The questions involving "90% chance of $1000 or 100% chance of $900" always bother me. I never understand why economists think that a rational actor would consider them equivalent; they're not, unless you are making that choice many many times.
But if I'm given that chance once (which is presumably what most participants assume, since that's not a choice that comes up often in one's life), it's really then a choice between "90% of a ton of free money or 100% chance of a ton of free money". Unless the dollar amounts are radically different, who in their right mind would take the choice that could possibly leave them without a life-changing sum the next day?
In short, there are three types of people: risk-averse, risk-neutral, and risk-preferring. (In the general case, people can exhibit all three types of behavior at different income levels, but let's keep things simple).
Imagine a graph, with income on the x-axis and utility on the y-axis. A risk-averse person will have a concave utility function (like a square-root function), whereas a risk-netural and risk-preferring person would have a straight-line and a convex utility function, respectively.
You have two income levels: $0 and $1000. Now take the two points (0, U(0)) and (1000, U(1000)) and connect them with a straight line. Since we're dealing with a 90% chance = .9 probability, find the point on that line which is 90% of the way between the two points (closer to the second point). This point represents the utility received from the risky situation, or the expected utility. This is not the same thing as the utility of the expected value! Call this point A, with coordinates (Ax and Ay)
Compare U(Ax) this with the value U($900).
For a risk-neutral person, the two values will be exactly the same, as the utility function is a straight line. For a risk-averse person, the second value will be higher, as the utility function is concave with respect to the origin. For a risk-preferring person, the first value will be higher, as the utility function is convex with respect to the origin.
In practice, the utility function may not have a constant concavity, which explains why people buy insurance (which is only justified under risk-averse behavior) yet also buy lottery tickets or gamble at casinos (which is only justified under risk-preferring behavior).
> Who in their right mind would take the choice that could possibly leave them without a life-changing sum the next day?
As you can see, the answer to your question is, 'A person who is risk-preferring' (or operating under risk-preferring situations which are quite common in practice).
Distinguishing between risk-averse/neutral/preferring seems like begging the question to me. Couldn't there be an objective answer to which of three behaviors is the most rational in some situation?
the term "rational" for economists has a very specific meaning. an actor behaving "rationally" has a utility function that satisfies some set of properties, and when confronted with choices, chooses in a way that maximizes that utility function.
Right but which metric is reasonable can (and I believe should) change with scale. I'm risk-preferring when it comes to small amounts -- opportunities to make such decisions come up all the time, so I'll be likely to realize the mean. But I'm risk-averse when it comes to large amounts -- I may only get to make one such decision in my life. Better to minimize the variance here.
This not only explains why people play lottery and buy insurance (playing the lottery non-compulsively involves risking only small amounts of money; not having insurance involves risking large amounts of money), but it also explains why those close to retirement should have risk-averse portfolios, while the young should have risk-preferring portfolios (those close to retirement have few "samples" left to take as it were).
The feeling stupid part got me here. Aftter that, I understood a little bit more. So thanks for that.
But I really believe, that it comes down to "how often" these chances come in ones life.
It can be seen in the gameshow "Who want's to be a millionaire". In Germany we have a fourth joker: people give up the savety-net at 16.000 for an aditional joker. till now everyone of the winners, who got the million, did not take this option.
16.000 is a lot of money, regarding, that you started with 0. on the other hand 500 (the second level net) is really not so much, when you are hanging at 125.000 and having to take a shot at the million. and falling down to 500 feels a lot more stupid. so people become risk adverse (risk of loosing a lot and feeling stupid) a lot faster and don't trust their answer when gambling for that million.
The interesting thing is not that people are risk averse (and thus choose 100% chance of $900), the interesting thing is that people become risk seeking when it comes to losses (and thus choose 90% chance of -$1000).
You're creating a bit of a straw man when it comes to behavioral economists and their view of "rational actors" - the whole field is built around the understanding that there is more to economic decisions than expected value.
That's because Kahneman gets the signs wrong in the OP.
Question 5a is: $900 @ 100%, or $1000 @ 90%
Most people choose $900 @ 100%
Question 5b is: -$1000 + $100 @ 100%, or -$1000 + $1000 @ 10%
Most people choose -$1000 + $1000 @ 10%
Written this way, the false symmetry vanishes, and we see that in both cases, people are risk averse when the payoff is low, and risk-seeking when the payoff is high. Which is to say, people value life-changing sums super-linearly as compared to insignificant sums.
But that's not what the research was about, if I'm understanding it correctly (the research has been mentioned a lot in popular economics literature, so I think that I am understanding it correctly, at least at the high level). The conclusion of the research is that people are more risk-averse when it comes to losses - i.e. they'd rather not win 100$ than loose 100$.
If I'm understanding you correctly, you're saying it's about the amounts; and I think I'd have to agree with you that for the examples to be equivalent, the amounts in 5b should be multiplied by 10. But then again, maybe that would introduce another comprehension hurdle or cognitive correction effect which would render the experiment invalid. Interesting question to ask the original researchers, although I presume that by now (after decades) they've addressed it somewhere already :)
Ya, my theory holds for negative sums too -- I'd rather have a chance of not losing [large amount of money] than lose [almost as large amount of money] for sure. A $900 loss could be enough to bankrupt me -- I need to take the 10% chance.
The problem with that question, to me, is that the 10% difference in outcome is nearly inconsequential. By the time I'm losing (or gaining) $900, what's another $100? If the proportions were different, I think the question would be more interesting.
Yes, however there is a slight chance of winning the odds and not paying anything. The risk is minimal. If the numbers were further apart I don't think the same logic would kick in.
A = $900 lost
B = $9000 lost with a 90% chance
Those are odds I wouldn't want to try. I would take the instant loss knowing that my odds are just not good enough to win if I were to choose B.
The reason that $1000 at 90% odds and $900 at 100% odds are used in this example is the expected value is the same in both cases, making the situations 'equivalent'.
A 90% chance of losing $9000 has an expected value of -$8100.
It seems odd to me that this disproves Bernoulli theory "that a person’s willingness to gamble a certain amount of money was a product of how that amount related to his overall wealth".
If I could pull $900-$1000 from my savings with no immediate consequences, I'd be more likely to spend the $900 at 100%. But if loosing $900-$1000 means I'll have to tell my landlord I'll be late with the rent and then finding someone to borrow it from, and paying it back with interest, the extra $100 aren't significantly more crippling - it's the transaction cost of going through all this bother that's problematic - I'll take a 10% chance.
Come to think of it, I actually did something like this: Prior to moving abroad a while ago, I consulted a lawyer to make sure I did everything right to avoid double taxation. That was a taking on a 100% chance of a rather big expense to avoid an unknown chance of an even larger expense.
It could also be that the utility of money is perceived to be logarithic, and then it depends on the base the individual uses in the personal utitlity function (which probably depends on the persons net worth) which choice is rational. For example,
ln 900 > 0.9 * ln 1000.
But the point is that research has show that almost all people have this bias that makes them much more risk adverse when avoiding losses than when they don't already have the money.
We can speculate a lot on the reasons, but that speculation isn't tested yet.
Economists do not all think that way. Just as there are many differing perspectives in other sciences (feel free to cringe if you are a mathematician, chemist, etc.), there are a range of schools in economics as well. Though I cannot fully delve into the topic at this time, variance is certainly taken into consideration by many economists. Depending on the situation, (number of betting cycles etc.) variance is very important. So, in a one-off bet, it makes sense that the utility between these choices would differ.
I tried to find a good resource that further explains this but wasn't able to quickly find one. If I am able, I will try and post one later today.
On a final note, all of the situations in this quiz are easily correctly answered (or in some cases, predicted) with a basic knowledge of statistics and economics.
By rescaling the numbers, the two questions can be turned into:
- "Would you pay $900 for a 90% chance to win $1000?"
- "Would you pay $100 for a 10% chance to win $1000?"
So the distribution of results really is different. It's not just a phrasing trick. I would still say no to the first and yes to the second. I like positive outliers more than negative ones. This doesn't seem irrational to me.
There's also the fact that we usually cannot estimate the probabilities of events with that kind of precision.
I'd say that most people rarely have enough data to split probabilities into more than about five bins: ~0%, fairly unlikely, coin flip (~50%), fairly likely, and ~100%.
I agree completely with a minor tweak:
"Would you RISK $900 for a 90% chance to win $1000?"
"Would you RISK $100 for a 10% chance to win $1000?"
It's all about managing the risk: generally speaking, I can afford to risk $100, but not $900. Furthermore, I've already spent/borrowed the second $1000 (We're TAKING my existing money, which I presumably have already planned on having). So the first is a windfall, but the second is a real need. So I WON'T risk a large amount of money for a windfall, but I WILL risk a small amount in order to meet a real need. I'd say that's 100% rational.
I don't understand. Kahneman's whole thing is showing that it's wrong to assume that humans are rational actors.
Your second paragraph is exactly the point - the choices are not equivalent to humans.
Humans are rational, just not in the 'mathematically rational' sense. I.e., not just using statistics and probabilities to make decisions. As long as decision-making involves a process (even if it's unconscious) of trade-offs to optimize total utility, it's still rational (well one can debate if should be called 'rational' or have some qualifier attached to it, but then it becomes a definition question, a rather boring one).
Agree 100%. There is so much wrong with all of these questions, and that's only one of the things wrong with this particular one.
In addition to that, there's very good reason for someone to act differently when it's a gain vs. loss at stake. For one thing, this difference is the whole reason that an insurance industry can exist! (And insurance, in turn, is the only reason many kinds of utility-enhancing ventures can exist at all!)
I used to wonder what the point of insurance was when you could just bear the risk yourself, but then I had an insight (that no one else arguing with me managed to bring up):
Utility as a function of how much of a good G that you have, usually increases at a decreasing rate. The first n units provide more of a utility gain than the 2nd n units, and so on. For much the same reason, losing your first n units isn't as bad as losing the 2nd n units, and so on. (It may help to visualize U(n) as a logarithmic curve.)
This is why people can rationally regard it as better to have a guaranteed loss of (at least) N rather than a (1/x) chance of losing x times N, while not also buying a lottery ticket for N that offers a (1/x) chance of gaining x times N. And that, in turn, shows the fundamental asymmetry between insurance and gambling.
Kahnemann must be on the phone with VF right now demanding they correct this article in about ten places.
I think, when the money you may gain or lose goes way over your possible wealth you will start to think really non-linear (non-rational).
but I agree that people with same wealth level will weight risk factor differently ( in each gain or loss). in other words simple utility function is not enough!
the actual question is wrong. to illustrate the framing effect, which underlies prospect theory, the question should be:
1. choose a) 90% for $1000 or b) 100% for $900
a. you just got $1000. choose a) 10% chance to loose $1000 or b) 100% chance to loose $100.
according to rational actor theory, people should choose the same thing both times. however, people often don't. its the framing effect. decisions are different when framed as losses or games.
this builds the foundation for prospect theory. rational actor theory says that your preferences are consistent. prospect theory says that you have a reference point and your utility function is inconsistent and changes depending on your reference point.
The book also discusses that. When the problem is _not_ about a life-changing amount, it is better to take the riskier choice when the expected utility is the same. The explanation is long-ish (and honestly, almost above my head - took me awhile to grok it) and involves the sum of all such incidents over a lifetime, and differences in accumulating utility vs accumulating wealth.
Maybe someone who read the book more recently could take a stab at describing it.
As Kahneman says in the book - every experienced gambler and trader knows that "you win some, you lose some". Although we may not get multiple chances to repeat the same exact gamble, our intuition tends to lead us to minimize risk when the risk is negligible,and to maximize certainty when things are already pretty certain. This is clearly not the optimal approach. By relaxing our personal constraints a little and adjusting our strategy, over the course of a lifetime and the many gambles we take (e.g., starting that web business) they may pay greater dividends than taking our "default" human strategy.
I think in Kahneman's book (unless I'm recalling incorrectly), the situation wasn't "90% chance of $1000 or 100% chance of $900).
It was more like "90% chance of $1000, or 100% chance of $850" (i.e., something a little less than P(X)*X). That was the whole point), people are willing to pay a premium for certainty - and the contrary (are willing to pay a premium to turn a 0.01% chance into a 0% chance)
Same deal. $850 and $1000 pretty much both equate to "some large sum of money" in my mind.
Now if the sums were $8.50 and $10.00 instead, I'd likely make the more rational choice (90% of $10), because such choices with smaller amounts of money come up far more often in my life: the sample size will be large enough that the mean approaches the expected value.
That's the point - you're willing (we all are, usually) to pay a premium for that certainty. In the book he uses all sorts of figures or probabilities (I remember one case, when it was like 99% chance to win one million dollars, or 100% chance to win ${800,000, $600,000, $400,000} -- starts getting a little tricky there, right?)
The importance is the order and context of the questions, both questions basically equates to a: Would you gamble with $1000 and b: Would you gamble with $100.
If only given question b and some time to think you would probably answer no (depending on your risk-preference). But because of question a, the amount and probability in question b seems insignificant which decreases your risk-averseness.
A thousand dollars is not a life-changing sum. It's well within the range in which the utility of money is linear in the amount. (Even if it's large compared to what you have in your pocket, by the time you spend it, your life will be the same as it is now.) If we were talking about a million dollars, your answer would be right.
Such as? Even living below the poverty line in a poor country with soft currency (in which case you probably won't be reading HN or participating in psychology experiments) you're still likely to get through quite a bit more than that in a year.
"In their right mind" or "reasonable" is not what "rational" means in discussions of economics. There also isn't as much of an implication of rational=good and irrational=bad.
But if I'm given that chance once (which is presumably what most participants assume, since that's not a choice that comes up often in one's life), it's really then a choice between "90% of a ton of free money or 100% chance of a ton of free money". Unless the dollar amounts are radically different, who in their right mind would take the choice that could possibly leave them without a life-changing sum the next day?