[EM] NPV vs Condorcet

[Dave Ketchum]

The first N*N matrix  below is what I was talking about - it takes the 
information from the FPTP votes and records that as if bullet votes.

Note that this example matrix is complete only for only three candidates. 
If there were seven candidates the matrix would be bigger, showing A, B, 
and C ranking over the other four.

On Wed, 22 Oct 2008 18:18:00 +0200 Kristofer Munsterhjelm wrote:
> Bob Richard wrote:
> 
>> I'm obviously missing something really, really basic here. Can someone 
>> explain to me what it is?
>>
>>  > Take it from the FPTP count and recount it
>>  > into the N*N array by Condorcet rules ...
>>
>> I still have no idea what this means. Here's an example:
>>
>> Plurality result:
>>   Able: 45
>>   Baker: 40
>>   Charlie: 15
>>
>> Here's a (very naive) NxN matrix (fixed-width font required):
>>
>>         Able     Baker    Charlie
>>         -------  -------  -------
>> Able        --       45       45
>> Baker       40       --       40
>> Charlie     15       15       --
>>
>> But it's not a Condorcet count because we have, for example, no idea 
>> how many of the Able voters prefer Baker to Charlie and how many 
>> prefer Charlie to Baker. As a result, the pairs of cells above and 
>> below the diagonal don't add up to 100. I still don't see how we can 
>> "recount it into the NxN matrix by Condorcet rules".

It IS a Condorcet count.
      Bullet voting Condorcet voters chose not to provide more information 
such as what the Able voters thought as to Baker vs Charlie.
      FPTP voters could have had similar thoughts, but had no way to 
express them.
>>
>> Someone please show me the NxN matrix that Dave Ketchum would use to 
>> combine these votes with the other votes that had been cast on ranked 
>> ballots.
> 
Condorcet N*N matrices are simply added together, element by element.  Gets 
a bit complicated, but is doable, to prepare such as the 3*3 matrix above 
for summing with a 4*4, 7*7, or any other (need is only to prepare, not to 
have to know how big the biggest other matrices may be).
> 
> If we consider the votes as bullet votes, then we can expand to:
> 
> 45: Able > Baker = Charlie
> 40: Baker > Able = Charlie
> 15: Charlie > Able = Baker
> 
> which produces the matrix you gave above.
> 
> That's the "consider bullet voters" idea. The other one is to count the 
> plurality vote locally, so you get:
> 
> 100: Able > Baker > Charlie

BUT, the FPTP voters could not express such thoughts.

...
-- 
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  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
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