Loss aversion

[Bill Spight]

That is a bit extreme, and nowadays we tend to think about the future in terms of probabilities. But the study of probability is modern, and not completely understood, even by experts. One thing that trips them up is absolute infinity. It is by no means clear that you can talk about...

This reminds me of debates between those with a "bayesian view" of probability and those with a "frequentist view". As I understand it, frequentists view probability as a measurement of an event that has happened. For example, if you flipped a coin 100 time, you can count the number of flips to come to a probability for that coin. It is purely observational.

The bayesian view of probability, in contrast, allows for probability to be measurement of uncertainty about future events. In the case of flipping a coin, you may have a prior belief/assumption that the coin will come up heads 50% of the time.

Using this practically ina learning algorithm, for example, you have your prior probability that really is like your hypothesis from the scientific method. Then you perform an experiment. Observe. Then update your prior and repeat.

From a frequentist's view, we do not set an initial prior probability because we go only on prior observation.

In the long run, the two methods converge.

However, am partial to the bayesian view because using experience from other endeavors can sometimes allow one to make guesses about the future more accurately.

But it's just a hypothesis, so the essential thing to remember is to update your belief if observation deems it necessary!

BTW, Keynes was a Bayesian.

[Bill Spight]

Oh?

Well, Aristotle thought that all statements about future events were false.

Oh, ya? Well that's funny, because happen to have Aristotle right here...

It is therefore plain that it is not necessary that of an affirmation and a denial, one should be true and the other false.

All necessary statements about future events are false. (That includes statements about necessary falsity, of course. I'm such a geek.)

I stand corrected. Thanks. I had not realized that Aristotle anticipated fuzzy logic.

In his Treatise on Probability, J. M. Keynes, also a smart guy and a modern economist, besides, proposes that not all probabilities are numerical, and are only partially ordered. He goes on at some length to explain why the practices of bookies, underwriters, and businessmen does not mean that all probabilities are numerical. Recent talk about Black Swans and unknowables is not just about "fat tails" of probability distributions. It is in the vein of Aristotle and Keynes.

But I don't think Keynes was against the lifetime income hypothesis. Was he? I mean, it's a little bit anachronistic to talk about Keynes position on this since the issue was only really fleshed out after he died, but I believe a lot of things he says about savings and investment only make sense if you believe that people spend as though they had a whole lifetime's worth of income to draw on on any given day.

To be sure, we do not know what Keynes would have thought about it. I do not think that he would quarrel with the idea that people's choices anticipate future income. However, I do think that he would quarrel with the idea that there is a numerical mathematical expectation of that income.

Like the (possibly apocryphal) woman who said, "The lottery is my pension plan." She plays the lottery even though she knows that it is unlikely that she will win and that she will likely have less money in her old age than if she put that money in the bank, because if she does strike it rich, she will enjoy her retirement, and if she does not strike it rich, she will enjoy it only a little less than if she put the money in the bank. Her choice is not the result of exact calculation, nor does it need to be.

[illluck]

Like the (possibly apocryphal) woman who said, "The lottery is my pension plan." She plays the lottery even though she knows that it is unlikely that she will win and that she will likely have less money in her old age than if she put that money in the bank, because if she does strike it rich, she will enjoy her retirement, and if she does not strike it rich, she will enjoy it only a little less than if she put the money in the bank. Her choice is not the result of exact calculation, nor does it need to be.

Yes. In finance this preference for possibility of large gains is actually numerically captured in skewness preference (though of course you are absolutely right that in the real world human beings don't really make decisions with such calculations). Other common factors of a return distribution that are often considered include risk (the focus here) and kurtosis (the "fat-tailed-ness" of the return distribution).

[shapenaji]

As someone with a math background, I realize that anything over 100 is a "good bet" however, for those poker players out there, never forget to factor in your Z, the number of bets you can reasonably make.

This is a GOOD question, (from a mathematical perspective) pure expectation value calculations can have a flaw. I forget the name of the paradox, but suppose I offer you this proposal,

you can either have

A: $10 now

or

B: I will flip a coin until it lands tails, you will get (2^X) * 50 cents where X is the number of heads.


I imagine most folks would take the first option, but purely mathematically, the second option has an infinite expectation value, if you are "reasonable" in your math, you should take the second option.


This led to the introduction of value functions, if you are deciding on a bet, you must also factor in the value that YOU receive from the reward. And in this case, you must factor in the damage that losing $100 would have on you.

Clearly, if you only have $100 to your name, you would never take this bet, because the value of that first $100 is worth considerably more than the value of the second $100.

[Suji]

As someone with a math background, I realize that anything over 100 is a "good bet" however, for those poker players out there, never forget to factor in your Z, the number of bets you can reasonably make.

This is a GOOD question, (from a mathematical perspective) pure expectation value calculations can have a flaw. I forget the name of the paradox, but suppose I offer you this proposal,

you can either have

A: $10 now

or

B: I will flip a coin until it lands tails, you will get (2^X) * 50 cents where X is the number of heads.


I imagine most folks would take the first option, but purely mathematically, the second option has an infinite expectation value, if you are "reasonable" in your math, you should take the second option.

While people should take the second option in theory, people should take the first option in practice. To get a bigger gain than $10, you need at minimum 5 heads to exceed the $10. That's only a 1/32nd chance (roughly 3%) of getting above the initial $10 on the first go around. While possible it's not likely, and I wouldn't take those odds and I'm someone with a math background as well.

[jts]

you can either have
A: $10 now
or
B: I will flip a coin until it lands tails, you will get (2^X) * 50 cents where X is the number of heads.

While people should take the second option in theory, people should take the first option in practice. To get a bigger gain than $10, you need at minimum 5 heads to exceed the $10. That's only a 1/32nd chance (roughly 3%) of getting above the initial $10 on the first go around. While possible it's not likely, and I wouldn't take those odds and I'm someone with a math background as well.

Eh. These odds are so hugely, hugely better than the odds of a normal state-sponsored lottery. Option B is the equivalent of thousands of dollars worth of lottery tickets, isn't it? The odds are hard to parse, but I have trouble believing that psychologists had trouble finding people who would prefer thousands of dollars of lottery tickets to $10.

[shapenaji]

As someone with a math background, I realize that anything over 100 is a "good bet" however, for those poker players out there, never forget to factor in your Z, the number of bets you can reasonably make.

This is a GOOD question, (from a mathematical perspective) pure expectation value calculations can have a flaw. I forget the name of the paradox, but suppose I offer you this proposal,

you can either have

A: $10 now

or

B: I will flip a coin until it lands tails, you will get (2^X) * 50 cents where X is the number of heads.


I imagine most folks would take the first option, but purely mathematically, the second option has an infinite expectation value, if you are "reasonable" in your math, you should take the second option.

While people should take the second option in theory, people should take the first option in practice. To get a bigger gain than $10, you need at minimum 5 heads to exceed the $10. That's only a 1/32nd chance (roughly 3%) of getting above the initial $10 on the first go around. While possible it's not likely, and I wouldn't take those odds and I'm someone with a math background as well.

So the reason why it's a paradox is that most of the time, the second bet is just objectively worse. But, the degree of the payout is in direct proportionality to the unlikeliness of the outcome, So the paradox arises because in an expectation value calculation, we assume that 1000 dollars is 10 times better than 100 dollars, even if it's 10 times less likely. There is a non-zero probability of millions of dollars worth of payout here. And even though it's a million times less likely, those possibilities add up.

[Go_Japan]

This reminds me of debates between those with a "bayesian view" of probability and those with a "frequentist view". As I understand it, frequentists view probability as a measurement of an event that has happened. For example, if you flipped a coin 100 time, you can count the number of flips to come to a probability for that coin. It is purely observational.

The bayesian view of probability, in contrast, allows for probability to be measurement of uncertainty about future events. In the case of flipping a coin, you may have a prior belief/assumption that the coin will come up heads 50% of the time.

Using this practically ina learning algorithm, for example, you have your prior probability that really is like your hypothesis from the scientific method. Then you perform an experiment. Observe. Then update your prior and repeat.

From a frequentist's view, we do not set an initial prior probability because we go only on prior observation.

In the long run, the two methods converge.

However, am partial to the bayesian view because using experience from other endeavors can sometimes allow one to make guesses about the future more accurately.

But it's just a hypothesis, so the essential thing to remember is to update your belief if observation deems it necessary!

This reminds me of something I studied in grad school on experiments comparing ability to process probabilities and frequencies. When experimenters asked individuals to evaluate fictional situations (like word problems), groups that were given problems described as frequencies did better answering the questions than those who were given the same problems described in percentages (probabilities). The theory behind the experiment is that our brains developed methods to understand frequencies over millions of years of evolutionary history - by watching how many times the sun comes up before it gets cold, etc. Our brains are not made to understand percentages from a biological standpoint because they are a modern construction.

[hyperpape]

Like the (possibly apocryphal) woman who said, "The lottery is my pension plan." She plays the lottery even though she knows that it is unlikely that she will win and that she will likely have less money in her old age than if she put that money in the bank, because if she does strike it rich, she will enjoy her retirement, and if she does not strike it rich, she will enjoy it only a little less than if she put the money in the bank. Her choice is not the result of exact calculation, nor does it need to be.

Yes. In finance this preference for possibility of large gains is actually numerically captured in skewness preference (though of course you are absolutely right that in the real world human beings don't really make decisions with such calculations). Other common factors of a return distribution that are often considered include risk (the focus here) and kurtosis (the "fat-tailed-ness" of the return distribution).

There is also the idea from behavioral economics that some people may realize that they lack the discipline to save money. If you think so, it may be rational to blow what you have right now on lottery tickets, booze or cigarettes.

[daniel_the_smith]

By "less than $110" do you mean "and more than $100" or "exactly $110."?

Yeah, I expect most people won't take one for less than $100

[daniel_the_smith]

you can either have

A: $10 now

or

B: I will flip a coin until it lands tails, you will get (2^X) * 50 cents where X is the number of heads.

I choose option B (assuming the coin flips are fair. Preferably we'll use a source of quantum noise ). But if you make the numbers $1,000,000 and $50,000, I'll probably choose A. Between those values I'd have to think hard.

The EV of B is infinite (I think it's actually a cool example of a "pascal's mugging"), but the expected utility is not-- as stated, people run the $ through a (probably bounded) utility function, and while $2 million is better than $1 million, it's less than 2x better.

Anyway, cool discussion. One thing does not make sense: How could Keynes possibly be Bayesian and think that there is no possible estimation of lifetime earnings at the same time?

[Suji]

you can either have
A: $10 now
or
B: I will flip a coin until it lands tails, you will get (2^X) * 50 cents where X is the number of heads.

While people should take the second option in theory, people should take the first option in practice. To get a bigger gain than $10, you need at minimum 5 heads to exceed the $10. That's only a 1/32nd chance (roughly 3%) of getting above the initial $10 on the first go around. While possible it's not likely, and I wouldn't take those odds and I'm someone with a math background as well.

Eh. These odds are so hugely, hugely better than the odds of a normal state-sponsored lottery. Option B is the equivalent of thousands of dollars worth of lottery tickets, isn't it? The odds are hard to parse, but I have trouble believing that psychologists had trouble finding people who would prefer thousands of dollars of lottery tickets to $10.

I suspect that you're right in that option B is the equivalent to thousands of tickets, but it's still a 3% chance to get more than $10. I would choose option B over ANY lottery.

So the reason why it's a paradox is that most of the time, the second bet is just objectively worse. But, the degree of the payout is in direct proportionality to the unlikeliness of the outcome, So the paradox arises because in an expectation value calculation, we assume that 1000 dollars is 10 times better than 100 dollars, even if it's 10 times less likely. There is a non-zero probability of millions of dollars worth of payout here. And even though it's a million times less likely, those possibilities add up.

Yeah, I can understand that. However, I did some quick math and 93.75% of the time you'll want to take the first option since you'll end up with less than $10, and 6.25% of the time take the second option since you'll end up with more than $10.

I fully recognize that from a pure mathematical view option B is superior. The person could throw 500,000,000 heads in a row. Likely, no, but it's still possible. In a mathematical setting, I'd choose option B everytime. In practice, I'd choose option A about 94% of the time.

[jts]

Anyway, cool discussion. One thing does not make sense: How could Keynes possibly be Bayesian and think that there is no possible estimation of lifetime earnings at the same time?

Bill is being controversial Don't blame poor Keynes. He definitely thought that people estimate their lifetime earnings. He just thought that those estimates (indeed, most economically relevant estimates) were uncertain, and thus prone to sudden sharp changes that were not, strictly speaking, warranted or unwarranted from a logical point of view.

This is a stab at an explanation, but I don't have time to finesse it or double check what I'm saying so I hope some of you will correct/improve it.

Keynes inaugurated the distinction between risk and uncertainty. The distinction between risk and uncertainty implies that in some cases, even with all the data that it's rational us for us to gather, we can still be wrong about the true probability of the event. However (ripostes Ramsey or someone), the "true" probabilities of events in a (fairly) deterministic universe is always 0 or 1, and the only way that it makes sense to talk about probability is as whatever number we've decided on after we've gathered all the data we care to collect. Thus, there's never any uncertainty. As I understand it, that's why Keynes is grouped as a Bayesian and his anti-uncertainty allies are grouped as frequentists. However, it's confusing because the anti-Keynesians were the ones who pioneered the idea that you could determine what probability someone really assigned to something by getting them to bet on it, which is currently a fad that (on the internet, at least) groups with calling oneself "Bayesian".

[daniel_the_smith]

Anyway, cool discussion. One thing does not make sense: How could Keynes possibly be Bayesian and think that there is no possible estimation of lifetime earnings at the same time?

Bill is being controversial Don't blame poor Keynes. He definitely thought that people estimate their lifetime earnings. He just thought that those estimates (indeed, most economically relevant estimates) were uncertain, and thus prone to sudden sharp changes that were not, strictly speaking, warranted or unwarranted from a logical point of view.

Alright, I still don't see why one's estimates can't take take all that into account. It's the whole point of doing probabilistic math, to quantify your ignorance...

Thanks for the explanation.

[jts]

Alright, I still don't see why one's estimates can't take take all that into account. It's the whole point of doing probabilistic math, to quantify your ignorance...

Thanks for the explanation.

Well, you'd want to read the Treatise on Probability to see why Keynes wanted to distinguish between risk and uncertainty for mathematical and logical reasons, and the General Theory to see why he found his earlier views on probability useful for economic analysis (Chapter 12 is most on point, iirc).