Re: So I have been thinking about the restricted case of 3 significant candidates.

So this is sorta the second half of my 3 candidate wonderings:

Also, I have been having some discussions with the people who created or promote STAR voting: Mark Frohnmayer, Sara Wolk, Hayden Sasswood, Arend Peter Castelein.  We know how to map a cardinal ballot to a ranked ballot, but it's not one-to-one, we don't necessarily know how to invert that mapping.

Now we Condorcetists generally think that failing to elect the Condorcet winner is a "bad thing" when such exists.  We know that when the CW is not elected, the election *must* be spoiled, there is an identified loser whose presence in the race altered the winner, and there are an identified group of voters that would have been better served by insincerely ranking (or scoring) their 2nd favorite candidate (or "lesser evil") higher than their favorite.

I've been thinking of how this Condorcet failure would happen with STAR when there are 3 candidates.  This is related to how an astute voter would mark their STAR ballot given their preferences: [A > B > C].  Their favorite is A, they hate C, and B is their 2nd favorite or lesser evil candidate.  How would they mark their STAR ballot to best serve their political interests?

We would normally expect them to score A with 5 and C with 0.  What would they do with B?  Well, either the STAR final runoff will be with A in it or not with A in it.  A is already "ranked" higher than any other if they end up in the runoff.  If A is not in the final runoff, it's B and C and all they need to do is score B with a 1 and B has all the power they can give B to defeat C in the final runoff.

What motivation would any astute STAR voter have to mark their ballot differently than [A:5, B:1, C:0]?  What we call a "5-1-0" STAR ballot.  They want A to win.  In order for A to win, A must get into the final runoff.  Increase the score for B (over 1) will do nothing more to help B defeat C in the final runoff in the case that A does not get there.  And increasing the score for B only reduces the odds for A to get in the final runoff.

Why would any STAR voter vote any differently than 5-1-0?  Why would any voter raise the score for B any higher than 1?  There is no reason *unless* they anticipate that A cannot defeat C in the final round, but B *can* defeat C.  And this can happen *only* in the case of the Center Squeeze, just like with IRV.

The 5-1-0 STAR ballot will work a lot the same as IRV (if everyone marks their ballot as so).  The first round cares essentially only about the top-scored ballot (the 1 scores contribute little).  We can show that a STAR election that fails to elect the CW is a lot like an IRV election that fails to elect the CW.  They fail for the same reason.  Indeed if either Burlington 2009 or Alaska August 2022 were STAR and people voted 5-1-0, they would both fail to elect the CW just like IRV did.

The STAR people like to say that, *if* you anticipate this, score B a little higher.  Maybe even [A:5, B:4, C:0], the 5-4-0 STAR ballot.  Then STAR *would* have elected the CW in Burlington or in Alaska.  My response to that is if I fear that A cannot beat C and that B has the only chance to beat C head-to-head, and I hate C like I hate Hitler or Trump, then instead of the 5-4-0 ballot, I would cast [A:0, B:5, C:0] and get 6 more points for B to make sure A stays the hell outa the final runoff, which would lead to C winning.  Now we're back to bullet voting and it's like FPTP.

In the case of 3 candidates, can any of you envision why any politically-motivated STAR voter would vote differently than 5-1-0 **unless** they anticipate that their favorite is too weak to defeat their most loathed candidate?  I cannot understand any other reason to mark ones STAR ballot differently than 5-1-0.

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r b-j . _ . _ . _ . _ [email protected]

"Imagination is more important than knowledge."

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