[EM] Strong Minmal Defense, Top Ratings

[Chris Benham]

In a recent EM post in another thread, I defined and recommended the
"Strong Minimal Defense, Top Ratings" method  (that I first proposed
in 2008) as "the best of the methods that meet the Favourite Betrayal
criterion, and also the best 3-slot ballot method":

*Voters fill out 3-slot ratings ballots, default rating is bottom-most
(indicating least preferred and not approved).

Interpreting top and middle rating as approval, disqualify all candidates
with an approval score lower than their maximum approval-opposition 
(MAO) score.
(X's  MAO score is the approval score of the most approved candidate on
ballots that don't approve X).

Elect the undisqualified candidate with the highest top-ratings score.*

I gather from one off-list response that this sentence of mine could have
been more clear:

'Unlike MCA/Bucklin this fails Later-no-Help (as well as LNHarm) so the voters have a less
strong incentive to truncate..'

I neglected to mention that I think it is desirable that after top-voting X, ranking Y below X
(but above bottom) should be about equally likely to help X as to harm X.

This implies that if one of the the two LNhs are failed, it is desirable that the other is also.

MCA/Bucklin meets Later-no-Help while failing Later-no-Harm. The voters have a big incentive
to truncate, and to equal-rank at the top, so with strategic voters it tends to look like  plain Approval.

In SMD,TR after top-rating X, middle-rating Y may harm X or may help X.

As discussed in 2008, it fails Mono-add-Top  (and so Participation).

8: C
3: F
2: X>F
2: Y>F
2: Z>F

F wins after all other candidates are disqualified, but if  2 F>C ballots are
added C wins.

Of course it is far from uniquely bad in that respect. A big plus for it is that it is virtually alone
in meeting my proposed  "Unmanipulable Majority" strategy criterion:

Regarding my proposed Unmanipulable Majority criterion:

*If (assuming there are more than two candidates) the ballot 
rules don't constrain voters to expressing fewer than three 
preference-levels, and A wins being voted above B on more 
than half the ballots, then it must not be possible to make B 
the winner by altering any of the ballots on which B is voted 
above A without raising their ranking or rating of B.*

http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023530.html

In common with MCA it meets mono-raise (aka ordinary monotonicity) and a 3-slot ballot version of
Majority for Solid Coaltions, which says that if  majority of the voters rate a subset S of the candidates
above all the outside-S candidates, the winner must come from S.


From the post that introduced SMD,TR:


It is more Condorcetish and has a less severe later-harm problem than MCA, Bucklin,
or  Cardinal Ratings (aka Range, Average Rating, etc.)

40: A>B
35: B
25: C

Approval scores:    A40,   B75,   C25 
Approval Opp.:      A35,   B25,   C75
Top-ratings scores: A40,   B35,   C25 

They elect B, but SMD,TR elects the Condorcet winner A.


Chris Benham


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