[EM] Re: Condorcet package-wvx

[Dave Ketchum]

I prefer wv over margins, since I remember convincing arguments for this 
(but seem not to have saved those posts).

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.

>>>
>>> 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.


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

> 
> * Neutrality of Spoiled Ballots: The addition of one or more ballots 
> that rank all candidates equal to each other will never change the winner.
   My first choice is do not count spoiled ballots, so they cause no 

trouble - else:

    seems like all three pass for, if = get counted, they get counted in 
every pair
-- 
  davek at clarityconnect.com    people.clarityconnect.com/webpages3/davek
  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
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