Comment by t_mann | Hacker News Reader

Comment by t_mann | Hacker News Reader

It's a really cool result when you tell people about it, but actually when you think about it, it doesn't seem as useful as it sounds at first. The combination of some fundamental assumptions - you know the number of candidates in advance and you can't go back to previous candidates (*edit - should have added another one here: that you don't know anything about the distribution from which candidates are drawn before you begin) - don't really seem to match any of the purported applications, nor any I could think of quickly off the top of my head.

In reality, you're usually be able to gauge some estimates of the moments of the population distribution before you have to make any decision (which also aren't always final). Ie, you'll be interviewing a couple of candidates before you send out any rejections, you'll see several potential mates before you narrow in on one, you know from experience what a nice appartment looks like when you visit one,...

There are also other problems in other potential applications: a gig economy worker needs to not only optimize the value of the next gig but also the time spent searching for the next gig, when buying a used car the biggest problem is the information asymmetry regarding the true value of the car, not that it's gone if you don't buy right away,...

The even more broken assumption is that the only success factor is to get the single best result. That's not how real life works either: even if the best one got away, there will still be many other options close to it in quality, you'll be perfectly satisfied with any candidate in the top-five percentile or similar.

The traditional example of an application is dating to marry.

The number of 'applicants' isn't what matters, what matters is how many dates the subject can get in the amount of time they're willing to spend looking, this can be estimated reasonably well.

The part where you can't go back, well, it's more true than not.

I say it's the traditional example of an application, but I rather doubt people choose their spouses this way, nor that they should.

My point is that the model assumes that you're starting with zero knowledge about the population when you start dating, that's why you need the burn-in phase where you reject everyone to get a good estimate. In reality, I'd think you'd have a pretty decent prior for the population parameters before you even start dating.

I'd disagree for the dating case; you know a lot about people, but you don't know what its like to spend 6 waking hours with someone every day for awhile until you try it, you don't know what the sex will be like, you don't know what being a whatever-in-law will be like. All things that have to be sampled over a period before you can build up a distribution.

Plus, for the dating especially, there's a lot of "je ne sais quoi" which requires sampling and can not be polled from the population at large.

You don't need to know number of candidates if you know the total amount of time (and assume candidates come in uniformly at random).

The most practical use case is selling a house.

There are also variations of the problem which model being able to go back to previously rejected candidates, as well as a probability that the candidate rejects you.

Right, selling a property might actually be a fairly good application of this model, I agree - you shouldn't leave a property listed for too long, and together with the feedback from your agent you should get a meaningful estimate of how many offers to expect in that period.

I'd be curious to see the agent's reaction when someone actually implements that and flat out rejects all the first offers.

It's a garbage premise entirely due to the fact that people - eg job applicants - can be so drastically different one to the next (whether amazing or horrible). The secretary problem fails to bake that in, because it can't handle it inherently (you have to actually interview people to know that). It doesn't actually work in reality.

There's no probability theory that is going to function properly so as to be very useful in such a context, because the best candidate in the world can just as easily show up on the tenth interview as the first or third. Your first three job applicants can be horrible, and the next three can be amazing.

People that buy into the false nature of the secretary problem / optimal stopping theory (that it's actually useful in reality), are falling for the premise that eg several roulette spins in the past directly impact the odds of the present spin. It's a bad premise to utilize for exactly the same reason: the quality of your last candidate doesn't have any strict relationship to the quality of your next candidate.

Optimal stopping theory is only useful for highly indecisive people that can't figure out what they want, so they fall back to handing off their decision-making to something else.

None of what you said is consistent with the derivation of the policy. Note the policy is probabilistically optimal, not guaranteed to hire the best candidate every time. If you're hiring 1 person, sure you might end up SOL. But if you were hiring 100, this method would get you the best workforce.

This can be directly applied to wholesale auto auctions

Hmm, for auctions I think you really need to also the other agents into account (auction theory builds on game theory). The stopping-time model doesn't have strategic interactions.

I don't know what the theory says but giving your bidders this rule of thumb works better in practice. Or at least it did some years ago

What does the rule of thumb even say? How high should they bid when they see an attractive lot?

If your rule of thumb says that you should only start bidding after a third of the auctions are finished, I hope you see that there's a pretty obvious way for others to arbitrage against you.

Auction theory studies both optimal bids and optimal auction designs - imho it's one of the more useful areas of economics: https://en.wikipedia.org/wiki/Auction_theory

I get that it seems implausible that there's just money sitting around waiting to be picked up, but it was there. Used autos is a hugely fragmented industry that is only slowly consolidating. Bids + bid strategy are likely still extremely far from optimal. Probably more easy wins out there.

I believe you, sounds like you're actually doing some business in that area. You should really look into the theory then. Feel free to reach out if you need help.

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