The Secretary Problem is the common name for a mathematical problem in optimal stopping. The challenge is to find a way to make the best choice when interviewing 100 applicants for a position, given that you must make a decision about each applicant immediately after you interview them, that is, once you decline you cannot go back. The same decision appears in many guises; for me as a young man in the days when petrol prices varied wildly it was, when passing through a town with several petrol stations, how soon do you stop for petrol, given that you do not want to have to turn around? Overshoot the cheapie and you have to turn around and go back.

The excellent Wikipedia article notes that the Secretary Problem is "also known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem. Its solution is also known as the 37% rule." The solution---namely to interview 37% of candidates accepting none and then choose as you go further the first applicant who bests all that have gone before---is extremely useful in life, but not of interest here. The first interesting observation is that this is clearly intended to be "the wife problem", though politically incorrect to say so even in the 20th century, because one could, of course, tell the secretaries that you will get back to them when the interviews are done, but that is not an option when you are searching for a spouse.

Now that we have established the theory and process, I next turn to internet dating. How long do you spend poring over profiles, meeting people, before being ready to settle? How to optimise the stopping process here?

First complication is that one must know what one is looking for in a date; without that you cannot compare two candidates. It took me well over a year to understand that, partly because my picture has changed as I have unwound and straightened myself out (I was quite bent out of shape by Waikato, NZ, and factors not on my radar, but that is a discussion for another time and place). Anyway, what one rationally seeks in one's sixties is not what one might have sought in one's thirties, and I have discovered that there are ladies who have worked this out too, but many who have not really thought it through---red flag. (What a rational expectation from dating at this age might be is also a discussion for another time and place.)

Second complication is that the number of candidates is not known in advance, plus there are various levels of "interview". The pool is large, but many can be eliminated by red flags (smoking, christianity, atrocious grammar, etc), others by a conversation, and some by lack of chemistry on 'date zero'.

Given a willingness to spend a couple of years, one might expect to review perhaps some tens or one hundred potentials to the "having a conversation" stage. Do not commit to any within the first 15--30 who come under serious scrutiny. Some of those will reject you, but you collect the calibration data anyway. As an aside, there is a superb article on the math and working behind the swipe-left/right style of dating engines: What Really Happens Inside a Dating App
Nevertheless, I met a lady recently who was at pains to let me know that she had other candidates who had already contacted her, as if she felt this might be cheating. I have no problem with that; same for others who have mentioned similar to me without any embarrassment. There will be some overlap.

Is overlap cheating? A big issue concerns exactly what is cheating. I would have previously said that you can't cheat without there being sex. I would have expected most males to say the same. Definitely not so in these woke days and from the female perspective. There is this thing called an emotional affair. Classic example is the existence of a 'work spouse'. The Wikipedia page is as interesting as its talk page, which provides a bunch of stories that exemplify meanings and contradictions of various definitions. The serious psychological literature is still appearing. One friend simplifies the definition to "cheating means keeping something secret", and I like the power and brevity of that definition.
I do not think overlap is an issue.

When I said "The serious psychological literature is still appearing" I was responding to the deluge of woke social-media would-be psychologists wanting to expand the definition of cheating to pretty much anything that causes a spouse discomfort or anger. I lived once with a lady named Antoinette who became militantly averse to my long-time female friends. She wanted control in our relationship. The talk page mentioned above discusses a spectrum of potential 'cheating situations' but does also point out that extending same to permit coercive control exposes the weakness in a definition that relies on someone's perceptions. One does not have the immediate right to suppress an activity purely because one personally is upset by it.

To cycle back to online dating and the stopping problem, my position is that some overlap is permissible or even unavoidable, but to remain ethical one must not keep secrets. Modern online dating has a "drinking from a fire hose" aspect to it, and handling the multiplicity of parallel possibilities requires what amounts to a soft version of Ethical Non-Monogamy. There must come a point when a party is ready to 'make a selection' and thereafter a 'front runner' may emerge. That open-to-selection point should optimally follow some number of 'calibration' dates, which sounds a bit harsh, but is a reality. I am also pretty sure that the act of selection requires a specific conversation if monogamy is demanded by a party. I personally feel that monogamy happens in a relationship naturally, not being a given. In the youthful instance monogamy is implicit at the point of deciding to cohabit, marry, breed, or whatever; not so in my age group.

Secretary is a charming romantic film where an unusual gentleman finds his ideal lady, despite her red-flag start in the story, and the two seem set up for the proverbial happy-ever-after life. This essay is really all about what is rational or acceptable in some principle surrounding a relationship such as dating/partnership/marriage. I find the film relevant because it illustrates that normal has no claim on healthy and uncomfortable no claim on offensive.