[EM] Motivation for Chiastic Approval (XA)

Michael Ossipoff email9648742 at gmail.com
Thu Oct 27 23:03:11 PDT 2016

Thanks for the explanation--That completely answers my question about the
reason for the XA rule.

With Forest's examples of how XA does very well in chicken-dilemma
situations, XA could be one of the very few methods that meets FBC &
doesn't have a problem with the chicken-dilemma.   ...without MMPO's
Plurality Criterion failure, and the resulting criticism-causing
bad-example shown by Kevin Venzke.

I'd use it like Approval, top-rating my entire top-set, and bottom-rating
everyone else.   ...except that if I expected likely chicken-dilemma
defection from the faction of a member of my top-set, I'd use Forest's
strategy of giving them a 1/3 rating.

But I've only read these postings once, and this is a complicated topic
that calls for more than one reading, and the study of examples. I'm sure
that I wouldn't, today, be qualified to vote in an XA election.

Michael Ossipoff

On Fri, Oct 28, 2016 at 1:17 AM, Andy Jennings <elections at jenningsstory.com>

> Michael asked what motivated XA.
> When I came up with XA, I believe I was thinking about how voters might
> manipulate a score voting election if they had a target score for each
> candidate and were trying to make each candidate's mean score match their
> target.  I was thinking of an ongoing election where the voters can see the
> mean scores and change their votes at any time.  Whenever the candidate's
> mean fell below their target, they would change their vote to MAX and
> whenever it rose above their target they would change their vote to MIN.
> Score voting is not even required.  Approval voting would be good enough!
> If they could do this continuously (or hire a vote butler or write a
> computer program to do it for them), would there be an equilibrium point
> for a given candidate?  Yes, it would be the chiastic median (XM), the
> largest number, x, where at least x% of the people wanted a score of x or
> higher.  (For simplicity, we assume MIN=0 and MAX=100.)
> It's like a declared-strategy variant of score voting.  Once we know that
> we can just ask voters for their 0-100 score of each candidate and then
> calculate each candidate's XM.
> After that, I figured out that any voter who gave a candidate a higher
> score than their XM, if given the opportunity to change their vote, could
> do nothing to raise the XM.  Likewise, a voter who gave a candidate a score
> lower than the XM could have done nothing to lower their XM.  So voters
> should be honest, there's no reason to be dishonest when submitting your
> scores!  Whether the candidate ends up with an XM higher or lower than the
> score you submitted, your vote is, as much as possible, pulling their XM
> towards your score.  In essence, it turns your vote into an approval vote,
> approving everyone who society gives a lower score than you would like, and
> disapproving everyone who society gives a higher score than you would
> like.  So in this sense, the method can be called Chiastic Approval (XA).
> Of course, this all assumes that voters only care about making the
> candidate's final scores match their personal evaluations.  It ignores that
> they would strategize to affect the winner.  You can construct profiles
> where voters give honest scores and later discover that there were two
> frontrunners and they gave scores to both that were higher than their XMs.
> Those votes are pulling up on the XMs of both frontrunners, thus their
> votes are not really helping distinguish the frontrunners, which they might
> want.  (This is related to the chicken dilemma.)  You can construct
> profiles where the voters would change their votes and that would change
> the winner.  But whatever it's faults here, XA must be better than plain
> approval, no?
> In any case, I note that the more strongly a voter feels about the
> difference between two candidates, the bigger difference he will put
> between their scores, and it becomes much less likely that his scores will
> be on the same side of both their XMs.
> I also note that this method (XA) is appropriate for a society trying to
> decide one number, say an approval rating for the president.
> Lastly, I note that Rob LeGrand discovered this same system and studied it
> in his thesis.  Later, I discovered it independently and studied it in
> mine.  I have more to say about it if you want, but these are the basics.
> ~ Andy
> ----
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