Categories:
Behavioral Economics
Game Theory
Suppose you receive the following option.
- You flip a fair coin.
- If the coin is Heads, you acquire healthy immortality.
- If the coin is Tails, you instantly die.
The expected value of this option seems infinite: .5*infinity + 0 is still infinity, no? Even if you apply diminishing marginal utility to life itself, it’s hard to imagine that the rest of your natural life outweighs a 50% shot of eternity… especially if you remember that many of your actual years are unlikely to be healthy.
Nevertheless, I suspect that almost no one would take this deal. Even I shudder at the possibility. So what gives?
READER COMMENTS
David Henderson
Oct 16 2018 at 7:40pm
At age 90, I’ll flip the coin. Maybe even at age 85.
Valerie Kendrick
Oct 16 2018 at 9:32pm
I would delay my choice (being 25) if a delay were offered, but I was assuming the hypothetical was take-it-or-leave-it, in which case I would take it.
ALEXANDER V KAMENSKY
Oct 16 2018 at 7:41pm
You have to balance the expected value of infinite life with infinite death, and infinite death is much worse, than infinite life is good making the expected value negative.
Hazel Meade
Oct 17 2018 at 11:30am
Right. The value of death is not 0 , it is minus infinity.
Philo
Oct 17 2018 at 11:51am
I expect to live another twenty years. My death now would deprive me of the expected value of that span. But that’s definitely a finite quantity.
David R Anderson
Oct 16 2018 at 7:43pm
Loss aversion?
nobody.really
Oct 18 2018 at 12:14pm
Economist Steven Landsburg (author of The Armchair Economist, among other books) posed two related hypotheticals. (Ok, Landsburg’s hypotheticals explore completely different issues than Caplan’s hypothetical, but they still involve flipping a coin with a 50% chance of death, so nyh.)
I. Imagine aliens conquered Earth and demanded retribution for our resistance. Every human would face a 50% chance of instant death. But you alone are given the choice: A) You could flip a coin for each individual, and all the tails would die, or B) you could flip one coin for the entire human race; tails would mean human extinction, but heads would mean no one dies as a result of the alien retribution.
If we care about utility, presumably we’d pick option B. After all, death causes suffering not just to the dying, but to the bereaved. With a 50% mortality rate, the suffering would be unfathomable; forever afterwards, the Holocaust would be a mere footnote in history books. In contrast, universal extinction would eliminate (or at least shorten) all of that. And there’s even a jaunty Tom Lehrer song for the occasion: “We’ll All Go Together When We Go.”
Yet everyone’s visceral reaction is to favor option A. It seems as if we have a reflexive drive to preserve the species, even at incalculable personal expense. I interpret this result to demonstrate that our utility functions are less individualistic, and more integrated, than classical theory acknowledges.
2. You choose Option A–but then it falls to you to do all the coin-flipping for everybody. And as administrator, you’re given a lot of discretion, so long as everyone faces a 50% chance of death. A loving but reclusive couple comes before you. They have no family or other social connections. They ask you to flip one coin for them, ensuring that one of them will die, but that the other would survive to preserve the other’s memory.
Oh, and they aren’t the only couple who makes this request; you get these requests constantly.
You could C) grant each couple’s request, D) simply deny the request and just flip coins independently for each person, or E) say that you’re simply denying the request, but lie. Instead, you treat each couple as a unit, flipping one coin to determine if they both live or they both die.
This hypothetical differs from the first in that human extinction is no longer at issue, and neither is your personal fate.
Again, utility theory suggests that latter option. A surviving couple would regard themselves as especially lucky, and would rejoice with each other; a perishing couple would leave no one to grieve; their memories might be lost, but there’s be no one around to know it. Yet this option would entail substituting your judgment for the judgment of the people who are most intimately involved with the decision–basically, engaging in social engineering.
Thus, this hypothetical is akin to the famous Runaway Trolley hypothetical: Will you exercise your personal judgment and agency to promote greater social happiness, even when other people’s deaths are at stake? Or will you refrain, letting the decision be made by forces outside of you and thereby absolving yourself of responsibility, even if you can foresee that your inaction will lead to greater suffering?
Andrew Barber
Oct 16 2018 at 7:45pm
Isn’t this the St. Petersburg paradox in a different form?
Ken Broad
Oct 16 2018 at 7:46pm
myopic loss aversion
Steve Horwitz
Oct 16 2018 at 8:00pm
For me, these days, every day is something of a gift and my willingness to risk whatever I have left on that bet just isn’t worth it.
One other point: as attractive as healthy immortality is, and it’s always been very attractive to me, it means attending a whole lot of funerals. Part of what makes our lives as they are right now worth living (and not worth risking) is the people who we love and who delight us with their presence. Unless you’re going to promise my family and friends healthy immortality too, I’m not sure I want to watch them all die and go on with out them. Sure you can re-marry or make new friends, but who wants to go through that forever?
gwern
Oct 16 2018 at 11:31pm
Focusing on funerals is an interesting way of framing it. To point out the obvious, not flipping the coin guarantees you and everyone you love will die. Given a fixed number of loved ones/relatives, if you and your loved ones all flip it, then the expected number of funerals attended is only n/2 and n/2 of you die; but if none of you flip it, then all n of you will die – but your expected number of attended funerals is still only n/2 because you will on average die ‘half way through’ the list of deaths, so you attend the first half where the people before you die, and miss the second half, being already dead. (It balances because there are more funerals but less people to go to the funerals and suffer at them; the last person dying has no one attending the funeral at all eg.) So, if dying is at all bad, then everyone flipping the coins dominates no one flipping the coins: in both cases, you personally expect the same number of funerals, but the number of deaths is much smaller in the former case.
If the number of loved ones/relatives can increase over time as dead people are replaced, then flipping the coins is even more appealing, because now there are more funeral attendees…
B. Reynolds
Oct 17 2018 at 11:43am
I’m also thinking that your perspective on funerals would be different if you were immortal. The heaviness of a funeral is mostly about the loss of loved one, if that is who has died, but a good part of it is that it forces you to focus on your immortality in a very acute way.
Think about funerals you’ve attended for someone who is just an acquaintance. While you weren’t grieving, it’s still a heavy affair as you are forced to contemplate your own finality. At least that part would be gone.
John Alcorn
Oct 16 2018 at 8:02pm
My intuition is that many individuals who suffer chronic adverse health conditions, and individuals who have terminal illness, would flip the coin.
Ron
Oct 16 2018 at 8:02pm
You are mistaken thinking that few would take the deal. For many in poor health, it would be a no-brainer, not even difficult to decide.
Andy
Oct 16 2018 at 8:06pm
Potential technical issues with using infinity in this formulation:
1. With discounting, present discounted utility of immortality is still plausibly finite, which solves the apparent puzzle (given risk preferences, at least).
2. Expected values are not well-defined on the extended real numbers. Or, in lay terms, adding infinity to anything is nonsense, doubly so for dividing infinity by 2. So, GIGO. Intuitively people will likely plug in “really big number”, i.e., we’re back to finite utilities.
3. We can arbitrarily rescale utility (at least with positive monotone transformations) and if you are allowing adding and subtracting infinities (which you *must* be if you’re calculating EV), then the utility of each state is easily rescaled to 0 if you live forever and -infinity if you die. (Just subtract infinity from utility in each state.) And now no one ever takes the bet. So merely rewording the problem to an equivalent yields an equally “obvious” answer that is totally different. The problem, of course, is that infinities don’t work that way.
All together, there’s a reason “standard” growth/infinity models have Inada conditions.
John Alcorn
Oct 16 2018 at 8:18pm
Another intuition: If the coin henceforth would be available to a group (or population), then social norms would develop about whether to flip the coin or not. I’m uncertain what the norms would be, but am confident that the emergent norms would shape choices by many (most?) individuals in the group.
Mark Z
Oct 16 2018 at 8:20pm
I think you’re making a rather simple error in your description of the utility function. Instant death isn’t 0. Getting nothing and losing nothing is 0. Instant death is negative infinity, in which case the expected value is: -.5*infinity + .5*infinity. And the (rational) tendency of people to be risk averse would explain why, rather than being a wash, people would almost always choose to abstain from the flip.
Valerie Kendrick
Oct 16 2018 at 9:35pm
Instant death is not negative infinity. That would only be the case if you expected otherwise to live for an infinite period of time.
Given that you will probably only live less than 10 more decades if you don’t take the flip, you give up a finite amount: the years you have left.
And surely we don’t regard each additional second as infinitely valuable. We make choices all the time that trade off future life expectancy in a minor way for other benefits. Like choosing to drive cross-country to visit family for Christmas instead of staying safe at home.
Hazel Meade
Oct 17 2018 at 11:35am
Fair point, but if you discount the future, then the value of infinite life years might not be plus infinity either, and the extra life years beyond your natural life span will be more heavily discounted the younger you are. So depending on your age and discounting factor, the possible loss of near-term life-years could be weighted more heavily than the poossible gain of extra life years many decades away.
Ted
Oct 16 2018 at 9:39pm
Death isn’t negative infinity. Many people choose to die, or choose to take risks that increase their risk of death. If death was negative infinity, then everyone would buckle their seatbelts and use their turn signals. The fact that they don’t means that either (a) death isn’t negative infinity, or (b) they are irrational in a way that makes negative infinity meaningless, meaning negative infinity is meaningless.
Mark Z
Oct 16 2018 at 10:21pm
I think it’s assumed that we’re not considering suicidal people here.
And note that I said instant (and certain) death is negative infinity. I may place a finite (negative) value on a .00001% probability of death while still placing an infinite value on certain death. How much would I need to pay someone to subject himself to a .00001% risk of death? For many people it would indeed be a finite number. How much would I need to pay him to subject himself to certain death? I suspect for most people no finite amount would do.
nobody.really
Oct 18 2018 at 9:50am
Oh, I think it’s not. Quite the opposite: If you’re going to live to infinity, what are the odds that you’ll NEVER become suicidal? I’d put those odds as darned close to 0.
In other words, I’d reject the premise that you can divide the world into suicidal people and non-suicidal people. We can only divide the world between those who are suicidal AT THIS MOMENT, and those who aren’t AT THIS MOMENT.
Kirsten Tynan
Oct 16 2018 at 8:44pm
I would not flip. I’m not convinced that the magnitude of the consequences are desirably balanced even though the probability of occurrence is equal.
What happens if there is some catastrophic disaster resulting in the extinction of humanity—all but you. Then you have to go on living forever by yourself in a horrific wasteland?
If I am going to flip, I want an escape clause from immortality that I can exercise when I want to.
Mark Z
Oct 16 2018 at 8:46pm
Now, there is still an interesting question here: intuitively, one might argue that a rational person would value infinity*.5 more than the finite number of years one can reasonably expect to live time .5. If I have about 50 years left, no amount of risk aversion should justify preferring .5*50 over .5*infinity.
However, it may be a mistake to assume this. If a typical person weights time less the more distant it is in the future, then the integral of their utility function even infinitely into the future is not necessarily infinite itself, but as t (time) approaches infinity utility may approach a finite number. E.g., the integral of y = 1/((t+1)*t^.5) over the interval from 0 to infinity is equal to Pi. So perhaps it’s plausible that, under some von Neumann-Morgenstern utility function, the magnitude of the loss of, say, the next 50 years exceeds that of gaining infinity years.
Mark Z
Oct 16 2018 at 8:51pm
“as t (time) approaches infinity utility may approach a finite number”
I should clarify: I mean, as t approaches infinity, y (utility at time t) approaches 0. The *integral* of the utility function may still approach a finite number as the upward bound approaches infinity.
SkepticProf
Oct 16 2018 at 8:53pm
As written, this is simply an obfuscated form of Pascal’s wager. Indeed, any small but finite chance of immortality “should” outweigh the chance of instant death, if the instant death has any finite value. (Remember that positive affine transformations don’t change utility orderings.)
This, all by itself, might suggest a problem with the formulation. (I believe that Tabarrok 2000, among others, have taken a shot at this: https://philpapers.org/rec/TABBIP)
I’d also like to point out that there is a time value of time. When we talk about the utility of having two cupcakes, one of which will be consumed today and one tomorrow, we discount the second one and thus get decreasing marginal utility for cupcakes as a result. If it’s possible to consume both cupcakes today, however, there is no a priori reason why the second cupcake must be less delicious than the first (the standard mathematical assumptions to the contrary.)
It is NOT, however, possible to consume next year’s life today. Thus, discounting is mandatory (as Andy pointed out above) and the “diminishing marginal utility of life” is the wrong argument to apply.
Another way to look at this problem is that, even with a large finite value of extra time to live in health and wealth, some people WOULD rationally take the flip. The infinity is a needless obfuscation.
Idan Eretz
Oct 16 2018 at 8:53pm
This is just plain risk aversion, which most people share to some degree. Try this thought experiment with the tails cutting a year of your life. Not so bad now, isn’t it? I’ll flip that coin. Maybe even for 5 years, and some people would flip it for 10. Using this experiment, one can actually determine his own degree of risk aversion regarding his own life.
In addition, the utility gain from eternal healthy life are defiantly not infinite. Loved ones will age and die, the would would change to a degree you wouldn’t know it anymore, and suffering can still happen even for a perfectly healthy person. Sudden death, on the other hand, is hands down frightening. It’s engraved in our minds and consciousness by million of years of evolution to avoid sudden death by any means necessary, and so we tend to averse risk. NOT flipping a coin is a very easy method of achieving such an avoidance, and so most people would choose it instantly.
Jess Riedel
Oct 16 2018 at 9:07pm
I would absolutely flip that coin. It would be scary but I would jump at the chance, just as dangerous transplant surgery is scary but desperately sought by those with failing organs.
I am very surprised at the contrary preferences and intuitions in this thread.
Valerie Kendrick
Oct 16 2018 at 9:30pm
I would take it, pretty easily.
I’m 25.
The only way I would not take it is if I assigned a lot higher probability to technologies granting effective immortality to currently-living people being developed in my lifetime.
This is also, of course, assuming that the “immortality” is of the indefinite lifespan kind, not literal inability to die even if you want to. I don’t think the latter is very relevant to real-world ethics, but literal inability to die would eventually result in some kind of infinitely bad failure state, like getting trapped in the middle of a star.
Eli
Oct 16 2018 at 9:33pm
My final 100000000000000000000000000000+ years will probably be sheer misery
So there’s that
Ted
Oct 16 2018 at 9:36pm
I don’t think anyone knows what healthy immortality means.
Does it mean we spend 99.9999999% of our lives floating in space after all the stars have extinguished?
Does it mean we will spend our lives hunted by governments who wish to experiment upon us to extract the secrets of healthy immortality, dooming us to a fugitive life followed by eventual capture and years of fruitless torture?
Does it mean we can sell our body technology and forever change the course of the human species and life in the universe as we know it?
A heuristic of saying no to deals that seem too good to be true and involve a 50% chance of death is not a bad heuristic.
I’d take the flip.
nobody.really
Oct 18 2018 at 12:27pm
Interesting thoughts.
Contrary to many of the comments here, I had wondered that a person might not have a social duty to take the flip. Even if I anticipated that immortality might eventually become a curse for me personally, should my own welfare override the good that having an immortal person around might provide for mankind?
But I guess there’s also the possibility that an immortal person around might prove to be a curse for mankind. So I guess we’d have to weigh that in the equation, too.
Mark Bahner
Oct 16 2018 at 10:23pm
I hope no children would take the deal while their parents are alive. But like David Henderson, I’d flip the coin. Maybe even before age 85.
Mark Bahner
Oct 16 2018 at 11:07pm
Another thing to consider is that the performance of the S&P 500 from 1928 to 2017 was about 10 percent per year. So in a mere 100+ years, you’d be pretty darn wealthy.
Jonathan S
Oct 17 2018 at 12:31am
How can one be certain that the an eternal life would be desirable?
A person living a happy, abundant life at the time of their decision may base their decision to flip the coin on their current state of mind, without regard to the possibility of eternity converging towards hell. Similarly, a depressed person at the time of their decision may base their decision to not flip the coin on their current state of mind, without regard to the possibility of eternity converging towards paradise.
Also, once committed to eternity, it seems that one would not be able to escape existence. The idea of existing forever and ever and ever, etc. seems as frightening as permanent death, however irrational the fear.
James R Phillips
Oct 17 2018 at 1:17am
The option is a gamble with infinite expected value that doesn’t seem worth it, in contrast with the value proposition offered by insurance.
When you buy insurance, it has a finite expected value, and the price you pay is always more than the expected value. So why would you buy it?
Not because of its expected value, but because it reduces the variance, or variability, in outcomes. We pay more than its expected value to get a reduction in variability of outcomes.
And variability is the issue with your option. The expected value sounds great, but the the 50% chance of losing the rest of your life – is too great. It isn’t worth it taking the chance.
To some people the chance is worth taking if the probability of losing your life drops low enough. The lower it drops, the smaller the variance in outcomes. So reduction in variance seems like something people value in general, and something we are often willing to pay for.
Take a look at the famous essay by Shaw, “The Vice of Gambling and the Virtue of Insurance” for further insights.
Salem
Oct 17 2018 at 5:02am
Millions long for immortality who don’t know what to do with themselves on a rainy Sunday afternoon. – Susan Ertz.
I’m not sure I want healthy immortality. I’m not too keen on death either, but even the most optimistic have to admit that life contains a lot of farting around.
I’m not taking the flip, because it puts far too high a chance of disrupting already-made plans. Who’s going to look after your wife and family, etc. The flip looks much more appealing if either you have a long time to plan for it, or you do it when very young.
Abe Niederhauset
Oct 17 2018 at 5:08am
The present value of an annuity that pays into perpetuity isn’t infinity. The same would apply to life. Each year provides utility, and the utility for distant years is discounted heavily. Combine this with the fact that people receive more disutility for a loss than utility for an equally sized gain, and I believe we have a reasonable explanation. For any given discount rate and life expectancy, we could calculate the age at which someone would be willing to flip the coin.
Knut P. Heen
Oct 17 2018 at 6:13am
It is a version of the St.Petersburg-paradox.
The game goes as follows. The pot starts at $2. The game stops if you get tails and you get the pot. The game continues if you get heads and the pot doubles. The game continues until the first tails appear. The expected pay-off is infinite because the probability for $2 is 1/2, the probability for $4 is 1/4, and so on. An infinite row of ones. Yet most people will not pay much to participate.
The standard answer is that the expected utility is a finite number. Daniel Bernoulli proposed log-utility already in the 1700s. The problem with this solution is that we can just change the pot rule such that it increases faster than the marginal utility declines. A pot that increases exponentially may for instance kill the log-utility approach (infinite expected utility).
My understanding of the present problem is that the good outcome gives something akin to infinite utility. The problem with infinite utility is that one should be willing to flip even if the probability of obtaining it is very small. I am not completely sure about the math, but I think infinity is defined such that one percent times infinity also equals infinity.
When I teach the St.Petersburg-paradox , I always end by saying that an underlying assumption in economics is scarcity. Hence, the casino must always default on the promise to pay infinity. I generally do not like infinity arguments in economics because I think it violates the scarcity assumption.
An interesting macro implication here is that if everyone accepted the bet, the population would immediately be reduced by one half, and the remaining people would live for eternity without having to spend resources on health or religion.
F. E. Guerra-Pujol
Oct 17 2018 at 6:25am
Two words: loss aversion.
Greg
Oct 17 2018 at 9:41am
The fact that suicide is a thing guarantees that some people flip a coin. If they’re serious and competent, their coin flip is heads: die, tails: die. This may say something about the value of death, or the definition of healthy. It probably says that the value tradeoff is variable.
Hazel Meade
Oct 17 2018 at 11:29am
Perhaps the value of dying should not be counted at “0”. I would think that a “zero” would be “no change to baseline” – as in you still get to live the rest of your life as normal. Dying instant would be a loss of negative infinity. So if you have a 50-50 choice between plus infinity and minus infinity the value of the flip comes out to zero.
Jonathan S
Oct 17 2018 at 1:09pm
Not necessarily. It just depends on the flavor of infinity. The outcome of that sum could be anywhere from negative infinity all the way to positive infinity.
B. Reynolds
Oct 17 2018 at 11:47am
If immortal, would suicide still be an option? I’d hate to be the only remaining human at some point.
Ben
Oct 17 2018 at 12:42pm
I say this with all the love in my heart, as an economics major myself: it would only occur to an economics professor to create a model where the value of immediate death is completely neutral, the value of living forever is infinite, and think “damn, this sure is a great model, why arent humans conforming to it?”
This is a nice hypothetical to show the limits of expected value calculations: they need to be more nuanced than this to allow for the fact that we already have a certain ballpark expected value for the rest of our life and that taking that expected value away from us should not be thought of as a value-neutral act
Mark Bahner
Oct 17 2018 at 7:49pm
+1,000,000,000,000. 🙂
From my engineering background…never confuse a model with reality. 😉
AlexR
Oct 17 2018 at 2:30pm
There’s no mystery here. Even if people were risk neutral, the overwhelming majority should reject the bet on present value grounds. Assuming, for example, a constant annual value of life and an annual discount rate of 6% (realistic for me), the expected present value of the bet is negative for anyone with a life expectancy of 12 years or more. The bet is even a worse deal, of course, at higher discount rates or with life values that decline with age.
Valerie Kendrick
Oct 17 2018 at 6:03pm
I think it is a mistake to take discount rates as a given here.
One of the most important reasons that it’s rational to have a moderately high discount rate is that we only have a limited life expectancy to enjoy the fruits of our investments. If I were to sock away everything I earned at a 2% rate of return until I turned 100, that would be silly (assuming I didn’t have solely altruistic purposes) because it’s unlikely that I would even live that long, and if I did, I probably wouldn’t have much longer to spend my hoard or the health to enjoy it.
Under a scenario of healthy immortality, that all goes out the window. It would be completely irrational to have a discount rate that high. You would still prefer earlier money to later money if you could get them at the same rate (but in a society of immortals, interest rates would drop like a rock), but to me there seems to be no reason at all to prefer an earlier year of life to a later one, if they’re both guaranteed and healthy.
Michael Gray
Oct 17 2018 at 3:43pm
The answer is easy, surely: who wants to live forever in a human body, albeit immortal, on this earth?
Scott Sumner
Oct 17 2018 at 5:47pm
I’d do it if given the suicide option after winning eternal life.
Seth
Oct 17 2018 at 5:51pm
What gives?
I’m not sure equating value with absolute time is valid.
It seems simple. If you shudder at the thought, you don’t value an infinite life nearly as much as you value avoiding instant death.
Maybe you can’t truly imagine the value of infinite life, or maybe you can and realize it would lose it’d luster relatively quickly and become worthless, in which case the value is much < infinity and < avoiding instant death.
Rob Rawlings
Oct 17 2018 at 8:07pm
It would not take a very high discounting of present years of life over future years of life before the high probability of 20-30 years of life had a greater present utility than a 50% probability of infinite years of life.
Plus most people place a very high disutility on present death, while the disutilty of death 20-30 years in the future is heavily discounted.
For these reasons combined I do not find it surprising that for most people the value of (50% chance of instant death , 50% chance of eternal life) is worth less to people than (90% chance of 2o+ years of life and guaranteed future death).
Warren Platts
Oct 17 2018 at 8:27pm
Eh… Who wants to live forever? Not me….
nobody.really
Oct 18 2018 at 10:00am
Some people do–explicitly.
LeviJ
Oct 17 2018 at 9:57pm
Applying the law of diminishing marginal utility to human lifespan is an interesting idea to consider. After all, as we grow older and older, our bodies begin to slow down and become more and more dysfunctional. The more years of life that we live, the lower the quality of life we will experience, and the lower each year’s marginal utility has for us. I always feel like many elderly people just get fed up with life and stop caring, so this concept kind of rings true to me. You would think that older people that had less in them left to lose would go for the risk, but I almost wonder if some people that were elderly and were already experiencing low marginal utility of life year to year, would rather just die than risk living forever.
The proposal of a coin flip that could give someone eternal, healthy life makes me question if an eternal life could exist without feeling the crushing weight of diminishing marginal utility from year to year. Sure, you will remain physically healthy forever, would such a life provide infinite mental health as well? Certainly, after so many years, you would get completely bored with existence and would be tired of everyone that you become friends with constantly dying and leaving you to your bitter existence to have to find new ones. I suppose if the coin flip could also provide eternal mental health, the flip would be far more worthwhile, and could maybe help reduce the diminishing marginal utility felt over the eternity.
Jacky Zhao
Oct 17 2018 at 11:07pm
The flip of a coin that is the determinant of one’s future is likely to only be taken by ones who are high risk-taker or by ones that lacks the present opportunity. In terms of the coin deciding the fate of eternity to instant death, the situation changes. We introduce the idea of marginal utility into the equation.
With each passing year, the idea marginal utility of life decreases which brings to the idea of diminishing marginal utility. But as life, in respect to age, rides the downward slope of diminishing marginal utility, the idea of the coin flip becomes more appropriate.
In perspective, the increase in one’s age to the marginal utility of life can be represented by a function similar to (1/X) when X>0. The idea of flipping the coin can be represented by a function similar to (X^2) when X>0. Graphing these two idea, there is a point when the idea of flipping the coin far exceed the marginal utility of life.
Daniel Cooke
Oct 17 2018 at 11:31pm
A life decision in dependent on the flip of the coin. We all make hard life decisions leaving something up to chance. While this decision seems like a larger decision, it is like others that we face every single day. It is important with every decision we make to consider all of the factors involved. While typically this includes simple pros and cons, another aspect is included with this decision, the value of life. The largest question that we face in this decision, as well as most other decisions we make is: what is the value of this? In this case, what is the value of life?
How does one quantify the value of life? What number can we put to life? As we can put a number to the number of days, hours, minutes, and seconds we have lived thus far, it is difficult to put a quantifiable value to it. Even if we do put a value to it, if we apply diminishing marginal utility to our lives, that would create the assumption that each successive day is slightly worse than the previous. Even if our lives were based on diminishing marginal utility, a person would not choose to flip the coin as each day for the rest of eternity would gradually get worse and worse. But there is a different reason that this situation makes us shudder. I personally believe that my best days in my life are still to be lived.
The majority of people do not look at their lives as though they have diminishing marginal utility. If this were the case, than we would not desire to live another day after the day that we were born. I would say that we do not experience diminishing marginal utility in our lives, we experience variably increasing marginal utility in our lives. The majority of people you ask will tell you that today is better than yesterday, or even if it was not, if you asked them if they felt that they had a chance to make tomorrow better, they would tell you that they felt that they could. If we did not have variable increasing marginal utility in life, everyone would begin to kill themselves as there would become a point where death is more valuable than life.
RPLong
Oct 18 2018 at 10:49am
I’m always surprised by the fact that questions such as these bring out many pessimists. I would love to live forever. I very much wish I could.
I think that perhaps “loss aversion” is the technical answer, but I think there’s something lost in putting it that way. We’re not merely averse to the unspent life we’ll lose; we’re averse to death itself. I suspect our natural sense of self-preservation kicks in here; we would rather keep living now for sure than risk dying. Similarly, I suspect that even a terminally ill man who found himself drowning in a lake would fight to get to the surface and swim to safety, no matter how little life he had left.
robc
Oct 19 2018 at 9:18am
I wouldn’t flip.
It makes it an easy decision when you already believe your soul is immortal.
Rafal M Smigrodzki
Oct 21 2018 at 1:22am
Where is the coin? How much do I need to pay you?!
Of course I’d take the chance right now, as you note, the expected payoff is so high it’s a no-brainer. I would take it even with a 1/20 chance of immortality. Not 1/200 though, my cryonics policy gives me most likely better odds.
Jonathan S
Oct 21 2018 at 1:04pm
Another way to ask this question, is how different would society be if other people chose to flip the coin. There probably wouldn’t be much change to society if a few random people flipped the coin in the past. But society may be radically different at this point in time if, say, Stalin flipped the coin when he was 20 years old.
Dzhaughn
Oct 25 2018 at 3:15pm
The promise of innumerable healthy days is doubtful. It appears to admit no empirical tests, and it is difficult to interpret its meaning.
What sort of god is it that can actually fulfill the wager, but only 50% of the time? If we could honestly stipulate to the existence of that god, why would we trust our ability to reason about the value of life and death?
Anton Maier
Nov 10 2018 at 7:32pm
our neural nets aka brains are converging against decisions that are relevant in real world settings.
I’d say youre inclined not to risk your life because the chance of you having the option to improve your life infinitely is pretty low and the chance that you misunderstood the situation quite high.
Loss aversion is not an irrational bias but a rational strategy in real world settings. Which become irrational in lab settings.
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