[EM] Can anyone help with straight-ahead Condorcet language?

[Kristofer Munsterhjelm]

On 9/1/21 5:12 PM, robert bristow-johnson wrote:
> responding to both Forest and Kristofer...

>>> My suggestion:
>>>
>>> (3) If it is determined that no single candidate is ranked ahead of
>>> every other candidate on more than half of the valid ballots,
> 
> what's a "valid" ballot?
> 

>> - A candidate is considered to be the victor of a head-to-head against
>> another candidate if the first candidate is ranked ahead of the second
>> candidate on more than half of the ballots.
> 
> "more than half of the ballots"???  as in an *absolute* majority??

I thought that was strange, too. I was interpreting Forest's "valid 
ballot" as "any ballot", which then leads to that conclusion. It kinda 
works if we disallow equal rank, but there's no reason we should.

Perhaps this could work:

- A candidate is considered to be the victor of a head-to-head against 
another candidate if the first candidate is ranked ahead of the second 
candidate on more ballots than the second is ranked ahead of the first.

- If, on a ballot, a candidate is left unranked, that candidate is 
considered to be ranked below every ranked candidate.

Your "marked to the contrary" definition would also work, I think.

>> - If a candidate is determined to be a victor in every head-to-head
>> against another candidate, that candidate shall be elected.
>> - Otherwise, [fallback method here].
>>
>> I don't know if legislative language allows for intermediate definitions
>> like that, though.
> 
> the final legislation will actually put in needed definitions early in the language.  but this template is more abbreviated.
> 
> Now, I understand that we could spell out the pairing of candidates, but then it starts looking like a mathematics paper:
> 
> "The ballot shall list N candidates (including Write-in) and there shall be N(N-1)/2 unique pairings of candidates (including combined write-in).  In each pairing of two candidates, if the number of ballots ranking a selected candidate higher than the other candidate is less than the number of ballots marked to the contrary, then the selected candidate is marked as defeated.  The candidate who is not defeated in any pairing shall be elected."

Yes, that seems to be a bit on the verbose side.

I also think that the best candidate Condorcet methods (if you want a 
pure Condorcet method) would be one where the Condorcet criterion is 
automatically satisfied, rather than the method having to be prefixed by 
"if there is a CW, elect that candidate, otherwise..."

So possibly something like minmax or Ranked Pairs. Not Black or 
"Condorcet else IRV".

However, you then have to deal with not only defining whether X beat Y, 
but also how decisively X beat Y. Winning votes resists strategy better, 
but margins is considerably easier to define.

-km