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Sniffnoy comments on Unknown knowns: Why did you choose to be monogamous? - Less Wrong
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n^2?
1
2+1=3
3+2+1=6
4+3+2+1=10
5+4+3+2+1=15
6+5+4+3+2+1=21
7+6+5+4+3+2+1=28
Let's see... (n-1)n/2. Yes, n^2 it is.
It didn't occur to me to think of it that way given how important that -1 and /2 are for most practical purposes but that just means I wasn't aiming high enough in with my hypothetical plans to require a harem of bisexual women (sorry guys...). More to the point I suspect I discount my expected exposure to other people's drama by more than a linear factor. With larger polyamorous entanglements I'm more likely to be affected by factional politics. Given how they work I'd estimate a drama exposure of order n*log(n).
Now for the real practical consideration... what is the relationship between number of polyamorous partners and expected depletion of my Pramipexole supply... Yes, Pramipexole enhances libido for both sexes and in the case of males reduces or eliminates the refractory period). ;)
General fact: Summing a polynomial of degree k results in a polynomial of degree k+1. This is easier to see if you use the x choose k basis, rather than the x^k basis.
This is even easier to see if you remember that summation is discrete integration, which is the opposite of differentiation, which reduces degree by one. I recommend Graham, Knuth and Patashnik's "Concrete Mathematics" for stuff like this.