the Gale-Shapley algorithm requires an authority (like the medical school establishment) to make it work. in real life, if you want to get married, you face a much more amorphous situation: a series of prospects, and with each a decision, "are they good enough"? i can't find it anymore, but iirc the answer was, to estimate the length of the game (say 20 years on the marriage market) and then just date for the first 1/e fraction of this time. and then say "yes" to the next person as good or better than the best you could have had during your trial/dating period. can anyone name the theorem or is this apocryphal?
> Estimate how many people you’re likely to date in your life, dump the first 37% but keep a photo of your favourite on your bedside table. Then, marry the first one after that who beats your sweetheart! Of course, every rule has exceptions and sometimes you get an offer that’s too good to refuse, 37% or not. Sometimes, mathematics doesn’t have all the answers!
> Using this process, we find that we can be successful in selecting the best from a group of N by letting
approximately 37% of the available positions go by, then selecting the first choice better than any seen before about 37% of the time. And this is true no matter how large N is! This is a strikingly high probability.
