# [EM] IRV vs Plurality (back to the pile count controversy)

robert bristow-johnson rbj at audioimagination.com
Thu Jan 21 15:35:33 PST 2010

```On Jan 21, 2010, at 6:30 PM, James Gilmour wrote:

> robert bristow-johnson  > Sent: Thursday, January 21, 2010 6:49 AM
>> but breaking it down to piles regarding every conceivable permutation
>> of candidate preference is *still* breaking it down to a finite
>> number of piles.  for 3 candidates, that number is 9.  if you or
>> Kathy say it's 15, then you're wrong (and it's your slip that's
>> showing).  for 4 candidates the number of necessary piles is
>> 40.
>>  for  N candidates, the number of piles necessary, P(N) is
>>
>>             N-1
>>      P(N) = SUM{ N!/n! }
>>             n=1
>>
>> not
>>
>>             N-1
>>      P(N) = SUM{ N!/n! }
>>             n=0
>
> I do not intend to comment on your formula, but I calculate the
> numbers of possible unique preference profiles for increasing
> numbers of candidates (N) as follows:
>
> N	Unique Preference Profiles
> 2	4
> 3	15
...

then your calculation is mistaken.  the fact that you ostensibly need
4 piles when there are only two candidates should serve as a clue.

--

r b-j                  rbj at audioimagination.com

"Imagination is more important than knowledge."

```