army1987 comments on Explicit and tacit rationality - Less Wrong

40 Post author: lukeprog 09 April 2013 11:33PM

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Comment author: gwern 10 April 2013 04:02:31PM 6 points [-]

Also, in real humans, rationality isn't all-or-nothing. Compare Oprah with an average person from her reference group (before she became famous). Is she really less rational? I doubt it.

That seems entirely possible. Consider the old chestnut that entrepreneurs are systematically overoptimistic about their chances of success and that startups and similar risks are negative expected value. Rational people may well avoid such risks precisely because they do not pay, but of the group of people irrational enough to try, a few will become billionaires. Voila! Another example: any smart rational kid will look at career odds and payoffs to things like being a musician or a talk show host, and go 'screw that! I'm going to become a doctor or economist!', and so when we look at mega-millionaire musicians like Michael Jackson or billionaire talk show hosts like Oprah... (We are ignoring all the less rational kids who wanted to become an NFL quarterback or a rap star and wind up working at McDonald's.)

Another point I've made in the past is that since marginal utility seems to diminish with wealth, you have to seriously question the rationality of anyone who does not diversify out of whatever made them wealthy, and instead go double or nothing. Did Mark Zuckerberg really make the rational choice to hold onto Facebook ownership percentages as much as possible even when he was receiving offers of hundreds of millions? Yes, he's now currently a billionaire because he held onto it and worth increased some orders of magnitude, but social networks have often died - as he ought to know, having crushed more than his fair share of social networks under his heel! In retrospect, we know that no one (like Google+) has killed Facebook the way Facebook killed Myspace. But only in retrospect.

Or since using these past examples may not be convincing to people since it's too easy to think "obviously holding onto Facebook was rational, gwern, don't you remember how inevitable it looked back in 2006?" (no, I don't, but I'm not sure how I could convince you otherwise), let's use a more current example... Bitcoin.

At least one LWer currently holds something like >500 bitcoins, which at the current MtG price could be sold for ~$120,000. His net worth independent of his bitcoins is in the $1-10,000 range as best as I can estimate. I am sure you are seeing where I am going with this: if bitcoin craters, he will lose something like 90% of his current net worth, but if bitcoin gains another order, he could become a millionaire.

So here's my question for you, if you think that it's obvious that Oprah must have been rational, and was not merely an irrational risk-seeker who among other things got lucky: right now, without the benefit of hindsight or knowledge of inevitability of Bitcoin's incredibly-obvious-success/obviously-doomed-to-failure, is it rational for him to sell or to keep his bitcoins? Is he more like Zuckerberg, who by holding makes billions; or more like all the failed startup founders who reject lucrative buyouts and wind up with nothing?

It is rational for him to:

Suppose he holds, and Bitcoin craters down to the single dollar range or less for an extended time period; do you think people will regard his decision as:

Suppose he holds, and Bitcoin gains another order of magnitude (>$1000) for an extended time period; do you think people will regard his decision as:

Suppose he sells, and Bitcoin craters down to the single dollar range or less for an extended time period; do you think people will regard his decision as:

Suppose he sells, and Bitcoin gains another order of magnitude (>$1000) for an extended time period; do you think people will regard his decision as:

Submitting...

Comment author: [deleted] 14 April 2013 09:06:05PM 1 point [-]

It is rational for him to:

Expanding on RomeoStevens' comment... Maths time! Suppose that he has now 10,000 dollars and 500 bitcoins, each bitcoin now costs $100, and that by the end of the year a bitcoin will cost $10 with probability 1/3, $100 with probability 1/3, and $1000 with probability 1/3. Suppose also that his utility function is the logarithm of his net worth in dollars by the end of the year. How many bitcoins should he sell to maximize his expected utility? Hint: the answer isn't close to 0 or to 500. And I don't think that a more realistic model would change it by that much.

Comment author: gwern 14 April 2013 09:55:57PM 1 point [-]

Khoth suggests modeling it as starting with an endowment of $60k and considering the sum of the 3 equally probable outcomes plus or minus the difference between the original price and the closing price, in which case the optimal number of coins to hold seems to be 300:

last $ sort $ map (\x -> (log(60000 - 90*x) + log(60000) + log(60000 + 900*x), x)) [0..500]
(34.11321061509552,300.0)

Of course, your specific payoffs and probabilities imply that one should be buying bitcoins since in 1/3 of the outcomes the price is unchanged, in 1/3 one loses 90% of the invested money, and in the remaining 1/3, one instead gains 1000% of the invested money...

Comment author: [deleted] 15 April 2013 08:18:43AM 0 points [-]

I've fiddled around a bit, and ISTM that so long as the probability distribution of the logarithm of the eventual value of bitcoins is symmetric around the current value (and your utility function is logarithm), you should buy or sell so that half of your current net worth is in dollars and half is in bitcoins.