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A 7% probability versus 10% probability may be bad news, but it's more than made up for by the increased number of red beans. It's a worse probability, yes, but you're still more likely to win, you see.
I don't understand. Do you mean you are more likely to win with 7 red beans rather than one but also proportionately more likely to lose with 93 non red beans rather than 9? You wink and suggest there is some great wisdom there. I simply don't even know what the hell you are talking about.
I think the idea of the game was you get one chance to pick a bean. After all, if you can just keep picking beans until you've picked all the reds, there's not really much point to the so-called game anymore, is there?
Topo, it's a simple unprobabilistic phase inversion topography manifold calculation, I can hardly see how you could fail to understand it.
A lot of the older comments are ported from Overcoming Bias, which doesn't have LW's thread structure. So if you see posts from 2008 or earlier that look poorly threaded, that's probably what caused it.
Ha, Spock vs McCoy. I think Kirk's position was that it's the affect heuristic that makes us warm, cuddly, and human, data processors, even if it can be faulted in some artificial situations.. This ties in with the other thread about how far we look down possible chains of results in deciding on an action. We're wired to look to proximal results with high affect, and I'm all for it.
The three parts of that paper that I found most interesting were:
Concentrated affect beats diffuse affect. Everybody knows what "obnoxious" means but "intelligent" could mean alot of different things, therefore obnoxious wins, carries a higher weight in the averaging of the descriptions. "More precise affective impressions reflect more precise meanings and carry more weight in impression formation, judgment, and decision making."
The fact that more people chose to accept a gamble when a small loss was involved, because the
BTW, significant data was withheld in the examples given : a) how many dips do you get at the jellybeans ? Do the red ones taste better ? What is their market value with the current weak dollar ? b) 10,000 people overall or 10,000 infected people ? Degree of infectiousness of the disease ? But that's what the affect heuristic is for : taking decisions in situations of incomplete data. 150 people is a single bounded set, 98% of x people sounds as though it just might be a replicable set. Go for it.
One of the things I found interesting in Eliezer's chapter on biases from his site was the repeated cautions about always being aware that these biases can affect us as well, even when we're aware of them. I certainly wouldn't trust the judgement of someone who chalks them up to the belief "most people are almost unbelievably stupid."
That chapter was a great read, btw.
All people are unbelievably stupid most of the time. Some people just manage to stop now and then.
"It's a worse probability, yes, but you're still more likely to win, you see. You should meditate upon this thought until you attain enlightenment as to how the rest of the planet thinks about probability."
rest of planet = retards
Or consider the report of Denes-Raj and Epstein (1994): Subjects offered an opportunity to win $1 each time they randomly drew a red jelly bean from a bowl, often preferred to draw from a bowl with more red beans and a smaller proportion of red beans. E.g., 7 in 100 was preferred to 1 in 10.
How many times do I get to draw, and is it with or without replacement? If I get to draw every bean in the bowl, the number of non-red beans doesn't matter. ;)
"I proudly include myself in the idiot category... no matter how smart you are, you spend much of your day being an idiot." - Scott Adams, wise man
"[I]t's a simple unprobabilistic phase inversion topography manifold calculation..."
Tosh. This ignores the salience of the linear data elicitation projected over dichotomous variables with a fully specified joint distribution.
So now five people have made the same comment, all with the same length (1 to 3 sentences), all with a relatively similar, bland style of expression. Caledonian incidentally also made the same comment. Hmmm...
I wasn't trying to say the rest of the planet is stupid. I'm saying that "probability" is a more difficult concept than it seems. E.g. Mr. Spock predicts a 98% chance of the Enterprise being destroyed, and he does this twenty times and it never happens once. That's the scriptwriter's concept of what the word "probability" means, and it's very closely related to the jellybean problem.
Probability is a "more difficult concept than it seems", you say, but in what sense is it difficult? It does not require a vast and complex formalism to avoid the sort of error we see in the jellybean problem, so clearly it is not an inherently difficult error to avoid. If it is a "difficult concept", then, it's difficult because our brains are fundamentally not wired to deal with it appropriately, which is a failure of the brain, or colloquially a "stupidity".
See also: Straw Vulcan, MillionToOneChance
Spock is half right; the reason the Enterprise isn't destroyed is the MillionToOneChance effect that, in fiction, makes what would otherwise be objectively improbable outcomes more likely because they make for a better story. Spock's just not smart enough to realize that the reason that the Enterprise never does get destroyed is that he's a character in TV show. ;)
On the other hand, maybe he's just afraid of the consequences of breaking the fourth wall...
In fairness to analysts, if you are judging stocks that nobody is familiar with, or even worse, that nobody except for people who are complete morons are familiar with, then the risk-return relationship will break down. In general, judging whether an investment is fairly priced depends on your confidence in the judgement of the informed traders (which may include you, if the investment is familiar). The ordinary economic theory you cite does not apply when the market may become inefficient.
Statistics is actually fun, as the notion of probability is so non-intuitive. There's a 1 in 6 chance of throwing a deuce. What does that mean in the real world ? Well, if I throw the die 6 times, it should come up once ? euh no... Well if I throw 100 sequences of 6 throws I can predict the number of times the deuce will show up ? euh, no.... Well, if I throw 1000 runs of 100 sequences of 6 throws...... sorry, you still don't know one damn thing about what the result will be. So what does probability mean ? It's great ! One of life's rich prizes is to watch someone making a prediction on a particular instance based on statistical reasoning.
I ran across a curious misunderstanding of probability in the SF novel Diamond Mask. In the murder mystery plotline of the book, the protagonist had collected and analyzed data on an (implicitly mutually exclusive and exhaustive) list of eight or nine suspects. The author used probabilities of lower than 20% as a shorthand for not too likely, probabilities of between 20% and 50% as moderately likely, and probabilities above 50% as indicating prime suspects. Unfortunately, there was ~300% total probability in the list. The author could have gotten away with it if she'd just used the word "likelihood" instead of "probability".
I don't think these people are quite as silly as is made out. Let's look at the morality rate example. When you give a morality rate instead of casualty figures, you haven't necessarily communicated what that means for a community, or what it means on a large scale. That information is implied, but you haven't handed it to people on a silver platter. A wise person would create that knowledge himself -- he'd realize that if 20% die, and 5k people are infected, that's 1k dead. He'd think of lots of things like that. He'd figure out what it means in a variety...
Elliot, I suspect something is missing from your comments. The technocratic knowledge you are describing is multiplication. It sounds like you are calling for greater education in basic arithmetic, or perhaps telling people "and use it." Knowing that 20% of 5,000 is 1,000 is not the mark of an exceptionally wise person; it is the mark of a competent elementary school student. There is perhaps a reason why we can support a game show called "Are You Smarter Than a 5th Grader?"
I do not have immediate access to the Yamagishi article. W...
The issue is not multiplication.
Suppose we "put things in perspective" by comparing the figures 1286 and 10000 to quantities people understand better. In my case, we might note my hometown had a bit over 10k people, and the high school had a bit under 1286. That could give me a less abstract understanding of what that kind of casualty rate means. With that understanding, I might be able to make a better judgment about the situation, especially if, like many people, I dislike math and numbers. (Which is perfectly reasonable given how they were sub...
Zubon, knowing when to use multiplication, how to use multiplication, why to use multiplication, and doing so reflexively and without outside prompting, is a bit more technocratic than you might think. Have you ever tried to teach math to someone who is not good at math?
Elliot wrote: "I don't think these people are quite as silly as is made out. " "What is alleged about people seems to be that they have very bad judgment, or they are irrational."
Clearly human beings have a brain relatively well suited to their world which is, nevertheless, far from infallible. Hence stock market crashes, wars, and all manner of other phenomena which demonstrate the imperfect judging ability of the human mind. The human mind commits errors. One needn't condemn the human mind, or the average capacity of humanity, in orde...
So now five people have made the same comment, all with the same length (1 to 3 sentences), all with a relatively similar, bland style of expression.
Great minds think alike. And fools seldom differ.
Eliezer, we could spend a long time commiserating on that one. I used to think the problem was that people never learned algebra properly, but I have begun to wonder how many have a firm grasp on applying second grade math. The hard part seems to be knowing what to divide or multiply by what (teaching Bayes' Theorem is fun for this). Real life is all story problems.
Recent adventures in math include baffling a room with the insight that 12*5/12=5 and explaining how to figure out what percent of 1200 300 is. Perhaps I should be more worried about the technocratic difficulties of addition; Division of Labour has an occasional series of "The Diff."
Eliezer is correct that lots of people are very bad at calculating probabilities, and there are all kinds of well known biases in calculating when affect gets involved, especially small sample biases when one is personally aware of an outlier example, especially a bad one.
However, the opening example is perfectly fine. Eliezer even has it: the higher insurance is to cover the real emotional pain of losing the more personally valued grandfather clock. How much we subjectively value something most certainly depends on the circumstances of how we obtained it. There is nothing irrational about this whatsoever. Rationality above all involves following that old advice of Polonius: know thyself.
With 7 beans in a hundred, I can just keep drawing beans until I get $14 worth, where with 1 in ten, the most I can get is $2. Not only that, I get to eat a hundred free jelly beans. This doesn't seem too mysterious to me.
Barkley Rosser,
The monetary payout isn't higher for the more emotionally valuable object -- it's $100 in both cases. If you missed that, that could explain why people paid more for it; they ignored the dollar figure and assumed that the more valuable item was insured for more.
But if you didn't miss that... Are you suggesting that the $100 is more valuable when it coincides with a greater misfortune?
"A 7% probability versus 10% probability may be bad news, but it's more than made up for by the increased number of red beans. It's a worse probability, yes, but you're still more likely to win, you see. You should meditate upon this thought until you attain enlightenment as to how the rest of the planet thinks about probability."
I think this says less about probability and more about people's need to keep an optimistic outlook on life. You emphasize the positive fact that there's an "increased number of red beans", while ignoring the...
"A 7% probability versus 10% probability may be bad news, but it's more than made up for by the increased number of red beans. It's a worse probability, yes, but you're still more likely to win, you see. You should meditate upon this thought until you attain enlightenment as to how the rest of the planet thinks about probability."
I think this says less about probability and more about people's need to keep an optimistic outlook on life. You emphasize the positive fact that there's an "increased number of red beans", while ignoring the...
P.S. There's something screwy with the comments on this page. My first comment didn't show up at all after I posted, so I reposted, and now it's showing up as "Posted by: Barkley Rosser"...
"This may sound crazy to you, oh Statistically Sophisticated Reader, but if you think more carefully you'll realize that it makes perfect sense. A 7% probability versus 10% probability may be bad news, but it's more than made up for by the increased number of red beans. It's a worse probability, yes, but you're still more likely to win, you see. You should meditate upon this thought until you attain enlightenment as to how the rest of the planet thinks about probability."
I snorted rather loudly upon reading this, and sent the quote to a friend...
A 7% probability versus 10% probability may be bad news, but it's more than made up for by the increased number of red beans.
The comedic timing was awesome! It just broke me into the giggles. They keep sneaking out. I can't stop. I'll be laughing for weeks about this.
One group saw the measure described as saving 150 lives. The other group saw the measure described as saving 98% of 150 lives. The hypothesis motivating the experiment was that saving 150 lives sounds vaguely good - is that a lot? a little? - while saving 98% of something is clearly very good because 98% is so close to the upper bound of the percentage scale. Lo and behold, saving 150 lives had mean support of 10.4, while saving 98% of 150 lives had mean support of 13.6.
Pragmatics of normal language usage prescribes that any explicitly supplied infor...
"Yamagishi (1997) showed that subjects judged a disease as more dangerous when it was described as killing 1,286 people out of every 10,000, versus a disease that was 24.14% likely to be fatal. Apparently the mental image of a thousand dead bodies is much more alarming, compared to a single person who's more likely to survive than not."
I'm not sure this is necessarily due to the mental image. My initial thoughts on reading this were that "1,286 people out of every 10,000" carries connotations implying that at least 10,000 people have b...
The link in the end of text is broken. I've found another one, would you update it?
Check whether it is the same pdf before posting. I believe it is.
I think some of these experiment results are better explained by a bunch of different quirks in human thinking, not Only the affect heuristic. Maybe I'm overconfident in my knowledge here, but still I'm going to go through them in order:
The thing about the clock is obviously the affect heuristic at work and there doesn't seem to be much more to it. The disease example I take issue with however. It seems to me that it's rather about framing than about the affect heuristic. Though peoples emotions about a deadly disease is at play too, the crucial difference...
Is this a derivative of the charity question, about saving the 20,000 birds? Seems very similar. And I love the bias you describe people having even when the stats themselves are not biased at all. This is like a mini phycology lesson! I love it!
Many of the examples given here suffer from what look to be deliberate ambiguities that leave the exact meaning of one of the compared elements wide open to interpretation. Note that I have not examined the source materials for consistency with your summary results, so perhaps this is an issue with the phrasing of your summary rather that the original research. For example:
My mind interprets "a disease [that kills] 1,286 people out of every 10,000" as: "for any given person, there is a 12.86% chance of dying of disease (A)". Since the s...
The way you're summarizing the "disease" study mangles what was described in the abstract, even though the abstract makes your own point. I haven't checked the rest. I went digging for the abstract:
...Participants assessed the riskiness of 11 well-known causes of death. Each participant was presented with an estimation of the number of deaths in the population due to that particular cause. The estimates were obtained from a previous study of naive participants' intuitive estimations. For instance, based on the result of the previous study, the num
The Denes-Raj/Epstein study makes me wonder whether the subjects would still have picked the jar with 100 beans (7 red) if, say, the other jar had been announced to contain 6 beans (5 red) . Is there any “tipping point” (any specific number or percentage of red beans versus other beans) at which the subjects finally choose to follow the probabilities instead of going with “more reds”? What if the other jar had been stated to contain only 5, 4, 3, 2, or 1 bean — but with ALL beans in that jar stated to be red? Would some subjects still go for the jar with
...I think on the disease example that the so-called heuristic interpretation is not necessarily irrational but depends on the ambiguous significance of each description of evidence. The statement that the disease kills 1,286 people out of every 10,000 can be interpreted as the report of a killing and is equivalent to "the disease is definitely fatal to at least some people". However the statement that the disease is 24.14% likely to be fatal can be interpreted as merely a speculation of the disease's potential fatality.
This may sound rational—why not pay more to protect the more valuable object?—until you realize that the insurance doesn’t protect the clock, it just pays if the clock is lost, and pays exactly the same amount for either clock. (And yes, it was stated that the insurance was with an outside company, so it gives no special motive to the movers.)
There's always the hope that, if enough customers pay the outside company enough, it'll be zealous and make the movers an offer they can't refuse.
The affect heuristic is when subjective impressions of goodness/badness act as a heuristic—a source of fast, perceptual judgments. Pleasant and unpleasant feelings are central to human reasoning, and the affect heuristic comes with lovely biases—some of my favorites.
Let's start with one of the relatively less crazy biases. You're about to move to a new city, and you have to ship an antique grandfather clock. In the first case, the grandfather clock was a gift from your grandparents on your 5th birthday. In the second case, the clock was a gift from a remote relative and you have no special feelings for it. How much would you pay for an insurance policy that paid out $100 if the clock were lost in shipping? According to Hsee and Kunreuther (2000), subjects stated willingness to pay more than twice as much in the first condition. This may sound rational—why not pay more to protect the more valuable object?—until you realize that the insurance doesn't protect the clock, it just pays if the clock is lost, and pays exactly the same amount for either clock. (And yes, it was stated that the insurance was with an outside company, so it gives no special motive to the movers.)
All right, but that doesn't sound too insane. Maybe you could get away with claiming the subjects were insuring affective outcomes, not financial outcomes—purchase of consolation.
Then how about this? Yamagishi (1997) showed that subjects judged a disease as more dangerous when it was described as killing 1,286 people out of every 10,000, versus a disease that was 24.14% likely to be fatal. Apparently the mental image of a thousand dead bodies is much more alarming, compared to a single person who's more likely to survive than not.
But wait, it gets worse.
Suppose an airport must decide whether to spend money to purchase some new equipment, while critics argue that the money should be spent on other aspects of airport safety. Slovic et. al. (2002) presented two groups of subjects with the arguments for and against purchasing the equipment, with a response scale ranging from 0 (would not support at all) to 20 (very strong support). One group saw the measure described as saving 150 lives. The other group saw the measure described as saving 98% of 150 lives. The hypothesis motivating the experiment was that saving 150 lives sounds vaguely good—is that a lot? a little?—while saving 98% of something is clearly very good because 98% is so close to the upper bound of the percentage scale. Lo and behold, saving 150 lives had mean support of 10.4, while saving 98% of 150 lives had mean support of 13.6.
Or consider the report of Denes-Raj and Epstein (1994): Subjects offered an opportunity to win $1 each time they randomly drew a red jelly bean from a bowl, often preferred to draw from a bowl with more red beans and a smaller proportion of red beans. E.g., 7 in 100 was preferred to 1 in 10.
According to Denes-Raj and Epstein, these subjects reported afterward that even though they knew the probabilities were against them, they felt they had a better chance when there were more red beans. This may sound crazy to you, oh Statistically Sophisticated Reader, but if you think more carefully you'll realize that it makes perfect sense. A 7% probability versus 10% probability may be bad news, but it's more than made up for by the increased number of red beans. It's a worse probability, yes, but you're still more likely to win, you see. You should meditate upon this thought until you attain enlightenment as to how the rest of the planet thinks about probability.
Finucane et. al. (2000) tested the theory that people would conflate their judgments about particular good/bad aspects of something into an overall good or bad feeling about that thing. For example, information about a possible risk, or possible benefit, of nuclear power plants. Logically, information about risk doesn't have to bear any relation to information about benefits. If it's a physical fact about a reactor design that it's passively safe (won't go supercritical even if the surrounding coolant systems and so on break down), this doesn't imply that the reactor will necessarily generate less waste, or produce electricity at a lower cost, etcetera. All these things would be good, but they are not the same good thing. Nonetheless, Finucane et. al. found that for nuclear reactors, natural gas, and food preservatives, presenting information about high benefits made people perceive lower risks; presenting information about higher risks made people perceive lower benefits; and so on across the quadrants.
Finucane et. al. also found that time pressure greatly increased the inverse relationship between perceived risk and perceived benefit, consistent with the general finding that time pressure, poor information, or distraction all increase the dominance of perceptual heuristics over analytic deliberation.
Ganzach (2001) found the same effect in the realm of finance. According to ordinary economic theory, return and risk should correlate positively—or to put it another way, people pay a premium price for safe investments, which lowers the return; stocks deliver higher returns than bonds, but have correspondingly greater risk. When judging familiar stocks, analysts' judgments of risks and returns were positively correlated, as conventionally predicted. But when judging unfamiliar stocks, analysts tended to judge the stocks as if they were generally good or generally bad—low risk and high returns, or high risk and low returns.
For further reading I recommend the fine summary chapter in Slovic et. al. 2002: "Rational Actors or Rational Fools: Implications of the Affect Heuristic for Behavioral Economics."
Denes-Raj, V., & Epstein, S. (1994). Conflict between intuitive and rational processing: When people behave against their better judgment. Journal of Personality and Social Psychology, 66, 819-829.
Finucane, M. L., Alhakami, A., Slovic, P., & Johnson, S. M. (2000). The affect heuristic in judgments of risks and benefits. Journal of Behavioral Decision Making, 13, 1-17.
Ganzach, Y. (2001). Judging risk and return of financial assets. Organizational Behavior and Human Decision Processes, 83, 353-370.
Hsee, C. K. & Kunreuther, H. (2000). The affection effect in insurance decisions. Journal of Risk and Uncertainty, 20, 141-159.
Slovic, P., Finucane, M., Peters, E. and MacGregor, D. 2002. Rational Actors or Rational Fools: Implications of the Affect Heuristic for Behavioral Economics. Journal of Socio-Economics, 31: 329–342.
Yamagishi, K. (1997). When a 12.86% mortality is more dangerous than 24.14%: Implications for risk communication. Applied Cognitive Psychology, 11, 495-506.