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PaperclipPerfector  10mo ago (text post)   3018 thread views

Wellness Wednesday for December 27, 2023

The Wednesday Wellness threads are meant to encourage users to ask for and provide advice and motivation to improve their lives. It isn't intended as a 'containment thread' and any content which could go here could instead be posted in its own thread. You could post:

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My modestly informed opinion that you dun goofed.

Of course, the optimal stopping problem and the sub-problem known as the Secretary Problem is relevant:

The basic form of the problem is the following: imagine an administrator who wants to hire the best secretary out of n rankable applicants for a position. The applicants are interviewed one by one in random order. A decision about each particular applicant is to be made immediately after the interview. Once rejected, an applicant cannot be recalled. During the interview, the administrator gains information sufficient to rank the applicant among all applicants interviewed so far, but is unaware of the quality of yet unseen applicants. The question is about the optimal strategy (stopping rule) to maximize the probability of selecting the best applicant. If the decision can be deferred to the end, this can be solved by the simple maximum selection algorithm of tracking the running maximum (and who achieved it), and selecting the overall maximum at the end. The difficulty is that the decision must be made immediately.

The shortest rigorous proof known so far is provided by the odds algorithm. It implies that the optimal win probability is always at least 1/e (where e is the base of the natural logarithm), and that the latter holds even in a much greater generality. The optimal stopping rule prescribes always rejecting the first n/e applicants that are interviewed and then stopping at the first applicant who is better than every applicant interviewed so far (or continuing to the last applicant if this never occurs). Sometimes this strategy is called the 1/e stopping rule, because the probability of stopping at the best applicant with this strategy is about 1/e already for moderate values of n. One reason why the secretary problem has received so much attention is that the optimal policy for the problem (the stopping rule) is simple and selects the single best candidate about 37% of the time, irrespective of whether there are 100 or 100 million applicants.

Let's assume it takes about a year to figure out if a longterm partner is The One, and you have a budget of 10 years or 10 LTPs. I'll assume a typical age range for "serious" relationships as somewhere from 25-35.

In that case, 10/2.72 is about 3.6, so you should go for about 4 steady relationships where you heartlessly break up, and then snag the next person who happens to beat all the ones that came before on whatever metric you care about. Unfortunately, you've spent 6 of said years, so not only did you break her heart, you did so in a less than optimal way :(

However, if I was in her shoes, I wouldn't even consider taking you back, someone who is willing to end an otherwise happy relationship over this isn't someone you wish to settle down with, not that I haven't felt the same way you did. However, when I did break up with my girlfriend of 5 years, it was something we both knew was coming for unavoidable reasons, and not a mere whim.

At any rate, good luck finding someone else, or at least having her take you back.

In that case, 10/2.72 is about 3.6, so you should go for about 4 steady relationships where you heartlessly break up, and then snag the next person who happens to beat all the ones

I do not think this is the right way to frame the Secretary problem result. The optimal solution to the secretary problem is that you should reject the first 1/e proportion of applicants and then accept the next best one to turn up. That would suggest you should spend 10/2.72 = 3.6 years searching for people and then selecting the first person after that point who happens to turn up better than everyone else, not that you should have 3.6 relationships where you break up, unless you're assuming that each relationship lasts exactly 1 year and that you immediately find another relationship after ending your current one. For instance if a relationship would last 3 years on average the 3.6 relationships here already put you outside the age range of 25-35.

Under this paradigm you should search around until 25+3.6 = 28.6 and then accept the first person who turns up who is better than everyone you've managed to get a relationship with between 25-28.6. This also has the benefit of being scale invariant to how easily you can find relationships, as if you can find relationships very easily you'll have lots of people in your 25-28.6 sample so will have a high floor for who you settle down with, but that's fine because you find relationships easily, while on the other hand if you were able to have no relationships between 25-28.6 this would suggest you accept the first person who turns up, which again sort of makes sense for you to do because you're probably not getting anyone else if you turn them down.

I am assuming each relationship lasts 1 year. Real life has enough additional complexity that I doubt that simplifying conclusion makes any difference, and on average, a year seems like the rough amount of time needed to know if things are going to work out in the longterm with a new partner.

There are all kinds of wrinkles in a real life context, such as being exposed to additional evidence regarding the quality of one's partners before "interviewing" them, not having to see strictly serially, not needing a strict amount of time for each relationship, having each relationship change your SMV and so on.

But either approach shows that OP wasn't being sensible in how he handled things.

Does it feel bad to make love in a relationship you already know is ending?

I've felt worse things, like appendicitis.

Actually, not particularly, it was when cuddling and being sweet that that the pain of separation chose to time travel back and hit me when it hurts.

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