[EM] NPV vs Condorcet

[Kristofer Munsterhjelm]

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".
> 
> 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.

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

which gives

    A   B   C
A  0 100 100
B  0   0 100
C  0   0   0

and which could be used for any voting system. I think the first idea is 
better, though.