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In theory, a female who is above average should reject most advances because they can afford to wait until they are approached by a male of high value. Whereas a female of low attractiveness can not afford to reject most advances.

But how does a female gauge here own attractiveness in the first place?

What would make sense is that in the fist few years of adult life a female should simply reject all advances. A process of simply collecting statistical data on her own attractiveness.

Then females who are approached at a low level during this period would become more easily approachable whereas females who are approached at a high level would become more stand-offish.

Does any of this correspond to reality?

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  • $\begingroup$ The theory you propose (regarding rejecting some offers) actually exists: en.wikipedia.org/wiki/Secretary_problem, but I haven't heard of anyone applying it to mating. Ok since according to that page it's also called "marriage problem", some probably did apply it but insofar I'm unfamiliar with that... and the wiki page doesn't get into who applied it to marriage/mating. The only reference there that mentions mating/marriage is Miller, Geoffrey F. (2001). The mating mind: how sexual choice shaped the evolution of human nature. Anchor Books. ISBN 0-385-49517-X. $\endgroup$ – Fizz Jul 22 '18 at 0:41
  • $\begingroup$ n.b.: pages 206-208 in the book. $\endgroup$ – Fizz Jul 22 '18 at 1:05
  • $\begingroup$ Yes, I seem to recall the example. I think it may apply somewhat. Since if a person reject all advances, say in the first year and then only accepts advances more attractive than that sample, this would correspond to the expected behaviour. It makes logical sense, but I wonder how it corresponds to reality? I mean gradually becoming less choosy with age combined with building a picture of relative self-worth. $\endgroup$ – zooby Jul 22 '18 at 1:18
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From p. 207 of Geoffrey Miller (2001). The mating mind: how sexual choice shaped the evolution of human nature. Anchor Books. ISBN 0-385-49517-X

In our research on mate search strategies, colleague Peter Todd and I found that a rule we call "Try a Dozen" performs as well as the 37 percent rule under a wide range of conditions. Try a Dozen is simple: interview a dozen possible mates, remember the best of them, and then pick the very next prospect who is even more attractive. You do not have to estimate the total number of potential mates you will encounter in your reproductive lifetime; you only have to bet that you will meet at least fifty or so. Humans seem to follow something like the Try a Dozen rule: we get to know a number of opposite-sex friends during adolescence, fall in love at least once, remember that loved one very clearly, and tend to marry the next person who seems even more attractive. Each individual is "satisficing"- looking for someone who is pretty good and good enough, rather than the absolute best they could possibly find. But at the evolutionary level, these satisficing rules impose sexual selection that is almost as strong as the most complicated, perfectionist decision strategy.

I also turned up a 1998 review by Miller and Todd "Mate Choice Turn Cognitive", which does get to mating strategies in its final pages, best summarized by:

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By sampling a much smaller number of prospects initially, say a dozen, one can actually attain a higher expected mate value than the 37% rule delivers (although a lower chance of finding the very highest-valued prospect), with much lower search costs and a much lower risk of being stuck with a low-value mate[64,65] (Fig. 3).
More importantly, the ‘secretary problem’ ignores the problem that a prospect you desire may reject you. This mutual choice constraint makes the search much harder[64,65]. Game-theory models of ‘two-sided matching’ address these complexities[61] directly, and propose various search strategies which guarantee that a population reaches a ‘stable matching’: a pairwise assortment of individuals where no individual would prefer to be mated with someone else who would also prefer to be mated with them. However, two-sided matching models typically assume strict monogamy (no ‘extra-pair copulations’), complete information and exhaustive preferences: everyone has complete, consistent, transitive preferences across all possible prospects that they encounter.

    1. Roth, A.E. and Sotomayor, M.A.O. (1990) Two-sided Matching: a Study in Game-theoretic Modeling and Analysis, Cambridge University Press
    1. Todd, P.M. (1997) Searching for the next best mate, in Simulating Social Phenomena (Conte, R., Hegselmann, R. and Terna, P., eds), pp. 419–436, Springer-Verlag
    1. Todd, P.M. and Miller, G.F. Heuristics for mate search, in Simple Heuristics that Make us Smart (Gigerenzer, G., Todd, P.M. and the ABC Research Group), Oxford University Press (in press)

So yeah, the problem is not that simple (as optimal stopping) if one considers mating a game (in the sense of game theory). I haven't yet looked at the latter line of research... but it's a whole book. The idea seems centered on the stable marriage problem. An optimal algorithm also involves a number of rounds, with rejection and "maybe" answers; from Wikipedia:

  • In the first round, first a) each unengaged man proposes to the woman he prefers most, and then b) each woman replies "maybe" to her suitor she most prefers and "no" to all other suitors. She is then provisionally "engaged" to the suitor she most prefers so far, and that suitor is likewise provisionally engaged to her.
  • In each subsequent round, first a) each unengaged man proposes to the most-preferred woman to whom he has not yet proposed (regardless of whether the woman is already engaged), and then b) each woman replies "maybe" if she is currently not engaged or if she prefers this guy over her current provisional partner (in this case, she rejects her current provisional partner who becomes unengaged). The provisional nature of engagements preserves the right of an already-engaged woman to "trade up" (and, in the process, to "jilt" her until-then partner).
  • This process is repeated until everyone is engaged.

So, Miller and Todd cleary don't think this stable marriage problem is too relevant for reality. Unfortunately, by the time of their review (which is now two decades old), there's wasn't much else proposed that was taking into account the mutual-choice aspect of mating and the "satisficing" nature of human choice in general (that Miller and Todd favor).

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  • $\begingroup$ That's interesting. I mean the evidence is anecdotal. But it seems a plausible. I'm not sure it explains how some get these dozen dates in the first place. Some people might struggle. It seems this is more from a male point of view. As in the man will marry the prettiest woman (that he has not been rejected by) that is more attractive than his highschool girlfriend. $\endgroup$ – zooby Jul 22 '18 at 1:25
  • $\begingroup$ @zooby: Looking more closely at Miller's Wikipedia page, some of his research appears controversial (never mind some of his less than scientific remarks). So keep that in mind. Also I found a review by Miller and Todd floaring around, probably has more details, but I'm not sure that's the primary research alluded to. $\endgroup$ – Fizz Jul 22 '18 at 1:27
  • $\begingroup$ Also on the Secretary problem page the 1/e law looks interesting. Assuming a girl must marry before the age of 30 and starts looking at 18. The 1/e law says she shouldn't marry before the age of about 23. Interesting maths. $\endgroup$ – zooby Jul 22 '18 at 1:31

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