[EM] ASCII maps showing methods' "distances"

[Kevin Venzke]

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.

The maps below are really 60 by 30, but compressed to be 60x15 so it looks
better on the screen. Basically a character is two units tall and one unit
wide.

The "Bucklin variant" mentioned below is this:
1. Voters specify one favorite, and any number of second preferences.
2. Call the first-preference winner A. All candidates "get" their first
preferences.
3. All ballots that didn't rank A first, contribute their second prefs.
4. If A doesn't have the most prefs, add in the second prefs of voters
who ranked A first and elect whoever has the most. Otherwise, elect A.

This method guarantees LNHarm to the A voters (at least in that a second
pref can't hurt A... certainly second preferences could hurt each other)
and also has an interesting placement on the map.

Legend:
FP: FPP aka Plurality
DS: DSC
DA: DAC
Bu: Bucklin, and also Approval would give the same results
BV: The Bucklin variant
WV: Winning Votes (Minmax/Schulze/Tideman/River)
IR: IRV
CI: Condorcet//IRV
KH: Condorcet//King of the Hill (my method from yesterday)
CA: Condorcet//Approval
QR: Quick Runoff (another method of mine)

............................................................
................Bu.........DA...............................
............................................................
............................................................
............................BV..............................
............................................................
...................CA.......................................
..................WV.......................DS...............
...................................................FP.......
............................................................
............................................................
...................KH...........QR..........................
........................CI..................................
............................................................
...............................IR...........................

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.

You can see that, predictably, C//A is on the Bucklin side of WV rather
than the IRV side. It's not surprising that QR, C//IRV, and C//KH lie
on the WV side of IRV, since it's pretty much the purpose of those methods
to mix IRV advantages with Condorcet advantages. QR sticks a bit more in
the DSC direction, I'm sure, due to preserving LNHarm...

The four LNHarm methods do all seem to be on the right-hand side, but
if we add MMPO to this diagram, it sits almost right on top of WV (which
is largely why I didn't include it).

If we take methods out we could, I think, find that the picture doesn't
remain stable. I've generated enough maps of subsets of the methods to
have confidence in the above map... If someone wants to see a certain 
subset, let me know.

Here I add a couple more methods.
K0: King of the Hill without the Condorcet filter
Wr: IRV where you eliminate the second-worst candidate!

..................................Bu........................
............................................................
.......................................DA...................
...............................CA...........................
................................WV..........................
......................................BV.............Wr.....
...........................KH...............................
............................................................
..........................K0.CI.............................
............................................................
.................................QR.........................
.............................IR.............DS..............
............................................................
................................................FP..........
............................................................

So as you might predict, K0 is less like WV than KH, but surprisingly
it's not very different from KH. The placement of the "Wr" method (on the
DAC/DSC side of the map) doesn't seem to be arbitrary, though I don't know
if it really means anything.

Kevin Venzke