[HN Gopher] Why people make dumb financial decisions on purpose
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Why people make dumb financial decisions on purpose
Author : CoffeeOnWrite
Score : 95 points
Date : 2022-09-02 14:59 UTC (1 days ago)
(HTM) web link (awealthofcommonsense.com)
(TXT) w3m dump (awealthofcommonsense.com)
| bcrosby95 wrote:
| Given my current financial situation, 1 million would let me
| retire immediately. What I see when I look at those buttons are:
| 100% chance of being able to retire early vs 50% chance of being
| able to retire early.
| randcraw wrote:
| All the classic economic models for choice that I've seen fail to
| consider that the perception of not only risk but reward are BOTH
| nonlinear. IMO, this has been an Achilles heel of classic price
| and game theory. The rise of behavioral economics in recent
| decades would seem to agree with this iconoclysm.
|
| 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.
| mgraczyk wrote:
| Not sure what you mean by this. Even in the most basic rational
| choice analysis, where the players are agents seeking to
| maximize a utility function, the "reward" can be nonlinear. I'm
| not familiar with any economic model that unintentionally
| restricts the agent's utility to be linear. Sometimes you
| assume that agents have a linear "utility of money", but
| everyone in economics knows that this is a taylor expansion
| around a small region where the linearity assumption is
| reasonable, and not an actual fact about human preferences.
| gardenhedge wrote:
| "A 50% chance of winning $50 million would equate to an expected
| value of $25 million."
|
| 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.
| BeetleB wrote:
| Serious question:
|
| 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.
| id wrote:
| If you have $100 million to your name, it'd be smarter to hit
| the green button. It really depends on what you're starting
| with.
| CrazyStat wrote:
| I'd go for the green button if I had $5 million to my name.
| Another $1 million isn't going to make a huge difference in
| my life, $50 million would.
|
| Somewhere around $3 million is probably where I'd switch
| buttons.
| [deleted]
| LorenPechtel wrote:
| The dumb is in the author thinking these are dumb decisions. $50M
| is nowhere near 50x as valuable as $1M, thus the green button is
| nowhere near 25x the value of the red button. For most people
| pushing red is the smart decision, not the dumb one.
| agentwiggles wrote:
| Honestly I'd hit the red button. I'd rather take a guaranteed
| payoff of my mortgage and all other debt, with plenty left over
| for a few neat toys, than chance walking away with nothing.
| BeetleB wrote:
| I wouldn't, because I can likely pay off my mortgage without it
| and still have money left over for some toys. My mortgage isn't
| a big burden. But I can understand it for folks who can't save
| much due to a mortgage.
|
| 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.
| ghaff wrote:
| The utility function, and to some degree, attitude towards
| risk is going to differ a lot among individuals. And I
| imagine that among those reading this here, some are probably
| going "A million is a nice sum but it's not really life
| changing whereas $50 million would let me retire _right now_.
| "
|
| And you can scale the numbers up or down and at some point
| almost everyone will choose red or choose green respectively.
| im3w1l wrote:
| Ironically 50 million would make me want to hire people to
| realize my visions, pulling me out of retirement.
| selfhoster11 wrote:
| Exactly.
|
| 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.
| Kalanos wrote:
| seriously flawed perspective. it's a 50% chance of nothing versus
| a 100% chance of a life-changing amount of money. if it was
| $1K:$25K or $100K:$2.5M then you'd take the risk.
| ghaff wrote:
| Totally depends on an individual. You can't generalize that $1M
| is life-changing for everyone and $100K is not for anyone.
| rotexo wrote:
| The response I saw on Twitter that made the most sense: "sell
| your button press for $5 or 10 million to a person who has $100
| million"
| rwmj wrote:
| Now I'm wondering what the expected value is if you were to
| auction this button pressing opportunity. Intuitively it seems
| to be over $1m (and less than $25m) so if I'm right then that's
| better than pressing the red button.
| rotexo wrote:
| Also made me think of the parallel universe to the show
| "Silicon Valley" where Richard Hendricks sells Pied Piper to
| Gavin Belson for like $10 million and happily retires in La
| Veta, Colorado.
| ghaff wrote:
| Assuming there's no risk to payouts being made/no fraud/etc.
| then presumably yes. It's probably related to hedges against
| commodity price increases/ foreign exchange fluctuation, etc.
| Not quite the same thing but somewhat similar in principle.
| rotexo wrote:
| On a tangent, and I'm just spitballing here, how is this for a
| business idea. I: have a PhD (which is not to say I'm smart, it
| is just to say I have been exposed to lots of facts that other
| people may not have been exposed to), and I have a bunch of
| ideas that may or may not be good ones, but I'm too risk-averse
| to act on any of them and start a business. You: have a bunch
| of money and are open to ideas. So you pay me, say, $100 bucks
| to just vomit my ideas out during a 15 minute phone call. Like
| a cheap loot box of ideas, most of which have a low probability
| of success, but there may be a nugget of gold in there.
| rwmj wrote:
| The thing you learn from start-ups is that ideas are worth
| nothing. It's execution that matters.
|
| _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.
| rufus_foreman wrote:
| Chris Sacca: Ideas are cheap; execution is everything.
| [deleted]
| dazc wrote:
| You can witness people buying lotery scratch cards every day in
| the UK and wonder why people are so dumb given the odds of
| actually winning a big prize.
|
| But then bear in mind that this person maybe has a big bill to
| pay and only PS5 to their name, do they keep the PS5 knowing that
| it isn't going make any difference or take a wild chance that
| will?
| paganel wrote:
| Those 5 pounds also give you the opportunity to just dream a
| little once in a while, as in "what would I do with all the
| money if I really win?", it's like a drug, takes you out of
| your not-ok (from a financial perspective) life.
| tpmx wrote:
| These two situations (the linked one and the one you're
| describing) aren't really comparable in terms of probabilities.
| dazc wrote:
| Yes, of course, but I'm mentioning an every day scenario as
| opposed to a hypothosis.
| Mezzie wrote:
| I buy scratchy lottos sometimes (the cheap 1-2 dollar ones)
| because I find the act of scratching them to be tactilely
| pleasing. $1-2 for a couple minutes of fun and the possibility
| of winning enough to get myself some candy for 'free' is nice.
| JasonFruit wrote:
| I once was down to my last dollar, and I bought my one and only
| lottery ticket ever. What could it hurt? I couldn't do anything
| to help myself with one dollar. I lost.
| tester756 wrote:
| I call it
|
| a small price for a dream / what if mood
| dazc wrote:
| Indeed, I have an ongoing subscription with zero expectation
| of winning but I do sometimes enjoy thinking 'what if'.
|
| 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.
| aloisklink wrote:
| If you think about it, isn't buying insurance pretty similar
| (especially if you pay extra for really rare insurance
| policies, like lightning strike insurance).
|
| 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.
| imtringued wrote:
| The rational behaviour is to make everyone press the green button
| and then give away a million dollars to anyone who didn't get a
| prize but the obvious problem is that no such thing happens.
| Instead of cooperating some people insist on getting the full 50
| million dollars as if they deserve it and were destined to get
| the money while the plebs who didn't get anything also deserve to
| stay poor.
|
| 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.
| majkinetor wrote:
| Co-op is definitelly best outcome. Find 20 people to each press
| green and divide equally total amount. U r then in worst case
| scenario better then taking 1m
| Tade0 wrote:
| > The mathematical answer is you hit green every time.
|
| 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.
| subsuboptimal wrote:
| I constantly run into situations where I spend money in ways that
| are financially non optimal, but socially good (in my mind).
|
| 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.
| WalterBright wrote:
| If you want to may more in taxes, the IRS accepts donations.
|
| There can also be good business reasons to charge below market
| rent. Having a lower vacancy rate, for one.
| subsuboptimal wrote:
| No, I don't think you understand. I'm not charging below
| market rate, I'm charging at cost. Whatever it takes to
| maintain the building and provide utilities, etc. The space
| is worth, perhaps, $2400 a month. My last tenant paid $600 a
| month. She needed a place to stay for a year while she built
| up a down payment. Being able to stay with us meant she could
| save tens of thousands and she was able to embark on her own.
|
| 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.
| subsuboptimal wrote:
| The IRS does not, in fact, accept donations.
|
| 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.
| [deleted]
| horsawlarway wrote:
| Expected value doesn't mean jack shit if the game can only be
| played once.
|
| > 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.
| mgraczyk wrote:
| The problem with the analysis in the article and with your
| analysis is that the expected utility of the player is not the
| same as the expected amount of money. Different people have
| different "utilities of money" reflecting their different risk
| tolerances, incomes, satiation rates (diminishing marginal
| utility), etc. The expected value analysis is the correct one
| if you use the right "value".
|
| 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.
| danielmarkbruce wrote:
| Exactly.
|
| 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.
| ghaff wrote:
| And expected utility (and decreasing marginal utility of
| money) does a good job of explaining why most people would
| change behaviors as you scale the numbers involved even if
| you keep the ratio of expected values the same.
| Kranar wrote:
| But the article does go over the utility and explicitly
| states that for many people the utility of a guaranteed 1
| million dollars is greater than a 50/50 chance at 50
| million, so I'm not sure what "people" you're talking about
| or if you even bothered to read the article.
| withinboredom wrote:
| "Go big or go home" comes to mind. Most people I know
| would take the 50/50 chance. In the worst case, nothing
| in their life changes. If they take the million dollars,
| something is going to change :)
|
| I'm also reminded that "people are happier when a choice
| is made for them" or some other thing I've heard thrown
| around.
| BeetleB wrote:
| > Expected value doesn't mean jack shit if the game can only be
| played once.
|
| 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.
| Kranar wrote:
| This is a much more profound statement than it seems at first
| and I wholeheartedly agree with it. Not only that but the
| gains compound over time.
|
| 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.
| cromd wrote:
| Well, life doesn't always give many chances to play a game.
| You can only work at so many failed startups, or have so many
| failed long-term romantic relationships before you've used
| your best years! Someone else already made the point about
| the risk of walking away empty handed, but I'm just pointing
| out that some domains allow for many retries and some don't.
| BeetleB wrote:
| > Well, life doesn't always give many chances to play a
| game.
|
| 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.
| cromd wrote:
| I assume you agree that some kinds of opportunities are
| limited. Not trying new foods because you're afraid of
| wasting your money would be silly, or not saying hi to
| your neighbor because they might ignore you would be
| silly, but some things are very complicated. I'm thinking
| of: surgeries, mate selection, college degrees, white-
| collar crime, etc. I'm just saying that utility and loss
| aversion come into play, and "life is long" can't always
| save the day.
|
| On startups, I think there are people who have been in
| situations where they have an expected value greater than
| something like a FAANG $300k/year over 3 years scenario
| (e.g. they own a large stake in a close-to-IPO company).
| And they should maybe still walk away, if the 50% chance
| of a tiny IPO payout would destroy their self esteem and
| make them feel even further behind their high-salary
| peers. (Also keep in mind that not everyone lands jobs at
| FAANG companies, so it shouldn't be super hard to find
| people who lucked into a startup where their EV is higher
| than their market salary over a few years). In other
| words: even if a startup somehow has higher EV, you may
| want to ignore the EV.
| bluetomcat wrote:
| This represents the trap of over-rationalisation which is
| so prevalent in the Western world. You cannot devise
| universal rational guidelines suitable for every situation
| and every subjective experience. There is a multitude of
| various different factors involved in every particular
| situation. The lean and precise rational model breaks badly
| simply because it doesn't (and can't) account for all the
| factors.
| phao wrote:
| > your life will have plenty of such games
|
| What are you talking about? Which life will have plenty of
| such games? In what way is that true?
| thfuran wrote:
| In the way that these are analogies for actual situations,
| not just pure whiteroom thought experiments.
| phao wrote:
| I suspected that much (that it was an analogy for some
| kind of actual situation).
|
| But what situation? How is it that a person's life has
| many of these chances in large enough volumes to make
| expected values worth it?
| UKR_anon wrote:
| Everytime you book additional insurances that cover small
| amounts of money. Like a airplane ticket insurance (that
| only covers the fee of the ticket if you cancel). Or a
| additional rental car insurance. Assuming that Insurance
| companies are not stupid and only offer an Insurance that
| is +ev for them, that means its -ev for you. If you are
| in the financial situation that 1-5k$ wont ruin you its
| rational to NOT take these kind of insurances.
|
| 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.
| phao wrote:
| I think I get it, but I'm not so sure I'm convinced.
| Those examples, however, don't resonate with me (don't
| have a car, nor a license to drive one; nor I own a
| house; I've been inside an airplane only once).
|
| 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?
| ghaff wrote:
| >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. T
|
| 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.
| ghaff wrote:
| Investing has a degree of this as well. And, in practice,
| most rational investors will diversify based on a number
| of factors into fairly safe but low return assets and
| into potentially higher return but riskier ones.
| phao wrote:
| The investor's situation, I believe, is very much
| different from the common person's. The investor put him
| or herself in the position of doing tons and tons of
| financial transactions and investments, etc, like that.
| He or she put him or herself in a situation such that EV-
| reasoning makes sense. It seems to be that this isn't the
| situation for the common person.
|
| 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.
| ghaff wrote:
| re: sports
|
| 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.
| BeetleB wrote:
| A very common one: You have a debt to pay off (typically
| mortgage). Should you put all your extra money to pay it
| off early or should you pay the minimum and invest the
| rest?
|
| 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.
| UncleMeat wrote:
| This is a key observation in more practical concerns like
| retirement planning. Often, maximizing expected value isn't
| actually what you want. For somebody with a comfortable
| retirement portfolio you care a lot more about not running out
| of money than ending up with a huge amount when you die. So
| you'll choose strategies that might have worse expected values
| but limit the frequency of worst case scenarios.
| petercooper wrote:
| Rory Sutherland (behavioural science chap) made a similar
| point on travel. He says that when he _must_ get to the
| airport on time, he takes the back roads that get him there
| in a _guaranteed_ 30 minutes rather than take the freeway
| that will take 15 minutes 95% of the time but could be
| heavily congested (and inescapable) otherwise. Sometimes
| urgency and efficiency are at odds!
| chmod600 wrote:
| Depends a lot on what the back roads are like, though. The
| freeway can be more reliable a lot of the time.
| incone123 wrote:
| You can turn around in the road if you encounter an
| accident on the back roads. Encounter one on the highway
| and you may be stuck until it's cleared. I always go back
| roads if I need to make a flight.
| divbzero wrote:
| Isn't it expected utility that matters, not expected value?
| From that standpoint taking $1 million guaranteed is rational
| unless you already have high net worth.
| whatshisface wrote:
| This can be captures pretty well by taking the logarithm of
| each outcome's dollar figure before computing the expected
| value, if you ever find yourself wanting to calculate how to
| balance a portfolio.
| fxtentacle wrote:
| Great idea. So you weight x10 the EV as +1 point.
| abnry wrote:
| You can derive what sort of variance a person will tolerate if
| they have a "utility function" quantifying the marginal value
| of each dollar. If you are risk averse (which people usually
| when they have a small net worth) then your utility curve will
| be concave. Think like sqrt(x) function.
|
| 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.
| anigbrowl wrote:
| EV is such a nonsense measure anyway once you step outside the
| realm of pure theory.
|
| 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.
| ghaff wrote:
| Increase the payout with a correspondingly lower probability
| and you're basically lowering the expected utility--down to
| some point where it crosses the sure-fire payout.
| drewg123 wrote:
| Why not form a "company" with 10 friends, and pool the
| winnings?
| yjk wrote:
| I'm not sure on your argument. I belive it's rational to make a
| decision that you would repeat every time you are presented
| with the decision, no matter if you knew beforehand how much
| times that decision would be presented to you.
|
| 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?
| lupire wrote:
| > Why
|
| "Variance" and "risk tolerance"
|
| There is only one of me, not a Large Number
| jstanley wrote:
| > 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).
| UncleMeat wrote:
| Not so. It can be throughly reasonable to make a choice that
| has lower expected value but has a distribution that fits
| your needs more closely.
| CrazyStat wrote:
| If one option doesn't fit your needs then it has lower
| utility.
| Bootvis wrote:
| No it's not, if you play the game 20 times you're almost
| certain to win 50 million and probably a lot more. Unless
| your utility function is flat after 20 million it does
| matter.
| orlp wrote:
| If you play the game 20 games you'll still be better off
| pressing the 1 million button 5-10 times, at the start if
| you don't know in advance how many presses you get, or at
| the end if you do and haven't won big yet.
| jstanley wrote:
| After you've pushed "give me $1 million" on your first go,
| your utility function looks _very_ different to how it did
| before (assuming you 're not already a millionaire).
| ghaff wrote:
| It's an interesting question (assuming you know the number
| of times you get to play up front).
|
| 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.
| anigbrowl wrote:
| _if you play the game 20 times you're almost certain to win
| 50 million_
|
| You can get any result you want if you just rewrite the
| problem conditions *_*
| Bootvis wrote:
| I replied to someone claiming that you should always go
| for certainty no matter how many games you play. If you
| get to play the game 49 times it doesn't make much sense
| to go for certainty 49 times because 2^-49 (or 2^-20) is
| really small.
| seanmcdirmid wrote:
| Unless you already have a million, then 50% chance at 50
| million can make more personal sense than another million.
| mrwh wrote:
| Agreed.
|
| 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).
| rblatz wrote:
| Would you stop working? Or would you take a break until you
| found something you truly wanted to work on?
| mrwh wrote:
| My job _is_ what I want to work on. But I 'm lazy, and I
| know myself well enough to know that if I didn't have to go
| through the things I dislike about my job (hello doing
| performance reviews), I'd stop doing it all. And it would
| ultimately be to my detriment. I wish it were otherwise,
| but there we go.
| xboxnolifes wrote:
| Not the person you replied to, but I would 100% stop
| working. Even when I find things I want to do (not work),
| those rarely last more than a month, usually a week.
|
| 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.
| WalterBright wrote:
| What people say they will do on a hypothetical is not the same
| thing as what they will do if actually faced with the decision.
|
| 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.
| _Algernon_ wrote:
| 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.
| derbOac wrote:
| 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 wrote:
| 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 wrote:
| >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 wrote:
| I'm talking about contests like, design our logo OR build
| the next rocket to the moon.
| roenxi wrote:
| 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
| CrazyStat wrote:
| 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.
| mjdowney wrote:
| 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 [2]
| http://www.eecs.harvard.edu/cs286r/courses/fall12/papers/Tho...
| crazygringo wrote:
| 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
| ghaff wrote:
| 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.
| burntalmonds wrote:
| 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."
| ajuc wrote:
| "You should only gamble with money you don't need." Which
| most people already know.
| baobabKoodaa wrote:
| 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 wrote:
| 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.
| [deleted]
| lostmsu wrote:
| 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.
| the__alchemist wrote:
| 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.
| cm2012 wrote:
| 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.
| 10000truths wrote:
| Other commenters have mentioned marginal utility, but this
| article is basically explaining minimax [0] decision making -
| people (and chess AIs) tend to pick the option that minimizes
| worst case losses.
|
| [0] https://en.wikipedia.org/wiki/Minimax
| k2enemy wrote:
| I don't know how that article is written without mentioning
| utility theory in economics and the concept of diminishing
| marginal utility of money and the risk aversion it implies. No
| need to even bring in behavioral economics.
|
| https://en.wikipedia.org/wiki/Risk_aversion
| tehsauce wrote:
| Agreed. The article claims the scenario is "mathematics vs
| circumstance", but really it's really naive math vs math which
| takes into account the nonlinear utility.
| moviewise wrote:
| There is a documentary about the psychology of financial
| decisions (behavioral economics): Mind Over Money: Nova (2010)
| https://moviewise.wordpress.com/2013/01/14/mind-over-money-n...
|
| "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...
| Hippocrates wrote:
| Given this choice I would press the green button.
|
| 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.
| jimmysnuka wrote:
| Admittedly, I'm not an expert at this stuff, but it seems like
| strictly using expected values to calculate optimum decisions can
| get you into some strange situations, like infinite expected
| value [1]. For some reason the author brings up lump sums vs
| annuities, which I don't think is at all comparable to betting
| (annuities from the US govt are guaranteed payments). That aside,
| a number of people have already mentioned Kelly criterion [2].
| This strategy would tell you that you should take the guaranteed
| $1 million, but this is a long-run strategy. I personally would
| take the $1 million because it is guaranteed. I'm also not sure
| if relying on math for a one-off event like this makes sense.
|
| [1] https://en.wikipedia.org/wiki/St._Petersburg_paradox [2]
| https://en.wikipedia.org/wiki/Kelly_criterion
| fegu wrote:
| This is similar to the choice between a salary (quite
| predictable) and a startup (maybe a lot, might just as well be
| zero). Or, in a company, between doing consulting or in-house
| product development.
| kwhitefoot wrote:
| > A 50% chance of winning $50 million would equate to an expected
| value of $25 million.
|
| No it doesn't. Statistics is the science of populations of
| events, expected value applies only if you have a sufficiently
| large population.
| synu wrote:
| I see this is being downvoted for some reason, but I have the
| same question. I get that if you keep replaying the game the
| expected value materialises over averages, but if you have one
| chance it doesn't sound right that you should expect 25M if the
| two outcomes are zero or 50M? And that this is so true and
| obvious that it is dumb to take the 1M?
| BeetleB wrote:
| It is the expected value if multiple people play the game. As I
| posted in another comment:
|
| 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?
| kwhitefoot wrote:
| No because each event is independent.
| stale2002 wrote:
| But the point is, that we can collect data, based on the
| information that we observed.
|
| The fact that we observed this data, means that this would
| effect our estimation of the situation.
| [deleted]
| BeetleB wrote:
| Fair enough.
|
| 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.
| shapefrog wrote:
| Schrodingers cat is half alive.
| MontyCarloHall wrote:
| This is a nice concrete refutation of the fallacious reasoning in
| Pascal's Mugging [0]. You can take this argument to its absurd
| conclusion by setting probability p arbitrarily small and the
| payout X arbitrarily large, such that p*X is arbitrarily greater
| than $1M, e.g. a 1/100000 chance of winning 100 trillion dollars.
|
| [0] https://en.m.wikipedia.org/wiki/Pascal%27s_mugging
| t_mann wrote:
| Fyi, an imho more illustrative example why we should think in
| terms of expected utility than expected cash flows:
|
| 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
| danielmarkbruce wrote:
| https://en.wikipedia.org/wiki/Expected_utility_hypothesis
| [deleted]
| scarmig wrote:
| Isn't the best solution here to find a wealthy investor and sell
| him the option to press the green button priced at $20M? You get
| $20M, and they get an instrument with an EV of $25M at the cost
| of $20M.
| BiteCode_dev wrote:
| Nassim Taleb famously destroys those lines of reasoning in his
| books: game theory is unpractical for most people, because it
| almost always ignore variables that don't exist in a lab but are
| crucial IRL.
|
| 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.
| codefreeordie wrote:
| It's a catchy headline, but the "decisions" used as examples,
| aren't really "dumb" under the complete set of facts.
|
| 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.
| Ozzie_osman wrote:
| It's just a bad title. Choosing a guaranteed 1M instead of a
| 50% chance at 25M isn't particularly dumb.
|
| "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.
| slfnflctd wrote:
| > psychological underpinnings
|
| 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.
| pid-1 wrote:
| I think you just repeated the article's main argument.
| kwhitefoot wrote:
| Why would anyone bother reading the article when the title
| and pretty much the first line are falsehoods.
| FunnyBadger wrote:
| It think they misstated the actual problem which should have an
| equal EXPECTED value: Expected Value = Value x Probability.
| paganel wrote:
| I still don't get it how hitting the green button (50% at 50
| mullion) is the "rational" choice, it isn't. 1 million in your
| pocket, no matter what, is exponentially and life-changing (for
| the majority of us) better than a 50% of getting nothing. Maybe
| if the value behind the red button would have been smaller (let's
| say $1000 or even $100) then things would have been different,
| but, again an $1 million in one's pocket no matter what is life-
| changing for most of us.
| compiler-guy wrote:
| On a pure, simplistic, naive, reading of expected value it is
| the "rational" choice because $25 million is more than $1
| million.
|
| 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.
| egypturnash wrote:
| Surprise surprise, people are not perfect emotionless economic
| units!
|
| 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.
| compiler-guy wrote:
| He didn't call them dumb. He called them wise, in spite of
| their decisions going against a simplistic expected value
| analysis.
| plorg wrote:
| The discussion here seems to be whether, if we can capture all of
| the relevant details, a certain person is making a rationally
| optimal decision. Taking this to its logical conclusion we're
| fitting math to a process of decision making and adjudicating
| which criteria are considered rational and which are not. Sure
| there is mathematics involved here, but it reads a lot more like
| a question of who is our isn't allowed agency, in this case in
| their economic and financial decisions.
| Cloudef wrote:
| Because people dont care about money if their life has no
| happiness or purpose in the first place
| TheAceOfHearts wrote:
| If there's multiple players with these buttons the optimal
| strategy is to pool your resources and distribute the winnings
| evenly.
|
| Teamwork makes the dream work.
| wizofaus wrote:
| If you could get 10 friends to agree on such an arrangement
| would you still have one press the red button to ensure
| everyone at least gets something? Or take the 1/1024 chance of
| getting nothing at all in return for the likelihood of everyone
| getting 25 million?
| jawns wrote:
| For those who say they would press the red button ...
|
| * 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?
| ghaff wrote:
| You can certainly fiddle with numbers to the point where you
| can basically force a given person to go with green or go with
| red. In general, as you get into certain payouts that aren't a
| big deal for an individual they'll tend to go with higher
| expected value at least up to a point. But as the odds get
| longer, most people will tend to go with certainty as long as
| it's a reasonable amount.
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