This is a fascinating collective decision making scheme. One potentially serious nitpick. In the "one dollar one vote" scheme, it makes a simplification that seems really bad. It's the same flavor of mistake as when you have the option of making a bet. If the expected return is positive, it says you should bet all of your money. In reality, people don't do this. Rational actors shouldn't even do this.
I'd love to see what an attempt at this same sort of number-of-votes-is-proportional-to-value comes to with a less simplified model of behavior. If I value outcome A at price $x and outcome B at price $y, I might not be able to afford $x^2+y^2, and this model doesn't say what I would or should do. A corresponding model that talked about how people allocate their finite money rather than a unit by unit spending description seems like it would better apply to reality.
It's simply not true that if EV is positive, you should bet all of your money. There's a classic formula called the 'Kelly criterion' to calculate how much of your money should be bet given your expected edge. The original paper (which came out of Bell labs, based upon noise over a transmission channel!) is a good read:
Can I check something - reading the wikipedia article on Kelly Bets it seems that one should take the expected chance of winning, double it and subtract 1.0 and use that as percentage of bet size
So when I win 3/4 times, that's .75 -> 1.5 -> .5 of my total wealth.
But this basically means never gamble till the odds are in your favour. (ie above .5 chance of winning)
Yes, although it is mathematically the ‘best’ way of increasing your bank, it is more aggressive than most people would be comfortable.
IIRC, at any point in time, you have a 50% chance of losing half of your wealth at some point in the future, when following Kelly staking. Most people choose some fraction of Kelly stakes in order to be less aggressive
Comments
This is a fascinating collective decision making scheme. One potentially serious nitpick. In the "one dollar one vote" scheme, it makes a simplification that seems really bad. It's the same flavor of mistake as when you have the option of making a bet. If the expected return is positive, it says you should bet all of your money. In reality, people don't do this. Rational actors shouldn't even do this.
I'd love to see what an attempt at this same sort of number-of-votes-is-proportional-to-value comes to with a less simplified model of behavior. If I value outcome A at price $x and outcome B at price $y, I might not be able to afford $x^2+y^2, and this model doesn't say what I would or should do. A corresponding model that talked about how people allocate their finite money rather than a unit by unit spending description seems like it would better apply to reality.
It's simply not true that if EV is positive, you should bet all of your money. There's a classic formula called the 'Kelly criterion' to calculate how much of your money should be bet given your expected edge. The original paper (which came out of Bell labs, based upon noise over a transmission channel!) is a good read:
https://en.wikipedia.org/wiki/Kelly_criterion
http://www.herrold.com/brokerage/kelly.pdf
Can I check something - reading the wikipedia article on Kelly Bets it seems that one should take the expected chance of winning, double it and subtract 1.0 and use that as percentage of bet size
So when I win 3/4 times, that's .75 -> 1.5 -> .5 of my total wealth.
But this basically means never gamble till the odds are in your favour. (ie above .5 chance of winning)
What does this say about founding a startup?
The most insightful thing the Kelly criterion says about founding a startup is "don't bet unless you have an edge".
No, there is the letter b indicating the payoff multiplier. So you should not bet if in expectation you lose on the bet, which seems intuitive.
I think you misread me. That's exactly what I'm saying. Or I misread you and you aren't actually trying to disagree.
Oops, sorry, I misread your comment and thought that you were saying the opposite!
Most people find the Kelly criterion terrifyingly aggressive.
Yes, although it is mathematically the ‘best’ way of increasing your bank, it is more aggressive than most people would be comfortable.
IIRC, at any point in time, you have a 50% chance of losing half of your wealth at some point in the future, when following Kelly staking. Most people choose some fraction of Kelly stakes in order to be less aggressive