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Manipulability correction for BTR-IRV

KM
Kristofer Munsterhjelm
Thu, May 16, 2024 11:50 AM

I implemented BTR-IRV relatively quickly because Robert mentioned it and
I thought it would provide useful context. It turns out my quick
implementation was a little too dirty and it eliminated losers
incorrectly when there was a tie for last.

It used to choose one candidate tied for last vs one candidate tied for
next to last for the bottom runoff. Now it picks two candidates tied for
last instead, which, in retrospect, seems much more sensible.

It improves the stats too. As with IRV, there's a candidate-dependent
tiebreak but it shouldn't matter because the generator is candidate
agnostic. Here's the new result:

Burial, no compromise:  62219  0.124438
Compromise, no burial:  2340    0.004680
Burial and compromise:  157    0.000314
Two-sided:              102669  0.205338
Other coalition strats: 1683    0.003366

---=======
Manipulable elections:  169068  0.338136

Ties: 0
Decisive elections: 500000

Condorcet//Plurality has a manipulability value close to ordinary
Plurality, but I think my tie handling is obscuring the improvement from
the Condorcet phase. So I should find a way to deal with ties before I
post its detailed stats.

So much to do and so little time.

What I can conclude is that BTR-IRV is not the same thing as
Condorcet-Plurality with four candidates or more. I kinda knew that
already though :-)

-km

I implemented BTR-IRV relatively quickly because Robert mentioned it and I thought it would provide useful context. It turns out my quick implementation was a little too dirty and it eliminated losers incorrectly when there was a tie for last. It used to choose one candidate tied for last vs one candidate tied for next to last for the bottom runoff. Now it picks two candidates tied for last instead, which, in retrospect, seems much more sensible. It improves the stats too. As with IRV, there's a candidate-dependent tiebreak but it shouldn't matter because the generator is candidate agnostic. Here's the new result: Burial, no compromise: 62219 0.124438 Compromise, no burial: 2340 0.004680 Burial and compromise: 157 0.000314 Two-sided: 102669 0.205338 Other coalition strats: 1683 0.003366 ======================================== Manipulable elections: 169068 0.338136 Ties: 0 Decisive elections: 500000 Condorcet//Plurality has a manipulability value close to ordinary Plurality, but I think my tie handling is obscuring the improvement from the Condorcet phase. So I should find a way to deal with ties before I post its detailed stats. So much to do and so little time. What I *can* conclude is that BTR-IRV is not the same thing as Condorcet-Plurality with four candidates or more. I kinda knew that already though :-) -km