[EM] number of possible ranked ballots given N candidates
Paul Kislanko
kislanko at airmail.net
Wed Dec 14 14:44:03 PST 2005
James Gilmour: wrote
>
> Maybe there are 4 million possibilities with 10 candidates,
> but you won't have 4 million actual combinations unless you
> have many more voters than 4 million.
I was going to mention this as well. From a practical standpoint, one only
need record the "forms" of ballots actually cast, then for each new ballot
see if it's "form" is already stored, and if so just add 1 to the number of
voters who used that "form".
>
> In the STV-PR 2002 election in Meath (Ireland) for which the
> full ballot "papers" are available electronically, there
> were 14 candidates for 5 places, so there were about 2.4
> ×10^11 possible combinations of preferences. However, there
> were only 64,081 voters, so the practical maximum was 64,081.
> But in fact, those 64,081 voters marked only 25,101
> unique sets of preferences. The most common preference list
> appeared on 1,618 ballots.
>
> Of course, this won't help if you are trying to develop an
> "all possible combinations matrix".
Just ininitializing an "all possible configurations" could be daunting. But
the method I described above can be done efficiently enough to run on a
laptop in a few seconds.
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