Utilitarianism seems to indicate that the greatest good for the most people generally revolves around their feelings. A person feeling happy and confident is a desired state, a person in pain and misery is undesirable.
But what about taking selfish actions that hurt another person's feelings? If I'm in a relationship and breaking up with her would hurt her feelings, does that mean I have a moral obligation to stay with her? If I have an employee who is well-meaning but isn't working out, am I morally allowed to fire him? Or what about at a club? A guy is talking to a woman, and she's ready to go home with him. I could socially tool him and take her home myself, but doing so would cause him greater unhappiness than I would have felt if I'd left them alone.
In a nutshell, does utilitarianism state that I am morally obliged to curb my selfish desires so that other people can be happy?
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.
Ultimately, to the degree that you value their life in comparison to yours.
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.
This is the selfish answer, not the utilitarian answer. (I think the selfish answer is stable.) Note, though, that you have some choice over how much you value their life- someone who strongly values autonomy might decide to get angry at being held hostage to reduce the amount they value the other person, making it easier for them to break up with them.
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