I grab wvx as a hopefully unique identifier, so that DAVE KETCHUM gets to define how it works. Once my definition gets heard we can debate whether it is useful - if it is we can think about a prettier name.
BTW - cycle resolution is the only place where it could be useful.
On Thu, 24 Feb 2005 20:45:57 -0600 Daniel Bishop wrote:
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.
Here we have THREE pairs, each treated as stated in the previous paragraph.
I explained what I understand by the terms winning votes, margins and relative
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.
margins earlier.
What you understand of these three HAS NO CONTROL over what I define as wvx.
Here's my argument about how to count an equal ranking:
Consider the two candidate ballot X1 vs. X2.
The following par. is not of interest, for wvx is not interested in your abstentions. In w>(a=b)>x, a and b are liked better than x, as well as each other, but not as well as w. Also, assuming the above is the complete ballot but abstains from c and d, wvx does not see them as a pair - they are ONLY rejects.
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.
wvx would see the zillion pairs, and treat each pair as defined for wvx, not as stated below.
Counting X1=X2=X3=...=X1000 as a fractional 0.001 vote for each candidate over
every other is both impractical and nearly pointless.
Daniel's first words - and I LIKE them (but remembering that wvx is much
like wv, and not like margins):
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.
wvx and margins pass wv fails if it does not count the X=Y votes.
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.
margins passes; wv passes if it failed above. wvx fails
My first choice is do not count spoiled ballots, so they cause no
* Neutrality of Spoiled Ballots: The addition of one or more ballots that rank all candidates equal to each other will never change the winner.
trouble - else:
seems like all three pass for, if = get counted, they get counted in every pair
--
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Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026
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If you want peace, work for justice.
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