robert bristow-johnson wrote:
On Feb 2, 2010, at 2:28 PM, robert bristow-johnson wrote:
Warren tells me that
C-1
SUM{ C!/n! }
n=1
has a closed form, but didn't tell me what it is. does someone have
the closed form for it? i fiddled with it a little, and i can
certainly see an asymptotic limit of
(e-1)(C!)
as C gets large, but i don't see an exact closed form for it. if
someone has such a closed form, would you mind sharing it?
Okay, I spent a little time working on this and figgered it out. The
fact that the number of distinct piles needed to represent all possible
manners of *relatively* ranking C candidates (no ties except unranked
candidates are tied for lowest rank) is
C-1
SUM{ C!/n! } = floor( (e-1) C! ) - 1
n=1
Now I wonder if there's a closed form for the number of orders with both
equality and truncation permitted. Since I don't quite get the proof, I
can't answer, though!
----
Election-Methods mailing list - see http://electorama.com/em for list info
