[EM] The easiest method to 'tolerate'

C.Benham cbenham at adam.com.au
Thu Aug 11 14:30:31 PDT 2016

Steve, Kevin, Kristopher, anyone interested,

Before joining discussion of the relative merits of  MJ, IRV, MAM and 
similarly-motivated single-winner methods
I confirm that I didn't invent MCA.  Also it is very disappointing that 
the EM archive at Electorama appears to only
go back to last year.

Those three methods have very different criterion compliances.  I (and 
Kevin and a few others) highly value the
Favourite Betrayal criterion and MJ is the only one of these 3 to meet it.

Another widely valued criterion compliance is Condorcet (unfortunately 
incompatible with Favourite Betrayal) and
of these 3 that is only met by MAM.

IRV is immune to Burial strategy and meets the "Chicken Dilemma" 
criterion (meaning that there isn't any "defection"

Of these 3 methods IRV is the only one that is best of its type (based 
on the above mentioned criteria,IMHO) and (so)
is the only one I like.  I like its set of criterion-compliances except 
that I'm not a big fan of  Later-no-Harm, because it
encourages light-minded expression of weak preferences  and makes it 
more likely that voters will go along with cynical
preference-swap deals organised between parties/candidates. Fortunately 
IRV meets Later-no-Help (as does MJ).
Without that IRV would have a random-fill incentive (which would be 
silly and bad for "Social Utility").

MJ  is a version of Median Ratings with a tiebreaker that looks (to me) 
a bit awkward to handle and motivated by
I'm-not-sure-what.  I don't like Median Ratings because  (a) it can fail 
to elect a candidate that is both the most Top-rated
and the pairwise-beats-all winner (b) it has a very strong truncation 
incentive (i.e. for voters to only use the top and
bottom grades) and (c) it fails the Irrelevant Ballots Independence 
criterion, that means that removing or adding a small
number of ballots that make no preference-distinction among the 
competitive candidates can change the winner.

Of the methods I prefer to MJ, the simplest and most similar is Majority 
Top Ratings. It uses a 3-slot ballot, default
rating is bottom. If any candidate is rated top on more than half the 
ballots then the most top-rated candidate wins.
Otherwise if more than one candidate is approved (i.e. rated above 
bottom) on more than half the ballots then the
one of those that is most top rated wins. Otherwise the most approved 
candidate wins. (It was invented by Mike

So it is another version of Median Ratings. Like MJ it meets Favourite 
Betrayal and Later-no-Help and unfortunately
also fails Irrelevant Ballots. I prefer it to MJ because it is much 
simpler and has a somewhat reduced truncation incentive.

A method I vastly prefer to both of these also meets Favourite Betrayal, 
but meets Irrelevant Ballots and has much less
truncation incentive (at the cost of strict compliance with 
Later-no-Help) and is much more likely to elect the Condorcet
winner is  "Irrelevant Ballots Independent Fall-back Approval" (IBIFA).

*Voters fill in ratings ballots with as many slots as there are 
candidates up to say 4. Say A-B-C-D grading ballots are used.
Default grade is D, meaning least preferred and not approved. Any other 
grade is interpreted as approval.

If any candidate X is A-rated on more ballots than any other candidate 
is approved on ballots that don't A-rate X, then
elect the most A-rated X.

Otherwise if any candidate X is rated A or B on more ballots than any 
other candidate is approved on ballots that don't
rate X A or B, elect the X that is most rated A or B.

Otherwise elect the most approved candidate.*

I invented this and first posted it on EM on 28/5/2010.

I don't like MAM  for various reasons and prefer several other Condorcet 
methods, but expanding on that can wait for
another post.

Chris Benham

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