Comment by cperciva
19 years ago
Then you're still wrong. I quote from the article: "For example, suppose Y Combinator offers to fund you in return for 6% of your company. In this case, n is .06 and 1/(1 - n) is 1.064. So you should take the deal if you believe we can improve your average outcome by more than 6.4%."
If by "average outcome" you mean "expected value of the utility function", and assuming that my utility-of-money function is sqrt($), I don't need to improve my "average outcome" by more than 6.4% for the deal to be worth accepting; it's enough if I can increase my "average outcome" by 3.2%, since that's how much UTILITY giving up 6% of the MONEY costs me.
Suppose your present hope of future utility from your startup varies linearly with the number of shares. (This is not a radical assumption; essentially all startup shareholders feel this, at least for numbers near that of shares they own.) Suppose you trade 6% of your stock in a deal that will increase your average future utility by 6.4%. You've made a straight trade of hope of future utility for future utility. We don't even have to introduce money.
IF the expected utility varies linearly with the number of shares (and thus the expected amount of money received in the end), you're absolutely right. But does it?
For large investment or VC funds, the utility-of-money function associated with any particular investment is almost linear. There's a very good reason for this: As far as Sequoia is concerned, a dollar earned from their Google stock is pretty much equivalent to a dollar earned from their Loopt stock. Not quite equivalent, since there are non-tangible advantages for a VC fund to have many smaller success stories instead of one Google; but close.
As you point out in http://www.paulgraham.com/vcsqueeze.html, founders aren't "rational" in the sense of having the same approximately linear utility-of-money function as VCs: "... letting the founders sell a little stock early would generally be better for the company, because it would cause the founders' attitudes toward risk to be aligned with the VCs'. As things currently work, their attitudes toward risk tend to be diametrically opposed: the founders, who have nothing, would prefer a 100% chance of $1 million to a 20% chance of $10 million, while the VCs can afford to be "rational" and prefer the latter."
There's another reason to think that most people have concave utility-of-money curves: The insurance industry. If you buy house insurance, you are lowering your expected number of dollars (because even ignoring market friction, the insurance companies have to make a profit), but raising your expected utility.
Yes, for most founders hope of future happiness varies linearly with the number of shares-- at least, in the region of the number of shares they have. If someone gave them 10% more stock, they'd feel 10% richer-on-paper. (There are anomalies at the extremes. E.g. if you got 100% of the stock, your cofounders wouldn't be motivated, and that would decrease the value of your shares.)
You seem more suited to the VC side of the table, rather than the entrepreneur side.
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Not to split hairs, but at different points you said
- that for essentially all startup shareholders, the present hope of future utility varies linearly with the number of shares, and
- that the utility function for most founders is a step function.
Both sound right to me separately, but don't they contradict each other? Maybe most founders just live with this paradox without realising?
No, I don't think they contradict one another. The reason is that the most likely outcome is just to the right of the step.
Most startup founders (initially at least) hope to get a few million, and wouldn't risk that to get a few billion. That's the step. And the most common form of liquidity event is a small-scale acquisition that gives the founders just that level of wealth, since otherwise they won't sell. So in the most common (and most commonly hoped for) good outcome, happiness varies linearly with the number of shares.
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If a man is wrong, you don't need to tell him so. Just give it a rest and let others form their own opinions.
Seriously, these issues, and a lot of other issues, are covered in "How to Win Friends and Influence People". Read it. If I could figure out a way to get you to feel like you came up with the idea to read it, I would, but I can't, so just read it.
I know you are well intentioned, but if I'm full of it I'd rather someone told me, preferrably in a respectful but blunt way. I'll form my own opinion anyway.
I know I took criticism personally and reacted very badly once or twice in the past, so I see your point. But I realised I was being a baby and grew from the experience. No speech on humility can make you humble. At best, it will convince you you should be humble, and maybe by acting humble some of it will sink in and stick. Real humility comes from realising your mistakes. [Edit:] That's painful at first, but necessary to get over your ego.
[PS: Sorry, I drifted into replying to other comments of yours, and the end result may be confusing.]
You're right, of course.
Actually, if someone is wrong about math you probably should tell him so.
I agree. In private.
You should tell him he's wrong, but you shouldn't be a jerk or gloat about it, which cperciva wasn't.
No, really.. It is wise to never publically tell someone they are wrong, unless you're defending someone. You should wait until his friends and colleagues have left his side, then whisper your opinion into his ear. In the Internet world, that means sending him an email. To not do so is bad karma in every sense of the word.. My post above was modded down because I publically pointed out that he was wrong to point out Paul's percieved flaws in public; maybe I should have sent him an email instead. This wisdom is proven true over and over. My #lisp fiasco convinced me of that (long story).
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