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There's diminishing returns on the utility of money. If you're living paycheck to paycheck that guaranteed million is gonna give you a higher expected return of

There's diminishing returns on the utility of money. If you're living paycheck to paycheck that guaranteed million is gonna give you a higher expected return of utility than the next 49 million combined. I disagree with the title calling it a "dumb" financial decision. It can be perfectly rational to take the million.

crazygringo 4y ago
Exactly. The fact that this article doesn't even mention the concept of marginal utility, and acknowledge that it's mathematical rather than "psychological", is borderline irresponsible. [1] https://en.wikipedia.org/wiki/Marginal_utility https://en.wikipedia.org/wiki/Marginal_utility
- burntalmonds 4y ago
  It does mention it. "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."
  - baobabKoodaa 4y ago
    No, it doesn't mention it, and in fact the quote you copypasted does not contain any mention of it. The author is oblivious to the concept and is erroneously concluding it to be merely a psychological effect.
  - bluetomcat 4y ago
    The takeaway is that a wealthier person can take greater risks without endangering their livelihood. 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.
  - ajuc 4y ago
    "You should only gamble with money you don't need." Which most people already know.
    - daniel-cussen 4y ago
      No, not even then. You shouldn't play games other people arrange in any way, except ie educationally, or for the pleasure of winning and nothing else. Not with money. 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.
- deleted 4y ago
  [deleted]
- ghaff 4y ago
  Marginal utility does let you view the pressing of the red button as an action a rational actor could take. That said, when you get into concepts like prospect theory in behavioral economics, there is definitely a psychological aspect as well.
derbOac 4y ago
There's also "purely statistical" problems with the argument the 50 million at 0.50 probability is the better decision: it makes an erroneous ergodicity assumption. In other words, it assumes that the expectation of a one-shot decision over people is the same as it is for the decision within-person. Sure, if you were making the choice over and over and over again, it would be better to repeatedly hit the green button. But that's not the situation. The situation is a mixture of outcomes, so for any given individual the expected outcome might be zero. 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).
- pnutjam 4y ago
  It's a classic spherical cow model. It has no bearing on reality, although this pay structure is becoming more and more common; albeit with less then 50% odds. How many companies have you seen with "contests" to get ideas or content. The vast majority of people end up with nothing.
  - ghaff 4y ago
    >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.
    - pnutjam 4y ago
      I'm talking about contests like, design our logo OR build the next rocket to the moon.
mjdowney 4y ago
Hear, hear! Tired of seeing these tirelessly dumb takes about expected value theory's supposed flaws or its psychological dimension. 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 https://en.wikipedia.org/wiki/Kelly_criterion#Criticism [2] http://www.eecs.harvard.edu/cs286r/courses/fall12/papers/Thorpe_KellyCriterion2007.pdf http://www.eecs.harvard.edu/cs286r/courses/fall12/papers/Tho...
lostmsu 4y ago
It is a dumb financial decision. You could find a third party you could agree with to give you 20mil now for whatever the coin toss brings you.
- cm2012 4y ago
  That's not the point of this hypothetical question though. It's like saying you decide to break the train tracks in the trolley problem.
  - lostmsu 4y ago
    The trolley problem implies urgency of action. This one does not seem to. In practice most financial decisions take long time to make.
- the__alchemist 4y ago
  The comment I'm replying to is showing a shade of grey, but this is a valid perspective, and reminds me of how Feynman attacked poorly worded, vague, or academic questions. I disagree that this reasoning is tangential to the question; it's an ill-defined question, and this comment's take pokes at that in the right place.
roenxi 4y ago
A useful formula is the Kelly Criterion [0]. I'm abusing the logic and probably going to apply this wrong, but... 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. [0] https://en.wikipedia.org/wiki/Kelly_criterion https://en.wikipedia.org/wiki/Kelly_criterion
- CrazyStat 4y ago
  This is an interesting way of looking at it that I hadn't thought of--turning the Kelly criterion around to ask "what would my bankroll have to be to make this bet worth it" rather than "what size bet should I make given the bankroll I have." 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.
  - ghaff 4y ago
    That feels about right. Depends on age, future earning potential, objectives, circumstances, etc. But it seems like somewhere in the $3-5 million net worth range is where most people would seriously start considering rolling the dice but you could probably imagine it as low as $2m if someone were confident that $1m today wouldn't really be life-changing.
daniel-cussen 4y ago
Yeah like why are the numbers so enormous? Game shows typically require signing up, a lot of waiting, backgrounders, castings even, they don't treat you great, and they tease money but never pay it. Like one time per game show, not per season, per show. 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.

crazygringo 4y ago

Exactly. The fact that this article doesn't even mention the concept of marginal utility, and acknowledge that it's mathematical rather than "psychological", is borderline irresponsible. [1] https://en.wikipedia.org/wiki/Marginal_utility https://en.wikipedia.org/wiki/Marginal_utility

burntalmonds 4y ago
It does mention it. "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."
- baobabKoodaa 4y ago
  No, it doesn't mention it, and in fact the quote you copypasted does not contain any mention of it. The author is oblivious to the concept and is erroneously concluding it to be merely a psychological effect.
- bluetomcat 4y ago
  The takeaway is that a wealthier person can take greater risks without endangering their livelihood. 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.
- ajuc 4y ago
  "You should only gamble with money you don't need." Which most people already know.
  - daniel-cussen 4y ago
    No, not even then. You shouldn't play games other people arrange in any way, except ie educationally, or for the pleasure of winning and nothing else. Not with money. 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.
deleted 4y ago
[deleted]
ghaff 4y ago
Marginal utility does let you view the pressing of the red button as an action a rational actor could take. That said, when you get into concepts like prospect theory in behavioral economics, there is definitely a psychological aspect as well.

derbOac 4y ago

There's also "purely statistical" problems with the argument the 50 million at 0.50 probability is the better decision: it makes an erroneous ergodicity assumption. In other words, it assumes that the expectation of a one-shot decision over people is the same as it is for the decision within-person. Sure, if you were making the choice over and over and over again, it would be better to repeatedly hit the green button. But that's not the situation. The situation is a mixture of outcomes, so for any given individual the expected outcome might be zero. 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).

pnutjam 4y ago
It's a classic spherical cow model. It has no bearing on reality, although this pay structure is becoming more and more common; albeit with less then 50% odds. How many companies have you seen with "contests" to get ideas or content. The vast majority of people end up with nothing.
- ghaff 4y ago
  >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.
  - pnutjam 4y ago
    I'm talking about contests like, design our logo OR build the next rocket to the moon.

mjdowney 4y ago

Hear, hear! Tired of seeing these tirelessly dumb takes about expected value theory's supposed flaws or its psychological dimension. 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 https://en.wikipedia.org/wiki/Kelly_criterion#Criticism [2] http://www.eecs.harvard.edu/cs286r/courses/fall12/papers/Thorpe_KellyCriterion2007.pdf http://www.eecs.harvard.edu/cs286r/courses/fall12/papers/Tho...

lostmsu 4y ago

It is a dumb financial decision. You could find a third party you could agree with to give you 20mil now for whatever the coin toss brings you.

cm2012 4y ago
That's not the point of this hypothetical question though. It's like saying you decide to break the train tracks in the trolley problem.
- lostmsu 4y ago
  The trolley problem implies urgency of action. This one does not seem to. In practice most financial decisions take long time to make.
the__alchemist 4y ago
The comment I'm replying to is showing a shade of grey, but this is a valid perspective, and reminds me of how Feynman attacked poorly worded, vague, or academic questions. I disagree that this reasoning is tangential to the question; it's an ill-defined question, and this comment's take pokes at that in the right place.

roenxi 4y ago

A useful formula is the Kelly Criterion [0]. I'm abusing the logic and probably going to apply this wrong, but... 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. [0] https://en.wikipedia.org/wiki/Kelly_criterion https://en.wikipedia.org/wiki/Kelly_criterion

CrazyStat 4y ago
This is an interesting way of looking at it that I hadn't thought of--turning the Kelly criterion around to ask "what would my bankroll have to be to make this bet worth it" rather than "what size bet should I make given the bankroll I have." 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.
- ghaff 4y ago
  That feels about right. Depends on age, future earning potential, objectives, circumstances, etc. But it seems like somewhere in the $3-5 million net worth range is where most people would seriously start considering rolling the dice but you could probably imagine it as low as $2m if someone were confident that $1m today wouldn't really be life-changing.

daniel-cussen 4y ago

Yeah like why are the numbers so enormous? Game shows typically require signing up, a lot of waiting, backgrounders, castings even, they don't treat you great, and they tease money but never pay it. Like one time per game show, not per season, per show. 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.