As much as 7 billion other people in your calculations. 1/7billion - not very much.

But this ignores actually doing the math! Suppose it is known that she would prefer abcd_z's company to the other fellow's, and abcd_z would prefer her company to no one's, and the other fellow would prefer her company to no one's, but his preference is smaller than theirs. The "stealing other people's partners is bad" is putting precedence above greatest good.* The claim that it's existentially risky is one that doesn't require utilitarianism; a selfish person is more concerned about those sorts of incentives than a utilitarian.

I am of the opinion that utilitarianism is wrong wrong wrong, but treating it as a moral decision procedure is even more wrong. If you're going to be a utilitarian, be a utilitarian at the meta level: think about what moral decision procedure will lead you (given your cognitive and other limitations) to maximize utility in the long run. I think there are many good reasons to believe that doing the math at every decision point will not be the optimal procedure in this sense. Of course, it would be if you were a fully informed, perfectly rational superbeing with infinite willpower and effectively infinite processing speed, but alas, even I cannot yet claim that status.

Given this unfortunate state of affairs, I suspect it is actually a better idea for most utilitarians to commit themselves to a policy like "Don't steal someone else's partner" rather than attempt to do the math every time they are faced with the decision. Of course, there may still be times when its just blindingly obvious that the math is in favor of stealing, in which case screw the policy.

Is this obviously true? Note the underlying assumption that you would break up eventually. Suppose you're dating someone, and the relationship gives you 1 hedon and them 3 hedons. You discover you have another option that gives you 2 hedons, but their next best opportunity gives them 1 hedon. (Suppose, to make things easy, those two other options are involved in a relationship themselves, which gives each of them 1 hedon.)

I don't think that's the scenario we're talking about here. Breaking up because you found someone better is (in observed folk morality) a dick move. But if you're less happy in your relationship than your long-term background level, the correct move is to break up now, even though that will push you both even lower in the short term.

That does still leave the question of what you should do in a relationship where you're mildly less happy than background (and note that long-term background is the correct comparison, not singledom) but your partner is substantially happier (and a future partner of you would not be so happy). The cheap answer is that empirically this seems vanishingly rare; if one partner is unhappy in a relationship, the other tends to also be, or at least to become so pretty soon.

But yes, you can in theory reach situations where you're obliged to reduce your own happiness for the sake of others. The moral obligation of westerners to give up almost all their wealth and donate it to charity is perhaps a simpler and clearer example.

You're pretty sure that you will be less happy in this relationship than other options you have, but think that they will pose a serious risk to themselves if you break up with them. To what degree can they manufacture an obligation for you to provide emotional support to them?

Ultimately, to the degree that you value their life in comparison to yours.

Consider a club where this injunction is taken seriously, and applied very early- basically, a woman is obligated to go home with either the first man she shows positive attention or with no one. Then this dramatically raises the bar for flirting, since she needs to be fairly confident the guy she's interacting with is her best option, but she needs to make that decision at first sight! In a situation where it's alright to compete at all stages of the process, then moving forward with one person has less opportunity cost, leading to more efficient pairings and means of discovering them.

Strawman. Consider the solution that actually happens, more or less: people flirt as much as they need to to make a decision, then go home together or move on; you are allowed to engage new people who've previously tried flirting with others and had it not work out, but not to start making moves on someone who's currently still engaged in pair-flirting.

No-one goes home with someone they don't want to, and many people find partners; most people get to make a reasonable number of attempts, and can flirt more comfortably knowing that for the moment they have their flirtee's full attention. The end pairings are "less efficient" than in a pure-competition situation, but what does that actually mean? Answer: more lower-status people find pairings (over iterated rounds), rather than all the action going to the top 80% all the time. Given diminishing returns this is probably closer to overall optimal.

I would consider a significant portion of existing managers to be exceptionally ineffective. Rather, if there were a majority that were effective, we'd be approaching Singularity significantly faster. The management case specified that the employee's heart was in the in the right place, so I must assume they aren't slacking off at the very least.

Suicidal tendencies, who would be happier with who, plenty of fish in the sea, and so on are examples of why dating is so ridiculously complicated. My own personal conclusion is that I am better off single for reasons you've described well thus far. I haven't done all the math personally, but it is my understanding that society naturally evolves the most stables practices; things do not become taboo for no reason, nor are taboo practices outright forbidden. The few that practice the taboo tend to reinforce the wisdom behind tabooing the practice. It seems like a significantly Bayesian-like process to me.