[EM] ASCII maps showing methods' "distances"

[Kristofer Munsterhjelm]

Kevin Venzke wrote:
> Hi,
> 
> I threw together a program that takes the DNA used by the method generator,
> and computes distances between methods based on the number of scenarios in
> which they give the same outcome. Then it tries to come up with a nice map
> that minimizes inaccuracy.

You could try using synthetic coordinate algorithms for mapping the 
distances to 2D. I did that for competing entries in a programming game, 
once, using the centralized Vivaldi algorithm as described in 
pdos.csail.mit.edu/papers/vivaldi:sigcomm/paper.pdf.

Another option would be to use principal components analysis, but I know 
less about that.

> Roughly left-to-right there seems to be a "all preferences" to "first
> preferences" emphasis spectrum. Top-to-bottom I am not sure. It is
> amazing to me that Woodall's two (related) methods DSC and DAC are so far
> from each other, yet there is little else between them. I wasn't going
> to include "BV" (which required me to define it) except for that it falls
> in this area. It's actually more similar to DAC than Bucklin.

To test the idea that left-to-right is "all preferences" to "first 
preferences", try including Borda... or antiplurality. They should be to 
the left if that's correct, because they don't privilege first 
preference very much. Perhaps Coombs would be down by IRV but 
significantly to the left.

As for finding something between DSC and DAC, you could try DHSC. This 
meets neither LNHarm nor LNHelp but might be "balanced" between the two. 
DHSC simply consists of creating both the DAC and DSC structures, then 
adding them up and running the DAC/DSC algorithm (intersect sorted sets 
until there's only one left, skipping intersections that would turn the 
set empty) on the result.

Adding the two structures together is simple. If {ABC} has a count of 20 
in one structure and a count of 15 in another, then the result gives 
{ABC} 20+15=35. Properly speaking, it should be the mean, not the sum, 
but since the DAC/DSC algorithm only involves relative magnitudes (that 
change the sorted order), it doesn't make a difference whether you use 
mean or sum.