I don't understand: the situation here is one where your only option is to be all in cash or all in the stock. The Kelly criterion only makes sense when you can choose an arbitrary fraction to be in each.

(And the Kelly criterion amounts to maximizing E(delta log wealth), which is exactly what I'm proposing. If you have to wager your entire bankroll, any gamble with a nonzero chance of bankrupting you has E(delta log wealth) = -infinity and just sitting on your cash is better.)

Nope. And if what you're after is the best long-run result and your utility is anything like logarithmic in wealth, this is exactly what you want.

(Although if Pr(lose everything) is small enough then the observation that you almost always get approximately the expectation in the long run is irrelevant unless the run is infeasibly long. So you might want to truncate your return distributions somehow, if you're prepared to accept a tiny probability of ruin for doing better almost all the time.)

[EDITED to add a missing right-parenthesis.]

Yes, but I mean doesn't the real world UN have standing orders about invasions? I thought the UN charter mandated defense of its members.

Please give a few concrete examples.

The Prime Number Theorem

A group of four people can stand two by two, but a group of five people can only stand five in a line. The number of numbers like five, and not like four, between two numbers, is the number of times you take two times what you had, starting at one, to get between the two numbers if the two numbers are close.

I were to be a tax lawyer, I would be directly harming the ability of the US government to spend on social welfare programs.

You could always go work for the IRS. It employs a lot of tax lawyers.

But there's a bigger issue: you think that the work of a (privately employed) tax lawyer intrinsically harms the ability of the US government to spend? That belief has LOTS of issues. I'll start with two: One, why do you think the capability of the US government to spend is an unalloyed good thing? And two, do you happen to know the volume (say, in feet of shelf space) of the current tax laws, regulations, and rulings? I'd recommend you find out and then think about whether any moderately complicated business can comply with them without the help of a tax lawyer.

If I worked on Wall Street anywhere but Vanguard I would be bilking people out of their life savings

Sigh. First, Vanguard is not part of Wall Street. Second... you really should not believe everything the popular media keeps feeding you.

I think the problem with elite common sense is that it can be hard to determine whose views count. Take for instance the observed behavior of the investing public determined by where they put their assets in contrast with the views of most economists. If you define the elite as the economists, you get a different answer from the elite as people with money. (The biggest mutual funds are not the lowest cost ones, though this gap has narrowed over time, and economists generally prefer lower cost funds very strongly)

I think the idea is that someone submitting CooperateBot is not trying to win. But I find this a poor excuse. (It's why I always give the maximum possible number whenever I play "guess 2/3rds of the average.") I agree that the competition should have been seeded with some reasonable default bots.

Submitting DefectBot makes you a CDT agent, not a troll.

I would have expected a few more metaevaluator bots which clean up the environment to prevent detection. Of course this can be an expensive strategy, and certainly is in programmer time. A metaevaluator bot would have probably broken several recursion detection strategies, or even defining set! out of the language.

This happened in Canon, and was done by Hermione herself, albeit in her I think 6th or 7th year.