Ted Stern wrote:
On 24 Feb 2005 at 14:17 PST, Dave Ketchum wrote: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.
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.
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.
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