Talk:Secretary problem

message: I disagree with the comment in the section 'Deriving the optimal policy' where it says (second best overall). This is not necessarily the case, the second best overall may occur AFTER i (the best), but we may still choose i as long as the best in the (i-1) options falls in the first (r-1) as stated. 
Hsenrab (talk) 09:53, 26 August 2014 (UTC)
replies: text: This is covered in the references I added.  I think an additional sentence is still a good idea. Spot (talk) 22:33, 25 February 2009 (UTC)
replies: text:  Actually I think it's worth a whole section, especially in light of what Ketelaar and Todd have to say, ie that using the 37% Rule you end up waiting on average 75% before finding a match, and the chances of being squeezed out at the end are high.  Making a faster decision substantially reduces the worst case, and in fact biological systems seem to do this.  Spot (talk) 00:45, 31 March 2009 (UTC)
thread_title: Untitled

message: Making precise: The optimality of a strategy to wait until a number r of applicants and then to select a candidate is
n o t proven here. This is why I have added " it can be shown ...."
Unknown number of options: This question is probably the most often asked about the secretary problems
(at least acccording to my experience) and should therefore figure in this article. The same holds for
the 1/e-law.
Perhaps it would be a good idea to make these two paragraphs a separate Wikipedia article under the title 1/e-law.
81.243.238.145 (talk) 21:04, 2 March 2009 (UTC)
replies: text: Why is 37% Rule is less clear than 1/e strategy? Both refer to the same thing. Spot (talk) 18:44, 9 March 2009 (UTC)
thread_title: Concerning Making precise+Unknown number+1/e-law

message: Could someone provide an explanation of the terms in the sum for the probability of finding the optimal candidate? The (1/n) term I can guess comes from each candidate having a 1/n probability of being the best, but the second term befuddles me. Thanks! Matt.matolcsi (talk) 00:23, 26 January 2010 (UTC)
replies: text: Why did you tag your edit as “minor”?  DES (talk) 21:44, 1 April 2011 (UTC)
thread_title: Deriving the Expression

message: I believe that the development of the solution is making an assumption not listed in the premises: That there is no upper bound to the quality of candidates. Suppose that you have a job to fill and that you have some quantifiable requirements. It is possible that one or many candidates fulfill those requirements completely. Then, you should accept such a candidate whenever he/she appears, for you can never do better, and there is a substantial chance that you may not find another 100% suited candidate later. Actually, even if you accept that there can always be a better candidate (ie, no upper bound on suitability), the proposed solution may be wrong depending on the assumed distribution of candidate's suitability. For instance, suppose you are to interview a total of 100 candidates. The given solution calls for unconditionally rejecting the first 37 or so. But suppose you also estimate that the percentage of very good candidates (for some definition of 'very good') is just 0.01% of the general population. Then, if the, say, second candidate that you interview is very good, does it make any sense to send him away? The expected chance of having some other very good candidate among those still waiting for an interview is very small, less than 1%.  —Preceding unsigned comment added by 93.102.239.14 (talk) 17:12, 17 September 2010 (UTC)
replies: text: Right, the stated solution to the Secretary Problem is the best possible only when there is no a priori knowledge of the distribution of values (eg, candidate's scores). Martin Gardner's formulation of the problem (as the Googol problem) makes this much clearer, since in the real world, in general, a prospective employer will have at least some notion of the job market he's hiring from. When this (even approximate) a priori knowledge is available, one can in fact do better (systematically) than the stated solution.  — Preceding unsigned comment added by 79.168.138.50 (talk) 01:08, 20 September 2016 (UTC)
thread_title:  Missing Assumption 

message: This is not my area, but CSP is used without being defined, I have no idea what it is.--Billymac00 (talk) 06:31, 6 March 2011 (UTC)
replies: text: It's been added in this edit, possibly it means Constraint satisfaction problem...? --CiaPan (talk) 11:53, 9 March 2011 (UTC)

text: Evidently it means "classical secretary problem", i.e., the problem as described at the top of the page, since (a) it refers to the n/e solution already noted as optimal, and (b) the phrase "classical secretary problem" does appear elsewhere in the article.  I've replaced CSP with this expansion.  Joule36e5 (talk) 01:45, 27 January 2012 (UTC)
thread_title:  Heuristics 

message: The article now has three *non-consecutive* sections about generalizations / variants: 
"cardinal payoff variant", "other modifications", and (4 sections later!) "combinatorial generalization". it would be great to somehow compile these together into a coherent section about generalizations. also, it should probably include more central variants: i know that in computer science the "matroid secretary problem" has been very popular - maybe someone with operation research background can make better suggestions.  — Preceding unsigned comment added by 2602:306:CE74:C530:0:0:0:3E8 (talk) 16:45, 26 November 2015 (UTC)
thread_title:  Generalizations / Variants 

message: I just added the following text to the bottom of the lead: 
It's assumed in this algorithm that the applicants have no knowledge of the decision algorithm employed, because the algorithm depends on the early applicants (who have no chance at all) bothering to actually show up, and then behaving as if the job is winnable. It also assumes that candidates always put forward the same performance, regardless of their own assessment of the depth of the competition, whereas in real life, people faced with long odds (or what they perceive or construe as long odds) tend to take greater risks in order to stand out.
It some ways, that's probably not suitable text. But perhaps it's better than nothing in pointing out some of the paradoxical assumptions involved in achieving this clean, simple abstract solution. 
The first moment I really thought about the algorithm, the part about assigning zero chance at all to the first n/e applicants, from the point of view of the applicants I LOLed because of my economics training.  
Way to wins friends and motivate people: involve them in an interaction where you have a high margin on the quality of their behaviour, but they have no upside at all on the quality of the performance they put forward. 
Clearly this can't work under any kind of accurate disclosure at all. 
"I've invited you here to prime the pump—with no chance of winning this job for yourself whatsoever—but do please put forward your most earnest supplication betters it matters to my own algorithm a great deal." 
It's almost an economic paradox to think this could ever work. 
One could even question whether this algorithm is ethical in all cases. 
Probably something should be said about this, somewhere in the article. — MaxEnt 13:35, 5 November 2018 (UTC)
thread_title:  Abstraction boundary 

message: Why isn't the formula \frac{0.25n^2}{n(n-1)} simplified to \frac{0.25n}{n-1}? MaigoAkisame (talk) 00:00, 15 July 2019 (UTC)
thread_title:  Probability of success of the "postdoc" variant (in the section "other modifications") 

message: This "secretary problem" just needs the application of common sense.    The algorithm totally fails if all the best applicants are in the first third to be interviewed !
As the interviews are random, the best applicant is equally likely to be the first, the last, or the middle one.
The best solution is so simple: interview all the applicants, then select the most suitable.
This whole "problem" (and many like it) demonstrate the way that many academics have their heads in the clouds and have lost touch with reality and plain simple common sense.  — Preceding unsigned comment added by Darkman101 (talk • contribs) 21:53, 3 April 2022 (UTC)
replies: text: It’s a fun math problem. Learning how to solve it teaches you how to approach real world problems, too. Of course it is totally unrealistic. Nobody takes it seriously. Part of the point is that if you are only satisfied with the best you’re often going to end up disappointed. Richard Gill (talk) 02:17, 4 April 2022 (UTC)
thread_title:  Whatever Happened to Common Sense ? 

message: In-line Harvard citations were deprecated two years ago. See Template:Harvard citation no brackets and WP:PARREF. I have changed a few of these, but it would be good to convert the rest of them. GA-RT-22 (talk) 17:54, 19 August 2022 (UTC)
thread_title:  Harvard refs