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

Kathy Dopp kathy.dopp at gmail.com
Thu Jan 21 16:35:58 PST 2010

```>> ballot to legally equivalent votes. The reduced set is this:
>>
>> A
>> B
>> C
>> A>B
>> A>C
>> B>A
>> B>C
>> C>A
>> C>B
>>
>> Note that this assumes a 2-rank ballot.
>
> no, it can be a 3-rank ballot where the voter declines to rate their
> last choice.  "3rd choice" is left unmarked.
>
>> It also assumes that majority vote isn't important.
>
> bullshit.  it (the number of consequential ballot permutations) has
> nothing to do with it (whether or not majority vote is important).
>
>> If it's important, as it would be in an IRV election under Robert's
>> Rules, we have some more possibilities. They are all the three-rank
>> permutations.
>>
>> A>B>C
>> A>C>B
>> B>A>C
>> B>C>A
>> C>A>B
>> C>B>A
>>
>>
>> Well, I won't speak about Kathy, but in terms of practical
>> elections in the U.S., she's right. You did not state enough
>> information to establish your reduced count, ...
>
> yes i did state enough information.  may i remind you?  i said that
> there is *no* consequential difference in these two marked ballots
> (in the case of N=3).  there is no consequential difference between a
> ballot marked A>B to one marked A>B>C .  there is no election
> scenario, whether it's IRV, Condorcet, Borda or any other method
> using ranked ballots that will count those two ballots differently.
> there is no need to separate the A>B and A>B>C into two piles.

OK. I understand now why you are confused Robert:

1. on the formula for the number of possible unique candidate
orderings for any rank choice voting method  you incorrectly assume
that the number of possible ballot rankings that a voter may fill out
is always equal to the number of candidates running for office and so
you can collapse "N" of the rankings, but this simply is not the case
in US IRV elections and it would just be unnecessarily confusing to
collapse rankings for the special (and unusual) case when there are
three candidates and three rankings, when a more general formula that
always applies to all situations regardless of the number of
candidates and allowed rankings could be used; and

2. on the fact that IRV and Condorcet must be reported similarly and
counted similarly, because there are different methods available to
count each one.

With Condorcet, you can easily count it with an NxN matrix and you
cannot count IRV that way at all generally (although I wouldn't put it
past you to find an unusual special case where you could).

With IRV, you can count it (albeit not easily depending on the number
of candidates) with sorting into piles, but you cannot count Condorcet
method that way.

You can count either Condorcet or IRV by sorting into unique vote
orderings, as I gave you the general formula for that works in all
cases earlier. However that would be a very difficult and
time-consuming way to count Condorcet since Condorcet is
precinct-summable in the far simpler n x n matrix.  It is the only way
to make IRV precinct summable using the formulas I gave you earlier or
you can look them up in my IRV report, unless you want to publicly
report all voters' individual choices. Minneapolis chose to use the
first method.

I.e. The counting methods available and ideally used for Condorcet and
IRV are different.

--

Kathy Dopp

Town of Colonie, NY 12304
phone 518-952-4030
cell 518-505-0220

http://electionmathematics.org
http://kathydopp.com/serendipity/

Realities Mar Instant Runoff Voting
http://electionmathematics.org/ucvAnalysis/US/RCV-IRV/InstantRunoffVotingFlaws.pdf

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