[EM] number of possible ranked ballots given N candidates

[James Gilmour]

> rob brown Sent: Wednesday, December 14, 2005 9:50 PM
> Unfortunately with 10 candidates, there are about 4 million 
> possible unique ballots, so this non-lossy compression scheme 
> may be less helpful than I hoped

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.

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".
James Gilmour