Why people make dumb financial decisions on purpose
awealthofcommonsense.com
awealthofcommonsense.com
> Expected value (also known as EV, expectation, average, or mean value) is a long-run average value of random variables.
If you can only press a button once - you should take the guaranteed money in almost all circumstances (assuming you have finances that look like most Americans - if you're already a millionaire... do what you want, this game doesn't matter much to you).
Basically - This is a dire misunderstanding of how statistics works in general. The population at large might be better off pressing the 50% at 50 million button (because then you are running this game many times and you will likely achieve the expected value) - but as an individual, who can only roll the dice once, you are much better off just taking the immediate and guaranteed win.
And that's not even accounting for the drop off in marginal value of each dollar as you accumulate them - that first million is far more impactful than the next 49.
This is in fact the reason you should take the million.
How many times you get to play the game is irrelevant. Your whole life is filled with potential but uncertain payoffs, and you should maximise expected utility every time (where utility is not the same as dollars).
In reality, with these numbers, the best strategy for most people who aren't already very wealthy would probably be to get a sure-fire nest egg and then play the odds.
If you have to play the same every time, I'm not sure. Again, with these numbers, the utility function is looking pretty flat after $20 million for the vast majority of people. And "almost certain" != certain.
You can get any result you want if you just rewrite the problem conditions ◔_◔
Thinking like this was the mistake I've made.
While you can play a given game only once, your life will have plenty of such games. So there definitely is a relevance to "expected value". And this is easily to simulate with a program. The expected value of the wealth for those who take the chance when the "local expected value" is better than the certain outcome does tend to be higher.
What are you talking about? Which life will have plenty of such games? In what way is that true?
But what situation? How is it that a person's life has many of these chances in large enough volumes to make expected values worth it?
Every spot in life that you encounter that can be seen purely from an EV perspektive should be played as that. Only exceptions are longtail ruinous outcomes, like House Fire insurance, Health Insurance. Thats why in many western nations these types of insurances are mandatory.
But I agree... If you are an investor, or maybe a professional poker player, then you'd have put yourself in a position that favors reasoning guided by EV.
There are other ones as well, non-money related. For example, in sports. I believe basketball players probably try to do this. There are so many shots. They're probably using EV to guide their strategy and practice.
Five Thirty Eight writes about this from time to time. Three points shots in basketball. Going for it on fourth down. Going for a two point conversion. You can work out the stats for all this sort of thing--and there are apparently biases for various reasons why coaches/players don't always follow the EV strategy.
However, I believe I've done similar things with used electronics. I tend to favor buying a really cheap used ones for [sometimes] 1/5 of the price instead of a new one. It could break or be of low quality, but chances of that are small and thus (over time -- making an EV-ish calculation), I spend less money on electronics.
I also believe I do this in buying new products. In many situations, I can pay extra for an extra year or two of 'guarantee' (not sure if the right term is 'guarantee' or 'insurance'). However, very often, the first 6 months or 1 year of guarantee is given and has its cost embedded in the price of the product. The question becomes: how likely it is for the product to fail given it hasn't failed for the first year. I believe the chances are small so I don't buy it. I guess it's also an EV kind of calculation (just like you gave as an example).
However, those don't seem that common, really. Maybe it's just the kind of life that I live.
Is the situation 100%1M vs. 50%50M supposed to exemplify these ones? These not-so-frequent ones for small amount of money?
Another thing is that expected value has to do with a limit in this situation:
(1/n) x SUM [j = 1 to n] outcome(j) -> E for n -> oo
(there is an ergodicity assumption going on here -- which doesn't always hold in practice). That limit can be E while the first idk how many hundreds of values of outcome(j) be very distinct from E.
How many times will things like that happen in your lifetime? Some dozen? What if you separate away the large-scale ones (like the 100%1M vs 50%50M)? The small-scale ones will be more frequent and you just blindly follow the EV approach to them. The large scale ones will be extremely rare, and maybe another approach is better. No?
Extended warranty which is basically insurance. Leaving aside the fact that some credit cards provide it for you anyway and things like that. Yes, for most purchases, this is a bad deal because the expected value is almost certainly negative and--probably--if something does break you can replace it.
Here we're talking about losses rather than gains. The certainty of small losses (extended warranty purchases) vs. the chance of a relatively large loss. But it's the same idea with a negative sign.
To me, the choice looks like "solve your financial issues with the red button; 100% chance" vs. "solve your financial issues and get extra money you won't really need, but with 50% chance through the green button".
I'd have a hard time choosing the green button.
It's curious because I'm a mathematician. I feel like I should know this better, but I've never really studied probability, much less statistics or economics.
(edit)
Another issue is what would it mean, in practice, that "50%" statement? I guess it means that if you'd play the game long enough, 50M would come out roughly half the times (by counting). This could mean a system in which the first 10 always fails, the second 10 always succeed, and the ones after that have their results based on a fair dice (1,2,3->50M; 4,5,6->0). This would certainly fit the frequency "definition". In practice, these probabilities don't mean a clean neat thing very often. Another issue is that the definition of that 50% means if you played that game long enough, you'd observe the half-half split, but you'll play it only once. Again, there is a statement about a limit (a statement about a_n, for n large), but you're only looking at a_1 (it often seems to me that people believe that information about EV transfers to information about a_1 -- it really does not). Even though I can mostly think of artificial examples (stuff like the one above), I'm not sure it'd be clear [in an actual situation] what is the meaning of that '50%'.
Even for a one time event, at some point it makes more sense to place the bet depending on a number of factors.
If it's hard to conceive of in this scenario, pick numbers about which it's easier to have intuition. What if you could take $10 for certain vs. a 50% chance of getting $500? Or pick some other values with the same ratio. 50% in this case just means a coin flip. You're right that no one gets the expected value. They get zero or they get $50m. But that may be a good bet depending on circumstances.
As another commenter pointed out: Most investments involve this. In the RE circles you often have the same dilemma: Buy a house for rental in a LCOL area where you get (mostly) guaranteed net income, or buy in a place like California where the rent income won't cover all the expenses, but you feel you can pay the difference and rely on profiting off the hoped appreciation.
Insurance is also a good example someone else pointed out.
Even: Get a guaranteed low paying job as a relatively unskilled worker, or get into deep debt to go into medical school, do a residency, and earn a lot. The latter can have significant risk: Some people don't do well enough to get a residency. Others get the residency but don't have what it takes to complete it. In both cases you're left with a huge amount of debt.
It's not about the expected value of any one opportunity, it's about the expected value among every opportunity you will encounter in your life. This also implies that one should do what they can to expose themselves to said opportunities especially while they're young.
Disagree. Sure - you don't get many games involving millions of dollars, but you do get many for smaller amounts.
I could put all my extra money into paying off a low interest mortgage (guaranteed return), or I could put it in an index fund (higher average return, with no guarantees, and a potential for a loss).
And working at startups: Not sure the expected value is high there. May be higher than working at a FAANG. I doubt it.
On startups, I think there are people who have been in situations where they have an expected value greater than something like a FAANG $300k/year over 3 years scenario (e.g. they own a large stake in a close-to-IPO company). And they should maybe still walk away, if the 50% chance of a tiny IPO payout would destroy their self esteem and make them feel even further behind their high-salary peers. (Also keep in mind that not everyone lands jobs at FAANG companies, so it shouldn't be super hard to find people who lucked into a startup where their EV is higher than their market salary over a few years). In other words: even if a startup somehow has higher EV, you may want to ignore the EV.
Let's account for the marginal value of each dollar to set the number 50 to be some number that equated to triple the utility of the first million.
Why would it make less sense to choose the 50%? Assuming you would definitely take a 99.9999% chance of 50 million over 100% of 1 million, at what percentage do you switch over to the higher percentage?
"Variance" and "risk tolerance"
There is only one of me, not a Large Number
And well, if everyone played the game, then the population at large would still be better off taking the million. I can well imagine there being fewer social problems if we all get a million fun bucks versus half of us getting fifty million. But then that's a different effect kicking in.
Personally, a million would affect my life positively (I'd buy a house), 50 million negatively (I'd stop working).
Anything that expects me to wake up at the same time every day, or working for a set amount of hours, or prevents me from stopping or taking a break (weeks, not hours) when I get bored of working on it is out of the picture. That leaves zero work options as far as I'm aware.
Had I taken the back roads, if there was an accident, there would be tons of options to get to where I needed to go.
If you need to be somewhere at a certain time, do the tried and true 100% guaranteed way.
It's how it is.
So there's that.
Maximizing the min/max outcomes are common alternative preferences. Like, suppose I have a 1% chance of being tortured for a year and a 99% chance at being the next God-Emporer. I can't actually average those futures; I'll be in one or the other, and I might want to have a 0% chance of torture or if the odds are flipped maybe I'm okay with being tortured for the tiny chance at being God-Emporer.
Such preferences are hard to cover under the umbrella of maximizing expected utility because it introduces (neg)infinite utility to certain outcomes. Instead recognizing that you might be optimizing something else is a cleaner way to handle the problem.
For example, the EV in this example (50% chance of $50m, or $0) is $25m. The EV of a 2.5% chance of $1 billion is also $25m, but your probability of getting nothing is 20 times higher. Is it more rational to choose this over the certainty of $1m? I don't think so. Is it rational to chose a 0.0025% chance of $1 trillion over $1m? At that point I think even the most avowedly rational economist would choose the cash.
If you are only playing the game once, then any rational agent should attempt to maximize expected utility. Here "rational" just means that preferences are consistent in a particular way. For the purposes of this game played just once, almost all humans are rational. When humans play multiple times, they quickly lose the ability to calculate and make rational decisions.
Econ 101 covers expected utility, and it's one of the few pieces of useful econ theory. It's like people write these articles without an elementary understanding of the theory which might be able to sensibly explain the situation.
I’m also reminded that “people are happier when a choice is made for them” or some other thing I’ve heard thrown around.
It's written as though they stumbled across this esoteric idea written by some dude 100 years ago. There is a whole set of papers, Bernoulli is one of the guys who did research on it and there are a bunch more. There is a whole field, the ideas have been pulled together. It's introduced in any half decent microeconomics class.
What's next? An article suggesting maybe we can predict how long it will take an apple to hit the ground? That some guy named Newtown penned a few useful ideas on it back in the day? And pretending "physics" isn't a field?
OTOH, insurance companies can afford to have a roughly linearly utility function (because, as pointed out, they play the game much more often than others), which is why they are in business.
> Bernoulli once wrote, “The utility [of probabilistic decisions] is dependent on the particular circumstances of the person making the estimate. There is no reason to assume that the risks anticipated by each [individual] must be deemed equal in value.”
Risk over non-fungibles (body parts, sentimentally valued heirloom pieces, ...) are obviously subjectively valued. But even for platonic (ideal) fungibles like fiat money the risks depend on the person because modeling reality as if everyone is treated equal in commerce or has equal access to and treatment in the courts etc. is a very strong assumption to make.
Let us first assume contracts are never reneged etc, and let us thus first assume agreements are rigorously respected.
Let us further assume the subject has the usual goal of maximizing its capital, here denoted in dollars.
Since currencies are a social construct and only hold value in the context of a society, we assume the subject is in prolonged contact with a society that values this currency. (If not the subject doesn't care which answer to give.)
Contrary to all the comments here in HN (nonlinear utility etc.), if the goal of the subject is to maximize capital, then the correct answer (assuming absence of things like conscientious objection) is unconditionally the green button with the highest Expectation Value, non-linear utility functions, or one-time-ness of the offer, or subject poverty be damned!
To understand why: even if the offer is one-time, and even if the subject can not afford the regret of missing out, the subject is still in contact with society. This society has companies regularly dealing with large sums, and optimizing expectation value.
THE SUBJECT CAN SIMPLY GO TO A BANK AND TRADE THE HIGH ROI FOR STABILITY WITH THE BANK:
For example the subject and bank can agree to the following:
* Bank pays subject $20 million
* subject presses green button
* If subject receives $50 million, it forwards this to the bank, otherwise nothing
In this scenario the subject wins $20 million unconditionally, and the bank spent $20 M with an expected return of $25 M, so the bank sees an expected ROI of a handsome +25%.
The real catch is not personal utility function, one-time-ness, etc ... but reliability of contracts and trustworthiness of the system enforcing them, which one can read between the lines of Bernoulli's comments.
All the comments and observations about how poor people "should" take the certainty with the lower amount is just echoing the indoctrinated "learn and embrace your lowly position in society" wheither thats low in rewards, or low in reliability of fair enforcement of the law.
I find it hard to read intellectually capable people concoct artificial examples to make people distrust mathematical rigor when it can be entirely relied upon. The real element of unreliability is in the systems under which we are subjugated.
"If you don’t have a dime to your name you should take the guaranteed million dollars all day, every day. But what if you have some money? What if you’re already a millionaire? At that level of wealth taking the 50/50 shot at $50 million might be far more tempting."
A wealthy person, could, for example risk buying an older used car that would potentially need costly repairs. In case it needs these repairs, they will suffer some financial losses but would still be able to derive utility from the car. In case it doesn’t need them, they get rewarded for the risk with a functional car that costs considerably less than a new one.
For a broke person the same decision is much harder. Not being able to repair the car would unlock undesirable 2-nd and 3-rd order effects, like, not being able to go to work.
Prizes for challenges, maybe. Chess tournaments with a buy-in, that I respect because no luck involved, meaning no tipping the scales no cheating.
So the problem in gambling is when you just lost a big bet of money you didn't need and the only way to recover is putting up a tiny bit of money you do need. By nature gambling--and by the way it's sold--is designed to fuck with that fine line.
There's also I think an implicit stationarity assumption built in, that if you say you'll pay me X amount over time, that you'll actually do that, that inflation wont eat it into oblivion, etc. It's a classic case of theoretical models not working in reality.
This is kind of the point of the essay, but I think it could have been made more rigorously (as people here are pointing out).
How many companies have you seen with "contests" to get ideas or content. The vast majority of people end up with nothing.
Yeah, but you see the same thing with giveaways at trade shows, for example. Even for a fixed giveaway budget, there's an argument to be made for having a drawing for a nice prize, rather than giving everyone some cheap swag.
Poker players make bets based on bank roll size and very good understanding of expected value. They either use Kelly criterion[1] or develop competing heuristics for value at risk[2].
Plenty of areas where psychology adds an interesting human dimension to decision making, but this and other risk-neutrality scenarios are not part of this category!
[1] https://en.wikipedia.org/wiki/Kelly_criterion#Criticism [2] http://www.eecs.harvard.edu/cs286r/courses/fall12/papers/Tho...
In practice most financial decisions take long time to make.
I think this counts as a 24:1 bet (we notionally have $1 million, we can gamble to get another $24). The Kelly bet is 0.5 - 0.5/24 ~= 0.5. So we would want to put about half our wealth into this gamble and that implies it starts becoming attractive around the time we have $2 million to invest. Up till then we might take the gamble but we don't have enough money to really feel comfortable.
It's worth noting that it can often make sense to be more conservative than the Kelly criterion would suggest, depending on your risk tolerance. So I would consider your calculation a lower bound.
And it fucks people's reasoning about money up, you can't go into a raise negotiation with those game show numbers getting your personal finances and your leverage and expectations out of whack. Same as fashion magazines, just seeing a pretty shirt and seeing it costs $45000 for instance instantly fucks your notion of the value of a dollar.
But ... if you were an oracle (religious, not database) who sometimes foretold the future, would there be a marketplace for your ideas? In 2003 if you described a social network would that be valuable information? I tend to think no since there were social networks before Facebook but FB were lucky and executed very well.
Comments have been explaining which ones already apply to this article, I'm not going to repeat them.
But there is an another example from Taleb that always makes me smile:
- If the other player tosses a coin and gets 9 tail in a row, what are the chances of getting tail on the next toss?
- 50%!
- No, 100%. The other player is cheating.
I’m also quite puzzled that nobody mentioned yet that if you were offered a chance like this in real life, it would likely be the only time in your life that you get a chance like that. Unless you get a repeat, or you are rich, it would be foolish to not press the red button.
The problem with the scenario is that the disparity is so high: $1M vs expected value of $25M. 50% is high enough that for people like me, it's clearly a green button option.
But how about this:
Guaranteed $1M vs a 4% chance of winning $50M. Now the expected value is $2M - still a lot higher than $1M. But ... 4% chance? Suddenly the guaranteed $1M is a lot more attractive.
And you can scale the numbers up or down and at some point almost everyone will choose red or choose green respectively.
If you hit the green button you either get $50 million or 0$. Hitting the red button gives $1 million.
Unless you don't want $1 million or don't need it, you're going to hit the red button and not the green button.
Somewhere around $3 million is probably where I'd switch buttons.
There are 20 people in line ahead of you. Each one of them hits the green button, and you physically see that half of them made $25 million.
Would you not be tempted to hit the green button?
$1 million will make a big difference to me, but in many cities it's not enough to retire on - especially with children. While $25M isn't worth 25x more to me, it's certainly worth a heck of a lot more than $1M.
Nope. There's a whole field of research about this - decision theory - which doesn't agree with this decision.
Most people appear to go with the Minmax approach - they minimize potential losses(or in this example: maximize minimal payouts).
For one-time events it's a sound strategy.
Finding one mathematical concept and saying "mathematics say this" is so strange.
I don’t think it’s a good look for the “Director of Institutional Asset Management at Ritholtz Wealth Management” to call perfectly sensible decisions by people whose net worth is many orders of magnitude smaller than his “dumb” just because he can afford to pass up a guaranteed million.
An easy to understand example is, I believe I should pay more in taxes and everyone as wealthy as I am should too.
I rent an apartment, but I rent it out at the cost it takes to maintain it in good condition, because I think profiting off rent is unethical. This means I'm generally renting much much cheaper than local rents, and my tenants can therefore build savings.
There can also be good business reasons to charge below market rent. Having a lower vacancy rate, for one.
Could I have charged $1000 and pocketed a little profit? Of course. But it would have come directly at her ability to succeed. I think that's deeply unethical. I think it's morally repugnant to profit from housing.
But the point is that I believe we should all chip in more to help each other out. If you make, eg, $750k a year like I do an increase in taxes isn't really going to hurt your ability to live comfortably. I'm confident I could travel anywhere in the world, buy a second home, etc. I could still do those things if I payed more in taxes. Just... Not as often.
Really, what this is about is that the typical mathematics used to discuss a certain type of financial decision (mostly things like investments) uses an incomplete model that doesn't consider appropriately the actual values involved -- for example, failing to consider the wildly nonlinear curve of the marginal value of one dollar.
"Dumb" decisions might be playing the lottery, or spending a windfall instead of saving it. But even those dumb decisions have reasonable psychological underpinnings for the person doing them.
Another example of a 'dumb' decision: torpedoing a career to preserve relationships.
My prospects are abysmal, my savings insufficient and I'm still dysfunctional, but I'm better off than I would've been in many ways if I had not decided to give my loved ones (and my mental health) higher priority. I like to think I can make a comeback one day, but it's okay if I don't.
[1] https://en.wikipedia.org/wiki/St._Petersburg_paradox [2] https://en.wikipedia.org/wiki/Kelly_criterion
"Emotion may lead you to make bad financial decisions. For example, people who feel sad will pay more, sometimes four times more, for a consumer product than those who do not feel sad."
The "Nash equilibrium" also delves a bit into the psychology of decision making: https://www.reddit.com/r/math/comments/1tc80g/is_the_explana...
If I need $1 million right now or else a loved one dies, then it doesn't matter how big the reward of a riskier alternative choice may be. I take the million NOW. If the additional reward is a victim of decreasing value as that offer rises, it's only rational for the decider to show diminished interest in choosing the greater reward (even if the marginal odds are only a tiny amount less likely).
Disregarding the reward curve of the individual is going to consistently misjudge economic choice and will surely be a poor basis for any economic model.
* Imagine the payout on the red button were not $1M but $100K or $50K or $10K. Is there any point as it diminishes toward zero that would make you switch buttons?
* Imagine the payout on the green button were not $50M but $100M or $500M or $1B. Is there any point as it increases toward infinity that would make you switch buttons?
For those who say they would press the green button ...
* Imagine the payout on the red button were not $1M but $2M or $5M or $10M. Is there any point as it increases toward $50M that would make you switch buttons?
* Imagine the odds on the green button were not 1:2 but 1:3 or 1:5 or 1:10. At what point, as the odds diminish, would you switch buttons?
No it doesn't. Statistics is the science of populations of events, expected value applies only if you have a sufficiently large population.
There are 20 people in line ahead of you. Each one of them hits the green button, and you physically see that half of them made $25 million.
Would you not be tempted to hit the green button?
The fact that we observed this data, means that this would effect our estimation of the situation.
What if you had a 80% chance instead of a 50% chance?
90% chance?
I'm sure at some probability before 100% you'd be willing to take that chance.
The author’s point is that the simplistic understanding of expected value isn’t always wise.
The audience is economists who use the economic equivalent of perfectly spherical cows and then wonder why their model isn’t all that good.
But then bear in mind that this person maybe has a big bill to pay and only £5 to their name, do they keep the £5 knowing that it isn't going make any difference or take a wild chance that will?
a small price for a dream / what if mood
Considering how much money I throw away on streaming subscriptions I barely use, books I never get beyond the first chapter of, food I buy that ends up in the trash, etc, it represents quite good value for money.
You're essentially making a bet with your insurance company that xxxx will happen. Just like with the lottery, the expected monetary value of insurance is always negative (it has to be, otherwise the insurance company won't make money), but the utility value of that insurance is different for each person.
E.g. for me, insurance on a phone doesn't make sense, since I easily buy a another cheap phone if mine breaks. But for somebody with less money, those few hundred dollars might have a much higher utility.
The way I've been able to deal with this personally is by thinking "what would I do if this was Monopoly money?" and then reconcile that with my emotional decision.
If I was flat broke, living on the street, or in debt even, I would find investors to pay, say 5 @ 200k each, for me to press the green button and reward them 1mm each in case of payout.
Your choice then becomes take $1 million from the red button, or sell the green button for $2 million.
I imagine most people would take the 2 million, especially because I suspect most people are poor at negotiating when life-changing amounts of money are involved. I have seen many naive people do silly house trades (or missing out on good trades).
Teamwork makes the dream work.
https://en.wikipedia.org/wiki/St._Petersburg_paradox
tl;dr: doubling winnings on each throw of heads and paying out on the first tail is a game with expected winnings diverging to positive infinity, yet probably no one would pay more than a few bucks to enter
In other words, the problem is that humans are cruel to each other and peace of mind vs other cruel people is worth more than a higher reward.