I've been thinking about an "inverse secretary problem" for choosing contract jobs:<p>1. I have a limited time in which to secure the next contract<p>2. Potential clients opportunities appear at a fixed rate (eg 1-2/week)<p>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").<p>4. If I quote a lower rate than the client's MDR, I have a new contract and the game stops.<p>Given my goal is to find the client who will pay the highest daily rate before the deadline, what is the best strategy?<p>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?
"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."<p>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.<p>There is no reason to think that common sense encompasses more reliable judgement than the simple maths here.
> "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."<p>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...<p>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.
<i>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.</i><p>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.<p>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.
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.<p>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.<p>I'm curious if anyone has found other useful methodologies for guiding these sorts of life decisions?
Shocker: Game theory falls apart in the real world.<p>Shocker: People aren't always rational.<p>Shocker: Initial conditions do not stay constant.<p>Shocker: People's priorities wildly vacillate even on short and medium scales.<p>Shocker: The economic ideal of the perfectly informed and rational consumer is a complete fantasy and violates multiple physical, computational, and biological theories.
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.
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.
Not so sure about this guys math, and I assume its because he distributed a lifetime of dating equally across an adult life.<p>I would guess I had done 36.8% of my dating by age 25 - not 39. Suddenly the model starts to fit better.
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.
> 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?<p>Do you know exactly how many "applicants" exist? No.<p>Does the length of the "contract" depend significantly on the length of "exploration"? Yes, but not in the model.<p>Instantly closing that site. <i>sigh</i>
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.<p>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.)
... 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.<p>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 <i>bad</i> idea to use it.<p>>The secretary problem does effectively demonstrate the general principle that in life we should spend some time exploring<p>I have no idea what the author is talking about here... There is no "exploring" in the stable marriage problem.