
The ‘secretary problem’ is so unrealistic it can't inform our decisions - robertwiblin
https://medium.com/@robertwiblin/the-secretary-problem-is-too-bad-a-match-for-real-life-to-usefully-inform-our-decisions-so-1cd29ae01024
======
ukoki
I've been thinking about an "inverse secretary problem" for choosing contract
jobs:

1\. I have a limited time in which to secure the next contract

2\. Potential clients opportunities appear at a fixed rate (eg 1-2/week)

3\. Each client has a different, unknown, maximum daily rate (MDR) they are
willing pay. I can discover the MDR only by quoting a higher rate ("sorry the
most we can go to is $XXX").

4\. If I quote a lower rate than the client's MDR, I have a new contract and
the game stops.

Given my goal is to find the client who will pay the highest daily rate before
the deadline, what is the best strategy?

My best guess at the moment is to start at a high rate, and gradually decrease
it as the deadline approaches. But how can I use the information I gather
about rejected client's MDRs to decide the best daily rate to quote future
potential clients?

~~~
soVeryTired
> _Given my goal is to find the client who will pay the highest daily rate
> before the deadline..._

Is that _actually_ your goal though? Are you sure you wouldn't prefer a client
who will offer repeat business at a decent but not maximal daily rate? How
about a client who will offer a more interesting job, or one who will offer
you the opportunity to learn something new?

In so many of these optimisation problems, the real difficulty is _specifying
exactly what you want to optimise_ (never mind making sure that the
specification is tractable). In general the solution you get from your
algorithm will depend sensitively on your objective: if you're not completely
sure about the objective, you shouldn't be sure about the solution.

~~~
BerislavLopac
> Is that actually your goal though?

When it comes to contracting, this is precisely the goal. Your questions refer
to freelancing rather than contracting, which is quite different.

~~~
ineedasername
I'm not sure that's the case. I work somewhere that has seen a very high
turnover in contractors, paid a decent amount above market averages. It's
because project assignments are poorly defined, bureaucratically controlled,
and by the time the initial term is up (usually 3 months) the contractor is
fed up and has some other work already lined up.

~~~
ukoki
Agree!

Changing clients is preferable as there are more opportunities for networking,
and there is a novelty factor: Each slow-moving bureaucratically-controlled
poorly-defined enterprise IT project is slow-moving, bureaucratically-
controlled and poorly-defined in its own way.

------
gcthomas
"For the advice coming out of this model to beat a very practical alternative
— following conventional wisdom or your own common-sense — we’ll need to deal
with many of them all at once."

Conventional wisdom and common sense really means "using an ill defined
heuristic", which isn't so obviously better than the discussed algorithm.
Common sense, as the saying goes, is neither common nor sense, and using this
phrase just hides the actual algorithms people really apply.

There is no reason to think that common sense encompasses more reliable
judgement than the simple maths here.

~~~
jakobegger
Our "common sense" has been shaped by the experiences of thousands of
generations before us, and it has worked out so far. I wouldn't dismiss it so
quickly.

~~~
dabbledash
Things started “working out” pretty recently, once we started applying more
rigor to our thinking. Life in the thousands of generations before was pretty
rough by comparison, to put it very mildly.

~~~
coldtea
That's a naive oversimplification -- the kind of modern thinking that
considers history some kind of shit-hole and ours the first enlightened era.

People had extremely rich lives, deep thoughts, and interesting problems to
solve, throughout the 3-4K years of history.

So Joe Sixpack today, or even a Joe IvyLeagueDegree today is no more
sophisticated than e.g. a citizen of ancient Athens or Rome or Bagdad in most
everyday matters.

~~~
dabbledash
Pre-industrial society was a shithole for most people compared to the present.
And I’m not basing that on metrics like literacy or access to political
franchise. I’m talking about things like “how likely are you to bury half your
children?”, and “how likely are you to be raped or murdered?” We’ve made
ourselves so comfortable now (which is great) that we’ve forgotten how unusual
our circumstances are and lost interest in how we created them.

It’s not a comment on the intelligence of the average historical person, or
the richness of their emotional life. It’s just an acknowledgement that the
tools we used to try to improve our lot for most of human history (including
“common sense”) were not very successful, at least compared to the ones we’re
using now.

------
mic47
> "Should we spend the first 36.8% of our adult lives dating casually, and
> then settle down with the first person we find who’s better than anyone
> we’ve dated so far? That would suggest men start seriously looking for a
> life partner at 39 — and women at 41."

The problem suggest anything like that. It suggest you should spend 36.8% of
dating time (or date count) on exploring, not 36.8% of your life...

Second problem with the blog, that it just produces lot of possible issues,
but does not show any example where 36.8 algorithm would fail horribly. Maybe
those drawbacks does not matter in practice.

~~~
LoSboccacc
Exactly, there are no real takeaways from this article, especially since there
are real applications* to the problem so it is worth exploring, even if the
original example was flawed.

He spend most of the time debating the exemplification without ever
challenging the solution, but the example is just there to entertain the
casual reader, the interesting part is the math behind.

*You're on a road trip and want to refuel ok the cheapest pump in range, that satisfied the uncertainties of the original problem plus the given constraints.

~~~
soVeryTired
That's not a real application. You would just google gas prices. Or you would
stop and ask someone.

~~~
mic47
Assuming you've got cell coverage (or cheap roaming).

------
stcredzero
_So. Should we spend the first 36.8% of our adult lives dating casually, and
then settle down with the first person we find who’s better than anyone we’ve
dated so far? That would suggest men start seriously looking for a life
partner at 39 — and women at 41._

Strawman alert! The rate at which people date varies tremendously with age and
life circumstance. To treat someone's dating life like a piece of uniform bar
stock which can be cut off at the 36.8% mark is so obviously a bad approach,
I'm immediately less sure of the article.

EDIT: It turns out the article's entire point is that the model is too simple.
It really rubs me the wrong way that he starts out with an implementation
which is way too simple.

~~~
robertwiblin
It rubs you the wrong way that I start with an example that clearly
illustrates the point I'm trying to make?

~~~
stcredzero
_It rubs you the wrong way that I start with an example that clearly
illustrates the point I 'm trying to make?_

Since it's such a clear strawman, it doesn't clearly illustrate the point
you're trying to make for those readers who can see through it. It's common
sense to exclude childhood as irrelevant to dating experience. It's common
sense, that people will be more active in dating during certain phases in
their life.

The whole point of the strawman, is that it appears to support a point by only
weakly representing the counterpoint. A fairer analysis has been posted
several times in other comments here.

[https://news.ycombinator.com/reply?id=19360311](https://news.ycombinator.com/reply?id=19360311)

~~~
robertwiblin
As I've said to others it highlights one weakness with the model - that it
will always say a longer possible search is better because it raises your odds
to success and the model features no cost for searching. When you add a cost
to delay the appropriate time to spend exploring drops massively.

~~~
stcredzero
_it highlights one weakness with the model_

By applying the strategy in an unintelligent way which seems designed to make
the model fail.

 _it will always say a longer possible search is better because it raises your
odds to success and the model features no cost for searching_

That's kind of the whole point of this tradeoff and of the analogies used with
it. That there is a cost for searching and not "finding."

------
matthewowen
I'm currently looking to buy a house, and although I can't say we've followed
the prescribed solution to this problem to the letter (partly because house
buying has partially overlapping option availability), I have found it to be a
useful way to frame our approach to evaluating options.

Concretely, we've very consciously had a "just looking" phase, where we look
at a bunch of houses with the rule that we absolutely will not buy one of
them, no matter how appealing: they're only there to give us a benchmark.
We've tried to size it in proportion to the number of houses we think we'd
plausibly want to look at, given our horizon for buying.

I'm curious if anyone has found other useful methodologies for guiding these
sorts of life decisions?

~~~
schnevets
I used a similar approach for job hunting at one point. Perform a few
interviews in an "exploration phase" where the purpose is less to impress the
prospective employer, and moreso to get a pulse on the industry. You won't be
able to separate company-specific red flags from industry woes until you
compare & contrast a few places.

------
AtlasBarfed
Shocker: Game theory falls apart in the real world.

Shocker: People aren't always rational.

Shocker: Initial conditions do not stay constant.

Shocker: People's priorities wildly vacillate even on short and medium scales.

Shocker: The economic ideal of the perfectly informed and rational consumer is
a complete fantasy and violates multiple physical, computational, and
biological theories.

~~~
msla
> Game theory falls apart in the real world.

It explains why people pollute pretty well.

Oversimplified models fall down in the real world. Game theory is useful
within a domain.

[http://theconversation.com/game-theory-and-the-
environment-y...](http://theconversation.com/game-theory-and-the-environment-
youre-on-to-a-winner-999)

~~~
ggggtez
Incorrect. Game theory predicts pollution. You just need to make sure the game
has the correct predicted payoffs for each move, and the set of moves you want
to measure, and their interactions...

You'll find Game Theory a lot easier to understand if you mentally replace
every instance of "Math" with "AI". (So instead of saying "The Nash
Equilibirum is...", just say "I trained an RNN and this is how it would
play"). That's really all it is. Usually the games are designed in a simple
way because the "AI" that is being run is nothing more complicated than min-
cut/max-flow.

"Pollution" specifically is a case of the "Free-Rider Problem", and there are
plenty of game theoretic results that explain it.

~~~
mattkrause
Wait, you're invoking RNNs as a _simpler model_ than game theory?

~~~
bitwize
It's not simpler, but it is bound to go over better on Hackernews.

~~~
ggggtez
Exactly. People here sort of already know RNNs. You could use RNNs in your
game theory game (see AlphaGo, etc), but Game Theory is just a set of
principals for defining a "Game", and defining incentives, etc.

If the game doesn't properly account for some incentive, it's the problem of
the model designer, just like it would be the problem of the RNN designer not
gathering the right type of training data.

------
b_tterc_p
I am far more perplexed by the fact that this author believes too many people
are using mathematically derived models for making life decisions and that we
need a serious discussion of their merits to avoid suboptimal decisions than
any of the modeling concerns other people here have pointed out.

------
joker3
The secretary problem is the first and simplest problem in optimal stopping.
It's not the only one that people have studied, and while it is too simple to
describe many realistic scenarios, the insight you get from solving it is
valuable.

------
lsniddy
Not so sure about this guys math, and I assume its because he distributed a
lifetime of dating equally across an adult life.

I would guess I had done 36.8% of my dating by age 25 - not 39. Suddenly the
model starts to fit better.

~~~
btilly
Exactly.

And the reason why this matters is that the dating that matters is the dating
from when we can have children to when we're done. So if a woman starts
seriously dating at 20, and is done with kids by 35, then somewhere around 25
is indeed the proper cutoff.

Men can have children longer, but at some point don't want to.

~~~
sib
Presuming that your goal is to have children...

~~~
btilly
Whatever you personally think, you're dealing with a lot of biological wiring
which is intended to optimize your life towards the goal of having children
successfully raised to adulthood until they also have children.

This wiring does not work with all individuals nor can it always cope with
modern life. But it is still a pretty big factor.

------
cortesoft
The other problem is that people/choices aren't strictly ordered... they each
have various strengths and weaknesses across a multitude of attributes that
are not readily comparable. Imagine you are choosing a car, and one is cheaper
but the other has higher top speed... how important is each factor? Is a 1mph
speed increase worth $1000? Even if you were able to figure out the ratio, it
wouldn't be constant, you would get diminishing returns.

------
zach_garwood
This article should be renamed "A Pedants Take on a Statistical Model, an
Exploration into Why I'm No Fun at Parties."

~~~
lliamander
A "Pedant's" take. Don't forget the apostrophe.

------
posterboy
> So. Should we spend the first 36.8% of our adult lives dating casually, and
> then settle down with the first person we find who’s better than anyone
> we’ve dated so far?

Do you know exactly how many "applicants" exist? No.

Does the length of the "contract" depend significantly on the length of
"exploration"? Yes, but not in the model.

Instantly closing that site. _sigh_

------
dragonwriter
I dunno that it can't inform our decisions; because real decisions don't
usually have the same constraints (but sometimes lose approximations of those
restraints), the optimal solution to the abstract problem isn't necessary
real-world optimal to even the best-fit scenarios, but it's often a good
solution and better than a naive solution would be.

It's also the case that the problems that best approximate it's constraints,
and for which it offers or suggests a good solution, are probably not usually
the familiar problems with which it is usually associated. (Though I can see
places that are decent fits that could exist upstream from those, like seeking
a parallelizable approach to filtering resumes to get M interview candidates
from a pool of N resumes while doing holistic comparison of resumes rather
than scoring against an abstract rubric.)

~~~
dllthomas
But surely all but the very best strategy for selection are equally worthless!

~~~
dragonwriter
I see what you did there, but it's worth noting that that's not true even when
the related extreme assumption underlying the secretary problem holds: that
assumption is that _every selection other than the very best is equally
worthless_. But _strategies_ other than the very best will have different
probabilities of picking the best selection, and so will have value
proportionate to that probability. (Since they will have a value equal to
value of the best selection with that probability, and a value of zero
otherwise.)

------
northisup
This algorithm is useful for picking parking spaces at shopping centers.

~~~
barbecue_sauce
I spent most of my adult life just parking arbitrarily in large lots. Didn't
even realize this until a girlfriend pointed it out to me. In retrospect, I
suppose I was optimizing for spending as little time in my car as possible. It
never even occurred to me that my goal should be "park as close to the
building as possible".

~~~
InitialLastName
My partner gets mad at me for my "park in the easiest spot to park in"
strategy too. We're both able-bodied humans, though, so there's no reason we
can't walk 40 extra feet to the store entrance.

------
sonnyblarney
FYI if you're applying math to your dating approach ... 'you're doing it
wrong'.

------
ggggtez
... Except there are a number of cases where it is used in practice with
success, including assigning medical students to to hospitals for their
studies.

I mean, I agree that any time you use an algorithm, you want to know under
what conditions it holds... but that doesn't mean that it's suddenly a _bad_
idea to use it.

>The secretary problem does effectively demonstrate the general principle that
in life we should spend some time exploring

I have no idea what the author is talking about here... There is no
"exploring" in the stable marriage problem.

~~~
essex_edwards
The secretary problem and the stable marriage problem are not the same thing.

[https://en.wikipedia.org/wiki/Secretary_problem](https://en.wikipedia.org/wiki/Secretary_problem)

[https://en.wikipedia.org/wiki/Stable_marriage_problem](https://en.wikipedia.org/wiki/Stable_marriage_problem)

~~~
ggggtez
So, is your point that using a Stable Marriage solution is ok and realistic in
the real world, but a Marriage variation is impossible and dumb?

All of the OPs complaints about the Marriage problem apply to the Stable
Marriage problem, and yet, the real world doesn't seem to care that the OP
thinks it shouldn't work. People use it anyway, and it largely works.

