[EM] A "top 3" to replace the "top 2"

[Kristofer Munsterhjelm]

On 09/16/2014 05:40 AM, Dick Burkhart wrote:
> Oregon is considering a "top 2" primary, a very regressive move in my
> opinion.
>
> So I thought what would be simplest "top 3" method that would give
> voters more choices, especially in regard to independent or minority
> candidates or parties. Less partisanship would be an added bonus.
>
> Below is a draft answer. Effective and simple, except for the modest
> complexity needed to counter strategic voting.

At first, this sounds like Borda. As you mention, Borda is known for its 
susceptibility to strategy, particularly teaming. So to handle this, you 
switch to a variant of Baldwin's method until the number of candidates 
is reduced to three.

Why not use straight Baldwin (Borda-elimination) all the way down to the 
winner? Most likely, the variant is not cloneproof nor monotone (just 
like Baldwin), but by using Baldwin all the way until one candidate 
remains, you can have Condorcet. Baldwin is simpler than the point 
redistribution method you're using, as well: just repeatedly eliminate 
the Borda loser. And if you use Nanson instead (repeatedly eliminate 
candidates with average or below-average Borda score), you get reversal 
symmetry as well. Furthermore, Nanson has already been used (in 
Michigan), a point you could use when advocating for it.

Also note that Borda, even restricted Borda, can fail majority. For 
instance (taken from Wikipedia):

55%: A>B>C
35%: B>C>A
10%: C>B>A

and B wins. B still wins even if the shares are 63%, 27%, and 10% 
respectively, or for that matter if the shares are 66%, 33%, and 1%. 
That means that a near two thirds majority vote for A can be overridden 
by the B-voters.

Perhaps this could happen if A was a Democrat, B was a Republican, and C 
was a further-right figure. The Democrats prefer the lesser right-wing 
candidate B, the Republicans here prefer the right-wing to the "leftist" 
Democrat, and the right-wing candidate's supporters prefer the 
Republican to the Democrat.

In any case, if something like this happens, you'll have to be prepared 
to defend why the person who had a considerable majority of the first 
place votes failed to win. In contrast, if you use Baldwin or Nanson all 
the way to a single candidate, A wins because both of those methods pass 
Condorcet, which implies Majority; in the particular case above, C is 
eliminated first, then A wins with a majority preference against B.

If you'd like a top-three second round, just use Baldwin or Nanson in 
the first round until three candidates are left, gather ballots for the 
second round, and apply Baldwin or Nanson to the second round ballots to 
find the winner.

Now you might say that if there are more parties, then the elimination 
stage will remove the similar right-wing candidates; but that still 
leaves the problem in place if there happens to be only three (say D + R 
+ further-right independent).