the-researcher, leading people to give estimates conditional on supernatural personal luck existing.

Of course, it's also plausible that without such a prime, people might infer that the researcher wants to hear the rational result. But even if that justifies the method, it doesn't make the present results stronger... (I wonder whether the question was framed the same way in the sample without winnings. Anyone know if the conventions of the field make this implied by default?)

The direction of the deviation is interesting to me -- I'm not sure I could have predicted it -- but it still seems more likely to me to be a result of the experimental situation than a reliable revelation of expectations in actual games. If people haven't considered the question before, it seems like an invitation to confabulate the result that will make the subject look best. It seems like a high estimate would look better if the interviewer believed it, but worse if it did not sound credible, so it seems plausible that people would give the highest answer that they can feel relatively sure of attaining.

It's a bit hard to square this interpretation with the general trend towards overconfidence, though. Maybe because it is very easy to do an objective test, and very hard to influence the results, so personal luck, if it did exist, would be a particularly hard-to-fake ability? (But perhaps that's a bit too detailed an explanation to be particularly likely?)

if there is no gain associated to the coin tossing, the average is 4.9

This is the scariest bit. If you take ten pence from them when they lose, does the result fly up over 5?

Benja, you're no doubt right about the nature of the question, but let's be honest here - anything but 5 is unforgivable.

We already know that we tend to attribute our successes and the failures of others to dispositions, and our own failures and others' successes to circumstances/luck. Since most people are not unusually successful, they will wind up attributing an unusual amount of bad luck to themselves.

For a lot of these experiments, I strongly suspect that the bias is one of eliciting sympathy. Signalling that you have high capability and low standards due to unfortunate circumstance makes you an ideal trading partner.

And the most reliable signal is one you believe yourself.

So, when it's cheap to underestimate one's luck, one will. I expect you'd see a different result if there were any reason to try to be accurate rather than sympathy-seeking. Say, if you paid based on correctness of estimate rather than on outcome regardless of estimate.

I do know someone who seems to have been unusually lucky at coin flips in the Pokemon Trading Card Game, and we joke together about his "Polish Luck". We started doing so when, during one game, he got nine heads in a row. (Incidentally, there's some speculation that the cardboard "coins" that came with the cards are either biased or manipulable.) We don't take it particularly seriously, though, and we've played an awful lot of games, so there's a reasonable chance that someone would hit a lucky streak that had a one-off probability of 1 in 512.

I've recently come to the conclusion that my bad luck is a real phenomenon. I decided that after about the 100th occurrence of this exact template:

Me: I have problem X.
People experienced with X: Oh, that's easy! You just have to do Y.
Me: *does Y, catastrophically backfires several times over*
Me: Um, hey people, I did Y and let me tell you what happened...
People experienced with X: No. No. No way. There is no way that could have possibly happened. We defy the data.
*after audit of my experience*
People: Holy ****! You just got a bad draw there! Well, once in a blue moon something like that happens, just gotta ignore it and move on...
Me: !!!

So, am I off-base in drawing the inference I did? It's part of why I seriously considered popping the oil bubble and ending the food riots this summer by going long on oil... Good thing I didn't go through with it or I'd be thoroughly convinced I had magic powers.

Actually, maybe I should call up these researchers, answer their question, and then tell them to go through with the coin tosses where I benefit on heads, and see what the average turns out to be...

You. Do. Not. Have. Bad. Luck.

The concept of "bad luck" requires there to be an ontologically basic mental thing called "luck". Now we all know by now that's not allowed.

What does that leave? Well, there's an old saying: "You are the only common denominator in all your failed relationships." Or you could just be reading too much into chance. Take your pick.

Silas: Perhaps you tend to rely on wrong authorities on various subjects?

I think Dagon is right. My suspicion is that social circumstances are overwhelming rational estimation. If this same question were asked in written form or through a computer terminal, I suspect the pessimism effect would diminish or disappear. Note that the effect was more predominant in women, who are more socially aware.

Like the epsilon-delta definition of a limit, the theory of expected value took a

long time to develop. Sorry about the broken comment.

As a poker player, the results don't surprise me given how the question was phrased. People like to credit good luck to skill and mistakes to bad luck, which is made especially obvious in poker. This leads to a large lucky/unlucky imbalance when people are asked to make an estimate "according to his/her experience and his/her luck".

If you polled professional players whose income relies on knowledge of probabilities and who have seen hundreds of losing players exhibit this bias, and you asked them if their luck has been worse or better than average, I'm sure (and based on my small-sample-sized experience) the vast majority would say they've been unlucky. If people with this much education and awareness regarding this bias are still prone, your average person is hopeless.

As a player, I am grateful on whole for this bias. The fact that luck is often the determining factor in poker short term allows this bias to enable massive self delusion regarding one's skill level. Luck is the perfect scape goat. It can also help people to quit however, as often they get convinced they are permanently unlucky in poker and use this as their reason to stop playing.

Isn't this related to risk-aversion somehow?

Jay, Carl, Weldon [the "good luck attributed to skill, therefore people think they have bad luck" faction]: I think I'd buy your explanation if it turned out that the majority of the subjects really try to come up with an estimate based on experience (if somebody came up with a clever way to test for it), but the way I'm imagining the situation, it seems much more likely to me that most subjects confabulate an answer that feels right. Maybe it's because I don't have enough experience with games of luck to form an opinion based on that, and therefore imagine average people don't either? -- On the other hand, I like to play Tali (a Yahtzee-clone) on the computer, trying to beat my own highscores (of all the silly ways to waste time, this must occupy a special place), and I pay attention to the order of types in Tetris, and in both cases I actually get the feeling (not being taken seriously, don't worry) of being lucky above chance; and still I can see myself answering <5 in the study more easily than answering >5.

Dagon's (and Wagster's) position hits closer to my intuitions, for what that's worth...

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