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.)
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.
Since you're talking about step functions and expectation, the final equation should be framed with a binary parameter in mind: x=0 (no liquidity event occurs), x=1 (liquidity occurs).
"The reason is that the most likely outcome is just to the right of the step."
"So in the most common (and most commonly hoped for) good outcome [...]"
Isn't the omission of good in the first paragraph a lapsus, i.e., do you mean most founders think success is the most likely outcome? Or do you mean founders should ignore the possibility of failure for the purposes of making these decisions about stock?
