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.
Re:The Equity Equation
by dpapathanasiou on Friday July 20, 2007 @09:18AM
(#35575)
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?
- 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?