[EM] Re: Condorcet package-wvx

[Daniel Bishop]

Ted Stern wrote:

>On 24 Feb 2005 at 14:17 PST, Dave Ketchum wrote:
>  
>
>>I am adding "-wvx" to the subject to debate a=b - time enough to think 
>>about labels if my idea, once understood, survives debate.  My thought is 
>>that a=b expresses interest in this pair, just as a<b or b>a do for wv, 
>>but ranks them equally and therefore should not affect margins (of which I 
>>only care about equality vs inequality, but not magnitude).
>>
>>Has nothing to do with margins, for such counts do not change margins.
>>
>>Only counting explicit a=b (as each incrementing vote count by .5 for each 
>>side of that pair) - not counting how many pairs can be made from rejects.
>>
>>Can combine - can say a=b=c to declare more than 2 - here a & b, a & c, 
>>and b & c.
>>
>>Ted talks of margins and relative margins being different - HOW?  He 
>>offers a definition at 15:54.  Perhaps relative margins would be useful in 
>>resolving cycles - I hope not.
>>
>I explained what I understand by the terms winning votes, margins and relative
>margins earlier.
>
>Here's my argument about how to count an equal ranking:
>
>Consider the two candidate ballot X1 vs. X2.
>
>A voter can vote for X1, X2, or abstain.  Current public election practice
>does not allow the voter to cast fractional votes or multiple votes.  
>
>Say we now are using a ranked ballot.  Leaving the ballot blank (abstaining)
>is equivalent to an equal rank X1=X2.  So casting a ranked ballot vote of
>X1=X2, which isn't a vote for either X1 or X2, must be equivalent to
>abstention.  When a voter has abstained in an election, you don't enter a vote
>for either side.  If you want to count the number of abstentions, you can
>always subtract the total votes for both candidates from the total number of
>ballots.
>
>Now consider the case of 1000 candidates.
>
>Counting X1=X2=X3=...=X1000 as a fractional 0.001 vote for each candidate over
>every other is both impractical and nearly pointless.
>  
>
Don't you mean half a vote for each candidate over every other?  Of 
course, if you're using margins, it doesn't make any difference.

At least for single-winner Condorcet elections, I don't think it's 
necessary to explicitly count X=Y as (0.5 X>Y + 0.5 Y>X) as long as they 
are equivalent in the sense of

* Pairwise Cancellation Criterion: If there is one ballot that ranks 
X>Y, and another ballot that ranks Y>X, and both of these ballots are 
changed to rank X=Y without affecting the relative ordering of any pair 
of candidates other than {X, Y}, then the winner must not change.

It might also be a good idea to require:

* Neutrality of Equal Rankings: The addition of one or more ballots that 
rank X=Y will never change the winner from X to Y or vice-versa.

* Neutrality of Spoiled Ballots: The addition of one or more ballots 
that rank all candidates equal to each other will never change the winner.