Jameson Quinn wrote (18 Oct 2010):
I edited Electowiki to essentially replace the Bucklin-ER article with a
new, expanded MCA article. In this article, I define 6 MCA variants. I find
that as a class, they do surprisingly well on criteria compliance. Please
check my work:
http://wiki.electorama.com/wiki/Majority_Choice_Approval#Criteria_compliance
Criteria compliances
All MCA variants satisfy the Plurality criterion
<http://wiki.electorama.com/wiki/Plurality_criterion>, the Majority
criterion for solid coalitions
<http://wiki.electorama.com/wiki/Majority_criterion_for_solid_coalitions>,
Monotonicity <http://wiki.electorama.com/wiki/Monotonicity_criterion>
(for MCA-AR, assuming first- and second- round votes are consistent),
and Minimal Defense
<http://wiki.electorama.com/wiki/Minimal_Defense_criterion> (which
implies satisfaction of the Strong Defensive Strategy criterion
<http://wiki.electorama.com/wiki/Strong_Defensive_Strategy_criterion>).
It is well known that in general run-off methods fail mono-raise (aka
Monotonicity), and these methods
are no exception.
22: A
23: A>C
24: B
27: C>B
02: D>C
06: E
(104 ballots)
TR scores: A45, B24, C27, D2, E6.
Approval scores: A45, B51, C52, D2, E6.
I am assuming that 3-slot ballots are used, and since no candidate has
either a Top Ratings or Approval
score that reaches the majority threshold the runoff will be between the
TR winner A and the Approval
winner C.
A wins that runoff 45-29, but if the 2 D>C ballots change to D>A the
Approval winner changes to B and
now A loses that runoff 47-49.
22: A
23: A>C
24: B
27: C>B
02: D>A (was D>C)
06: E
(104 ballots)
TR scores: A45, B24, C27, D2, E6.
Approval scores: A47, B51, C50, D2, E6.
Also I would quibble that methods that use ballots that don't allow
voters to express a full ranking of the
candidates really properly meet Majority for Soild Coalitions, but
instead just meet a restricted form of
it (which is nonetheless very valuable).
And I'm surprised that a MCA advocate doesn't mention the Favourite
Betrayal criterion. Of course the
suggested runoff "variants of MCA" also fail that.
Chris Benham
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