Problems in the dating market are often blamed on complex social factors such as differing preferences between men and women (she's the gatekeeper of sex, he's the gatekeeper of commitment), social factors (divorce law, physical danger), hypergamy, and whatnot. But if there are problems in the contemporary dating market, it makes sense to tackle the simplest problem first. I try to create the simplest possible model of a dating market and illustrate its breakdown based only on two factors: preference inelasticity and search costs.

My simplying assumptions- heterosexual, equal numbers of men and women, no difference in sexual behavior between men and women, enforced monogamy (LTRs only), simple distribution of sexual market value.

The male and female population are both distributed on a 1-10 scale of SMV. A 10 is defined as, 100% of those of the opposite sex would LTR, a 5 is 50%, and so on. I assume an equal, linear, and identical distribution for both sexes.

That's pretty much it. As simple as you can get. The only complicating factor I will add to this is search costs. This is just the uncontroversial idea that it takes time and effort to find and evaluate a partner (costs), and the results are not always perfect (you could end up accepting someone who turned out not to give you want you wanted, or rejecting someone who would have been good for you.

Now let's start mating this market assortatively. The 10's (men or women) are desired by 100% of their opposites, so anyone they choose becomes a match. Since they can choose anyone, they choose other 10's, and the 10's pair off.

The 9's are desired by 90% of their opposites, and since the 10's are paired, prefer other 9's. But for every 9, they only have a 90% chance of being willing to pair with them, and only a 90% chance of being desired by another 9. So only 90%x90% = 81% of meetings between 9's will result in a pair.

80%x80%=64% of meetings of 8's result in a pair.

...

10%x10%=1% of meetings of 1's result in a pair.

Hence, 1's don't just meet other 1's and pair assortatively with them as easily as 10's meet other 10's, even though we are strictly enforcing that 1's can only date other 1's. An average 1 will have to meet 100 other 1's before he meets someone that he both desires and who desires him. However, with the introduction of search costs, he may find that effort not-worthwhile. The psychological toll of 99 dates and rejections to find that one is not something many people put up with easily.

The lower SMV folks can equalize their lot by enacting perfect preference elasticity - where one's own preferences are entirely determined by one's own value. Hence, if I'm a 3 and 30% of people are willing to date me, those 30% are all in the 3 or below category. Hence my SMV in the 3 group is actually a 10. But this is unrealistic- 3's who get with other 3's mostly do so because they have no other choice, not because the average 3 offers them the same value as an average 10 would. Hence they will be disproportionately dissuaded by search costs.

In conclusion, even in the simplest dating market, we do not have assortative mating, but rather a hard floor, whereas a portion of people below a certain SMV simply will not pair. This will occur simply due to probability and search costs, and it will occur primarily in the pool of lower SMV people.