The Drake equation for cryonics is pretty simple: work out all the things that need to happen for cryonics to succeed one day, estimate the probability of each thing occurring independently, then multiply all those numbers together. Here’s one example of the breakdown from Robin Hanson. According to the 2013 LW survey, LW believes the average probability that cryonics will be successful for someone frozen today is 22.8% assuming no major global catastrophe. That seems startlingly high to me – I put the probability at at least two orders of magnitude lower. I decided to unpick some of the assumptions behind that estimate, particularly focussing on assumptions which I could model.

EDIT: This needs a health warning; here be overconfidence dragons. There are psychological biases that can lead you to estimating these numbers badly based on the number of terms you're asked to evaluate, statistical biases that lead to correlated events being evaluated independently by these kind of models and overall this can lead to suicidal overconfidence if you take the nice neat number these equations spit out as gospel.

Every breakdown includes a component for ‘the probability that the company you freeze with goes bankrupt’ for obvious reasons. In fact, the probability of bankruptcy (and global catastrophe) are particularly interesting terms because they are the only terms which are ‘time dependant’ in the usual Drake equation. What I mean by this is that if you know your body will be frozen intact forever, then it doesn’t matter to you when effective unfreezing technology is developed (except to the extent you might have a preference to live in a particular time period). By contrast, if you know safe unfreezing techniques will definitely be developed one day it matters very much to you that it occurs sooner rather than later because if you unfreeze before the development of these techniques then they are totally wasted on you.

The probability of bankruptcy is also very interesting because – I naively assumed last week – we must have excellent historical data on the probability of bankruptcy given the size, age and market penetration of a given company. From this – I foolishly reasoned – we must be able to calculate the actual probability of the ‘bankruptcy’ component in the Cryo-Drake equation and slightly update our beliefs.

I began by searching for the expected lifespan of an average company and got two estimates which I thought would be a useful upper- and lower-bound. Startup companies have an average lifespan of four years. S&P 500 companies have an average lifespan of fifteen years. My logic here was that startups must be the most volatile kind of company, S&P 500 must be the least volatile and cryonics firms must be somewhere in the middle. Since the two sources only report the average lifespan, I modelled the average as a half-life. The results really surprised me; take a look at the following graph:

(http://imgur.com/CPoBN9u.jpg)

Even assuming cryonics firms are as well managed as S&P 500 companies, a 22.8% chance of success depends on every single other factor in the Drake equation being absolutely certain AND unfreezing technology being developed in 37 years.

But I noticed I was confused; Alcor has been around forty-ish years. Assuming it started life as a small company, the chance of that happening was one in ten thousand. That both Alcor AND The Cryonics Institute have been successfully freezing people for forty years seems literally beyond belief. I formed some possible hypotheses to explain this:

1. Many cryo firms have been set up, and I only know about the successes (a kind of anthropic argument)
2. Cryonics firms are unusually well-managed
3. The data from one or both of my sources was wrong
4. Modelling an average life expectancy as a half-life was wrong
5. Some extremely unlikely event that is still more likely than the one in billion chance my model predicts – for example the BBC article is an April Fool’s joke that I don’t understand.

I’m pretty sure I can rule out 1; if many cryo firms were set up I’d expect to see four lasting twenty years and eight lasting ten years, but in fact we see one lasting about five years and two lasting indefinitely. We can also probably rule out 2; if cryo firms were demonstrably better managed than S&P 500 companies, the CEO of Alcor could go and run Microsoft and use the pay differential to support cryo research (if he was feeling altruistic). Since I can’t do anything about 5, I decided to focus my analysis on 3 and 4. In fact, I think 3 and 4 are both correct explanations; my source for the S&P 500 companies counted dropping out of the S&P 500 as a company ‘death’, when in fact you might drop out because you got taken over, because your industry became less important (but kept existing) or because other companies overtook you – your company can’t do anything about Facebook or Apple displacing them from the S&P 500, but Facebook and Apple don’t make you any more likely to fail. Additionally, modelling as a half-life must have been flawed; a company that has survived one hundred years and a company that has survived one year are not equally likely to collapse!

Consequently I searched Google Scholar for a proper academic source. I found one, but I should introduce the following caveats:

1. It is UK data, so may not be comparable to the US (my understanding is that the US is a lot more forgiving of a business going bankrupt, so the UK businesses may liquidate slightly less frequently).
2. It uses data from 1980. As well as being old data, there are specific reasons to believe that this time period overestimates the true survival of companies. For example, the mid-1980’s was an economic boom in the UK and 1980-1985 misses both major UK financial crashes of modern times (Black Wednesday and the Sub-Prime Crash). If the BBC is to be believed, the trend has been for companies to go bankrupt more and more frequently since the 1920’s.

I found it really shocking that this question was not better studied. Anyway, the key table that informed my model was this one, which unfortunately seems to break the website when I try to embed it. The source is Dunne, Paul, and Alan Hughes. "Age, size, growth and survival: UK companies in the 1980s." The Journal of Industrial Economics (1994): 115-140.

You see on the left the size of the company in 1980 (£1 in 1980 is worth about £2.5 now). On the top is the size of the company in 1985, with additional columns for ‘taken over’, ‘bankrupt’ or ‘other’. Even though a takeover might signal the end of a particular product line within a company, I have only counted bankruptcies as representing a threat to a frozen body; it is unlikely Alcor will be bought out by anyone unless they have an interest in cryonics.

The model is a Discrete Time Markov Chain analysis in five-year increments. What this means is that I start my hypothetical cryonics company at <£1m and then allow it to either grow or go bankrupt at the rate indicated in the article. After the first period I look at the new size of the company and allow it to grow, shrink or go bankrupt in accordance with the new probabilities. The only slightly confusing decision was what to do with takeovers. In the end I decided to ignore takeovers completely, and redistribute the probability mass they represented to all other survival scenarios.

The results are astonishingly different:

(http://imgur.com/CkQirYD.jpg)

Now your body can remain alive 415 years for a 22.8% chance of revival (assuming all other probabilities are certain). Perhaps more usefully, if you estimate the year you expect revival to occur you can read across the x axis to find the probability that your cryo company will still exist by then. For example in the OvercomingBias link above, Hanson estimates that this will occur in 2090, meaning he should probably assign something like a 0.65 chance to the probability his cryo company is still around.

Remember you don’t actually need to estimate the actual year YOUR revival will occur, but only the first year the first successful revival proves that cryogenically frozen bodies are ‘alive’ in a meaningful sense and therefore recieve protection under the law in case your company goes bankrupt. In fact, you could instead estimate the year Congress passes a ‘right to not-death’ law which would protect your body in the event of a bankruptcy even before routine unfreezing, or the year when brain-state scanning becomes advanced enough that it doesn’t matter what happens to your meatspace body because a copy of your brain exists on the internet.

My conclusion is that the survival of your cryonics firm is a lot more likely that the average person in the street thinks, but probably a lot less likely that you think if you are strongly into cryonics. This is probably not news to you; most of you will be aware of over-optimism bias, and have tried to correct for it. Hopefully these concrete numbers will be useful next time you consider the Cryo-Drake equation and the net present value of investing in cryonics.