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Donald Rumsfeld, from http://www.defense.gov/transcripts/transcript.aspx?transcriptid=2636 "Reports that say that something hasn't happened are always interesting to me, because as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns -- the ones we don't know we don't know."
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.)
Ah, I missed that part of the OP. So then I think your argument is correct.
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.]
This doesn't seem right. Let's assume that the stock gives double or nothing, with 51% probability of double. The Kelly Criterion suggests giving 1% of the total payroll in stock. Yes, this neglects the balancing fee. Your argument seems to suggest that we should be all in cash. But the Kelly bet outperforms this.
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.
The few examples of UN lead responses to invasions that worked typically involved great powers backstopping the response. UN members are reluctant to expend blood and treasure without getting something in return. I think the only time it worked as intended was the Korean war, and that's because Stalin was sitting out for a bit.
In response to
Unpopular ideas attract poor advocates: Be charitable
Please give a few concrete examples.
Trotskyism is represented in the US by the Spartacist League. The members do not seem well adjusted socially.
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.
By "Wall Street" I'm including the Buy Side as well as the Sell Side. The big buyside firms like Fidelity and Charles Schwab sell products that most people shouldn't buy. Insurance probably has a better case to buy some actively managed products, or some exotic derivatives, but I don't know why it can't do it itself.
To the extent that finance reallocates risk it can provide a positive utility benefit. However, the very productive businesses have questionable utility. Promoting active trading, picking hot funds etc, all eat into the returns clients can expect. Justify the existence of Charles Schwab's S&P 500 index fund, with expense ratio twice that of Vanguards. The most profitable divisions of investment banks tend to be the ones with the least competition, and hence most questionable social benefit.
I'm aware Dodge and Cox is in SF, and Vanguard in Valley Forge, Blackrock in Princeton, etc. However, they are all on "the Street".
The IRS doesn't pay well: for government pay one might as well work for NASA and accomplish something fun.
In response to
Common sense as a prior
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.
How do we draw the line? Tit-for-Tat is very simple, yet does very well. Arguably before knowing how it performs it could be considered a troll.
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I'm not sure I agree with 9. There is a lot of SF out there, and some of it (Roadside Picnic, Stanislaw Lem's works) presents the idea that the universe is inherently uncaring in a very real way. Anthropomorphization is not an inherent feature of the genre, and fiction might enable directly understanding these ideas in a way that argument doesn't make real for some people.