Monogamy isn’t zero sum because not everyone is an equally good partner for everyone else. Like, Alice can date Bob or Carol, and leave the other one single. It’s unlikely that dating either of them is equally good for her; and it’s unlikely that dating her is equally good for each of them; so there’s probably a single outcome with the highest total utility.
By that definition nothing is zero sum. “Zero sum” doesn’t mean that literally all possible outcomes have equal total utility; it means that one person’s gain is invariably another person’s loss.
a mathematical representation of a situation in which each participant’s gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants.
Monogamy isn’t zero sum because not everyone is an equally good partner for everyone else. Like, Alice can date Bob or Carol, and leave the other one single. It’s unlikely that dating either of them is equally good for her; and it’s unlikely that dating her is equally good for each of them; so there’s probably a single outcome with the highest total utility.
By that definition nothing is zero sum. “Zero sum” doesn’t mean that literally all possible outcomes have equal total utility; it means that one person’s gain is invariably another person’s loss.
Wikipedia disagrees with you: https://en.wikipedia.org/wiki/Zero-sum_game
Emphasis mine.
(By your definition, it seems to me that almost everything would be zero sum. If I bake a tasty cake for my friends, and that causes one of them to not visit the bakery that evening, the baker has lost out. More generally, see my post “Pareto improvements are rarer than they seem”: https://www.lesswrong.com/posts/5AQBNwDoKW5YXDbvc/pareto-improvements-are-rarer-than-they-seem)