[EM] a response to Andy J.

[Kristofer Munsterhjelm]

David L Wetzell wrote:

> And I don't think the Condorcet criterion is /that important/, as I 
> think in political elections, our options are inherently fuzzy options 
> and so all of our rankings are prone to be ad hoc.  

If opinions are fuzzy, that means that the voters' true distribution 
within political space would differ somewhat from the distribution you 
would infer by looking at the votes alone.

In terms of the 2D Yee diagrams, this means that if the voters are 
centered on a certain pixel, their votes might behave as if it was 
centered on one of the neighboring pixels (since each pixel in a 2D Yee 
diagram gives who would win if the population were normally distributed 
around that point in political space and preferred candidates closer to 
them). So in a Condorcet method, this might sometimes lead to the wrong 
candidate being elected. It would do so in the case where the true 
distribution is on one side of the divider between two Voronoi cells, 
and the distribution inferred from the votes alone is at the other side.

However, fuzzy opinions can cause greater problems with IRV. Because IRV 
is sensitive to the order of eliminations, it doesn't just have the 
clean cell transitions of Condorcet; it can also have disconnected 
regions near the edges or in the middle of one of the regions. In 
essence, these are the same as the "island of other candidates" 
artifacts, but in two dimensions rather than one.

It may be the case that voters are not centrally distributed in 
political opinion-space, but I think the observation can be generalized. 
If I'm right, why put up with a method that, by sensitivity to the 
elimination order, amplifies the fuzziness of the votes?