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I like this explanation of the Secretary problem (aka optimal stopping problem) by @lpolovets [1] > The basic problem is this: there are N applicants for a sec

I like this explanation of the Secretary problem (aka optimal stopping problem) by @lpolovets [1] > The basic problem is this: there are N applicants for a secretarial position. The applicants are interviewed in random order, and you must accept or reject a candidate immediately after interviewing them. After you reject someone, there's no way to bring them back. There is only one position available, so as soon as you accept a candidate you are done. What strategy should you pursue in order to maximize the likelihood of hiring the best candidate out of the N applicants? > It turns out that the best strategy is to look at the first N/e applicants (i.e. the first ~37%), reject all of them, then accept the first applicant that is better than all of the initial rejects. It turns out this strategy has a ~37% (1/e) chance of picking the best candidate, regardless of how large N is. This is counterintuitive. It means that even if you have one billion applicants in some random order, you will find the very best one ~37% of the time with this strategy, even though you will (on average) make your choice without meeting the last few hundred million candidates. > I think this has some interesting practical implications. For example, as a VC, one possible strategy that I can pursue is to look for interesting sectors (3D printing, drones, bitcoin, etc.) and try to invest in the very best startup in each of those sectors. The Secretary Problem is a decent approximation of this. I can go on AngelList and see that there are thirty 3D printing startups in LA/NYC/SF, which are the markets I'm interested in. One way to pick the best one of these 30 would be to meet 11 of these startups, pass on all of them, then invest in the next 3D printing startup I meet that's better than all of those. Of course, this would be a jerk move. I'd be wasting the time of a lot of founders if I knew I was planning to pass on their startups no matter what. However, if I happened to pass on a dozen 3D printing startups by chance, and I knew that there were ~30 in total, then if the 14th one was better than the first dozen, I would know there was a pretty good chance it was the best one out of all 30 even though I had yet to see the last 16. [1] https://www.quora.com/Mathematics/What-are-the-most-interesting-or-popular-probability-puzzles-in-which-the-intuition-is-contrary-to-the-solution/answer/Leo-Polovets?share=1 https://www.quora.com/Mathematics/What-are-the-most-interest...

djrogers 9y ago
The secretary problem and investing have one important difference that throws this all out the window - you can meet with multiple startups without rejecting them, and make a decision when you've met them all (or all the ones you want to meet). There's no requirement in the real world to accept/reject immediately post-interview without any possibility of recall. > Of course, this would be a jerk move. I'd be wasting the time of a lot of founders if I knew I was planning to pass on their startups no matter what. On a macro-level, this isn't a jerk move at all - the other way would have you 'waste' the time of 29 founders instead of 11.
- dsr_ 9y ago
  No, the biggest problem is that nobody is perfect at ranking startups, period. And as proven by that "antiportfolio" page of a day or two ago, even generally successful VCs can't do that reliably.
posterboy 9y ago
and then theres a 37% chance the best was among the rejects and the algorithm fails.
- thefalcon 9y ago
  And there's a 26% chance that you'll never even interview the best because you hired someone before you ever saw them. But it's still an optimal solution to the problem, given the constraints.
indubitable 9y ago
Incredibly interesting, but I can't resist nitpicking! The with extrapolating this to real life would be that it's making assumptions that are not realistic. For instance it assumes infinite granularity in candidates. In other words the rating of a candidate can be from 0 to infinity instead of the granularity we really see things in which is going to be closer to 0-4 or very bad/bad/neutral/good/very good. It also assumes a normal distribution. Something that's perfectly reasonable for an unknown distribution, but in my experience the number of 'very good' candidates tends to be much larger than its equal but opposite 'very bad' end perhaps due to some sort of survivorship bias.

djrogers 9y ago

The secretary problem and investing have one important difference that throws this all out the window - you can meet with multiple startups without rejecting them, and make a decision when you've met them all (or all the ones you want to meet). There's no requirement in the real world to accept/reject immediately post-interview without any possibility of recall. > Of course, this would be a jerk move. I'd be wasting the time of a lot of founders if I knew I was planning to pass on their startups no matter what. On a macro-level, this isn't a jerk move at all - the other way would have you 'waste' the time of 29 founders instead of 11.

dsr_ 9y ago
No, the biggest problem is that nobody is perfect at ranking startups, period. And as proven by that "antiportfolio" page of a day or two ago, even generally successful VCs can't do that reliably.

posterboy 9y ago

and then theres a 37% chance the best was among the rejects and the algorithm fails.

thefalcon 9y ago
And there's a 26% chance that you'll never even interview the best because you hired someone before you ever saw them. But it's still an optimal solution to the problem, given the constraints.

indubitable 9y ago

Incredibly interesting, but I can't resist nitpicking! The with extrapolating this to real life would be that it's making assumptions that are not realistic. For instance it assumes infinite granularity in candidates. In other words the rating of a candidate can be from 0 to infinity instead of the granularity we really see things in which is going to be closer to 0-4 or very bad/bad/neutral/good/very good. It also assumes a normal distribution. Something that's perfectly reasonable for an unknown distribution, but in my experience the number of 'very good' candidates tends to be much larger than its equal but opposite 'very bad' end perhaps due to some sort of survivorship bias.