Bryan Caplan  

The Immortal Dilemma

Neuroscience and Policy: Bait ... My Planned Oral Remarks...
Suppose you were offered the following gamble:

1. With probability p, you will live forever at your current age.

2. With probability (1-p), you instantly, painlessly die.

What is your critical value of p?  If you combine expected utility theory with the empirical observation that happiness is pretty flat over time, it seems like you should be willing to accept a very tiny p.  But I can't easily say that I'd accept a p<1/3. 

Perhaps the main reason is that all the people I care about would suffer a lot more from my instant death than they'd gain from my immortality.  But even if I were fully selfish, I wouldn't be enthusiastic even at p=.5.  Should I get my head examined?

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The author at Belligerati in a related article titled A curious lottery writes:
    Bryan Caplan asks: Suppose you were offered the following gamble: 1. With probability p, you will live forever at your current age. 2. With probability (1-p), you instantly, painlessly die. What is your critical value of p? If you combine... [Tracked on December 9, 2008 2:04 PM]
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nicole writes:

I would go for this even for a very small p. The downside to dying instantly and painlessly is minimal, especially considering it could be getting you out of a long, drawn-out, painful death later. In fact, instantaneous pain-free death might even be better than immortality, which I'm surprised you haven't considered--there are downsides to living forever, I'm sure.

Andy McKenzie writes:

You should only accept a tiny p if you think that the rest of humanity will also survive for infinite time with you. This is a proposition that your colleague Tyler Cowen does not place a high probability on.

A life devoid of any other society would probably not be very fun, although perhaps you could figure out a way to reverse engineer other intelligent life to have somebody to hang out with.

My p would be about .1. So I'd accept a 90% chance of dying immediately. Imagine how valuable to humanity you would be if you were to live forever! From that perspective, it would be selfish NOT to accept a low p.

Jayson Virissimo writes:

I think I would have a hard time going for something over a 5% chance of instantaneous death. I guess I'm pretty risk averse when it comes to things that could end all of my plans for my life, but then again I'm in my early twenties. Perhaps, when I am 50, I wll accept much higher odds of death for that large a benefit.

Giovanni writes:

The life of any mortal, no matter how matter how great or how miserable, is ultimately finite, so it is basically inconsequential when deciding on something that is infinitely more important.

So the answer should be either close to 0% (if I believe that living for eternity would be a good choice) or over 100% (if I believed that living for ever would turn into an eternal curse).

Dick king writes:

If you discount the future at all than you need a high value of P.

Of course I will age in the remainder of my life, but for a healthy 20 year old who is likely to become a healthy 50 year old without the treatment, if being a healthy 50 year old isn't much worse than being a healthy 20 year old you need a discount rate of less than 3% to support a p of 0.5 and a discount of less than 1% to support a p of 0.2 .

Note that a nonzero discount rate is induced by uncertainty about the future. Even if you really believe the treatment works well when it works [have they remembered to stop my teeth from wearing?], there is uncertainty about whether the future will be an unpleasant place to live.


NW writes:

I wonder what will happen to immortality reseach by individuals such as Aubrey de Grey, as medicine becomes more and more socialized.

Steve Miller writes:

Okay, I give up, what's the catch to P=1?

Steve Miller writes:

As an answer, I mean?

I guess I'm asking what would be so great about living forever.

Zac writes:

Firstly, I think we have do some assuming. Let's assume first that by "live forever at your current age" means that you no longer age, but you can still die (be it via car accident or heat death of the universe). In that case, it is not really a trade off between immortality and instant death, more like instant death vs perpetual youth, which is very different indeed from immortality. I am a relatively healthy 25 year old, but I recognize I could die any moment or any day from any number of illnesses or accidents. I'd be enthusiastic about a p=.8, and would not accept a p<.5.

If indeed we are talking about immortality in the sense of like, a vampire or Superman, I'd probably accept a p of .1 and be very enthusiastic about a p of .2. By this I mean there are ways you can be destroyed, but they are specific and your probability of dying randomly is essentially zero.

If your immortality means you are completely impervious to any sort of destruction besides the end of existence, I am far less excited and would not accept any p. I am not sure I could handle the idea of never being able to die even if it would be utility maximizing for me to do so.

So I can't determine if Bryan needs his head examined until he more clearly defines what he means by immortality.

Full disclosure: I had this exact same discussion in high school sitting around a table in the school library playing Magic: The Gathering, but we were very explicit about what powers would be ascribed on the positive side (we settled with traditional vampire, weak against sunlight but also conferring eternal beauty, inhuman strength, etc) and experimented a bit with how the negative side would affect our value of p (instead of dying instantly, you spontaneously burst into flames). So thanks to TF, KG, DD, DR, and the rest of the guys for making me amply prepared for this very important blog discussion 10 years later.

Zac writes:

@Steve, people have been asking this since the 22nd century BC. Of course, there are different concepts of "living forever" - some more appealing than others (especially if they involve having other super powers). I think here we are really talking about simple biological immortality, meaning that your rate of mortality is unchanged as a function of your chronological age (you can still be killed). As to what's so great about this, I think eternal youth (if you are currently young), being spared from the pains of aging and deterioration, is worth something even if you did not have biological immortality. Beyond that, the question of what's so great about living forever is much the same as the question of what's so great about living to see tomorrow - there is value to living longer as opposed to shorter, ceterus paribus..

Another question that could be asked, and Bryan touched on, is what's so bad about dying an instant painless death? The answer to that question is key to answering the question "what's so great about living forever"

8 writes:

There have been several articles on immortality, and at which age the statistical probability of death approaches 1.

What is it like to be a high school teacher and constantly deal with people of the same age? In some sense, that would be your entire life as an immortal. All the world's a high school, and you are the lunch lady.

JR writes:

If we are utility maximizers, we assume a zero utility gained when dead and our utility function is "well behaved" would the answer not solely depend on what you think your probability of surviving to your ideal age as of the time the game is posed to you (taking into account a given discount rate, however this rate is assumed equal across both states of immortality and deciding not to play the game)?

El Presidente writes:

To have become familiar with the notion of your own mortality is admirable, something akin to wisdom. To have become comfortable with it is another matter altogether. I think your head is probably working just fine.

Dan Weber writes:

I'm reminded of the St. Petersurg Paradox. In a game where the expected return is infinity, shouldn't you be willing to pay your entire lifesavings to play?

Ah, but the first 200,000 dollars is worth a lot more than the millionth 200,000 dollars.

PJens writes:


Have you seen the recent movie Twilight? In it, Edward (a vampire), thinks being immortal is a curse. I agree. I personally would not like to see all my loved ones grow old and die while I could not. Especially since over time I would have anew set of loved ones periodically. I have experienced a close loved one die a prolonged, painful death, as well as some not so close friends and relatives go through similar. In my opinion, a long slow death is better than living forever.

Go have your head examined. I do suggest though that your family do it over a nice meal with good conversation.

Steve Miller writes:

Zac, I guess I should be more specific: what's so great about living forever in a world where everyone around you dies every 80 years, give or take a few decades? Would I really want to live forever if it meant seeing my children grow old and die many times over? Or would I avoid all that and be an immortal hermit? Living to see tomorrow is one thing, because you age another day. What if you don't?

SheetWise writes:

It depends on whether you're living to consume or to create. I see a common assumption among economists that wealth accumulated by an individual has decreasing marginal utility -- which assumes that the individual is living to consume. If you're living to create, the marginal dollar has increased utility.

Personally, I have a dozen commercial projects that I'd like to work through completion, and that I think would leave the world a better place -- but my lifespan will only allow a couple. That's not including the several dozen ideas I've already discounted, because I realize I'll never have either the time and money, or they're simply not important enough to me right now. That's not including the hundreds of new ideas I'd come up with if I was immortal.

Happiness is flat if you're stagnant. Life can turn on a dime, and I may die tomorrow -- in either case, I will die. My mind is certainly influenced by my children being grown. I would be enthusiastic at p = .5 -- I would accept, less than enthusiastically, p = .05.

botogol writes:

I'd be interested to see how the value of p changes with age: I would be good to see a graph of 'average p required' against age.

I'm not at all certain even what general shape to expect.
Personally I'd want 0.4. Aged 45.

hobo writes:

I'd like a small p. when you're dead, you're dead, so it doesn't matter how other people feel about it. When I get old, I'm gonna use the "exit bag", know what I'm saying? Now I'm depressed. thanks a lot Bryan.

Bob Hawkins writes:

A mathematician once observed that, if you lived long enough, you would eventually encounter a run of bad luck that would reduce you to despair, in which everything you trusted, would betray you. In place of this, he observed, we have death.

SheetWise writes:

"A mathematician once observed that, if you lived long enough, you would eventually encounter a run of bad luck that would reduce you to despair, in which everything you trusted, would betray you. In place of this, he observed, we have death."

Damn infinity!

GeniusNZ writes:

To complicate matters - will you in an infinite number of years really be the "same person"? Their values may be entirely different and have no memory of ever being you.

Still... I'd be ok with a pretty low number I think - although it would be a hard decision.

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