[EM] Condorcet Counting

[Dave Ketchum]

I had included this in a post to RangeVoting - should have, but  
apparently didn't, include EM.

Big point is that Condorcet, while similar with IRV for voters to  
vote, is better and is also more practical for human counting.

Begin forwarded message:
> Date: February 5, 2010 9:23:41 PM EST
> To: RangeVoting at yahoogroups.com
>
With Condorcet:
>      A ballot voted by IRV rules would have the same meaning, except
> that ALL the ranking would be counted.
>      A voter could assign the same rank to multiple candidates -
> meaning assigning the same liking when seeing that as appropriate.  No
> need to get picky as to relationship between ranks - Condorcet has no
> need to look closer than needed, for each pair of candidates, to
> choose among A>B, A=B, and A<B.
>      There is less need for having more than three ranks with
> Condorcet than with IRV - merits should be considered before deciding.
>
> Winner is the CW, which wins in above counts when compared with each
> other candidate.  If no CW we have a cycle of three or more members to
> analyze for a winner (a simple adjustment would be to ignore the pair
> that was nearest to a tie - that was supported by the fewest voters -
> repeat if still a cycle).  More complex methods have been proposed -
> which might be worth the extra pain?
>
> Runoffs?  Even with a cycle all the voters have had an opportunity to
> express their voting desires in detail, and to have all they expressed
> counted.  A true tie might justify a runoff, but it is worth thought
> as to how near you have to be to justify the expense ("majority" made
> sense for Plurality - you could need to recover from 49 like A, 45
> like B, and 6 like and voted for C, but prefer B over A - with
> Condorcet the C voters could have also voted liking B better than A).
>
> A bit about the Condorcet N*N matrix used above, to show that it does
> not have to be the pain to do that some seem to think:
>      A row and column for each candidate.  Do an extra column, here
> called "V", to count how many voters rank each candidate.
>      Think of write-ins.  If just a few, as often happens, could lump
> as if just one extra candidate.  If this indicates there are many,
> better treat each with many votes as a true extra candidate.
>      For each ballot, add 1 for each ranked candidate in column V.
> This column will later get added to each other column.  Effect is as
> if each of these candidates won over each other - correct when other
> is unranked; adjust below for each ranked pair.
>      For each ranked pair, such as A and B, adjust.  If ranks tied,
> add -1 to A,B and to B,A.  Else add -1 to the loser.
>      Above can be done in multiple matrices, such as for each
> precinct.  Could be some matrices are for different quantities of
> candidates, such as for write-ins.  If so, adjust by inserting needed
> rows and columns of zeros.  Then sum the array elements.  In this
> final matrix add column V to each other column.
>      Elements on diagonal, such as A,A, should be zero - so adjust
> for neatness.

Also:

Column V numbers are counting the same as Approval and often, though  
not always, identify the CW.

Above says add -1 to both when ranks tie - would  not affect which  
wins if this -1 was omitted on ties.

Above notes that count is correct when one of a pair is unranked -  
also does not notice, and thus correctly does nothing, when both are  
unranked.

Some IRV discussion promotes ranking of enough candidates to try to  
include the winner, whether the voter really does or does not care.   
USELESS to rank beyond your caring, for such guessing can hurt as much  
as help.
>
> Dave Ketchum
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20100221/1b696c4a/attachment-0002.htm>