[EM] Relative vs. Majority Condorcet

[Kevin Venzke]

Hi CLC,

Closed Limelike Curves <closed.limelike.curves at gmail.com> a écrit :
> Do the people on this list have strong opinions on whether it's better to satisfy
> No Favorite Betrayal and Majority-Condorcet, or just relative Condorcet?

Does "Majority-Condorcet" mean the CW needs to have a majority over every other
candidate? Or is this mutual majority?

As someone who feels bare Condorcet is not sufficient and possibly not necessary, I
feel like I am meant to vote for option one, but if I'm reading it right, then
option one isn't actually offering enough...

I picture single-winner elections as having a hypothetical median voter that the
candidates are trying to appeal to, and when you have a majority-strength pairwise
contest, I expect that the median voter is there on the winning side. It certainly
seems more likely than not.

The second option doesn't offer Smith, but if it did, I would note that Smith is a
poor guarantee of quality. Here's a 1025-voter election where a 2-vote candidate is
in the Smith set (along with all other candidates):

2: A>B>C>D>E>F>G>H>I>J>K
1: B>C>D>E>F>G>H>I>J>K
2: C>D>E>F>G>H>I>J>K
4: D>E>F>G>H>I>J>K
8: E>F>G>H>I>J>K
16: F>G>H>I>J>K
32: G>H>I>J>K
64: H>I>J>K
128: I>J>K
256: J>K
512: K

While this is not realistic, I do think it is realistic that a candidate of limited
interest to most voters would sometimes manage to pairwise defeat a more viable
candidate. And we should be ready to interpret this as noise.

Kevin
votingmethods.net