[EM] "Unmanipulable Majority" strategy criterion definition amended

[Chris Benham]

I propose to amend my suggested  "Unmanipulable Majority"
criterion by simply adding a phrase beginning with "without.." 
so that it now reads:

*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.*

(Later I might rephrase it just to make it more succinct and
polished).

The effect of  the alteration is to preclude Compromise strategy.
When I first suggested the original version I knew that many methods
fail it due to Burial and/or  Push-over, but I mistakenly thought that
my recent 3-slot method suggestion (defined below) meets it.


*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.*

My preferred name for that method is now "Strong Minimal Defense, Top
Ratings" (SMD,TR). 

45: A
03: A>B
47: B>A
02: X>B
03: Y>A

Approvals:   A98,  B52,  Y3,   X2
Max. AO:    A2,    B48,  Y95, X95
Top Ratings: A48, B47,   Y3,  X2.

X and Y are disqualified, and  A wins.

A  is voted above B on more than half the ballots, but if all the ballots on
which B is voted above A are altered so that they all plump for B (top-rate B
and approve no other candidates) then B wins.


45: A
03: A>B
49: B 
03: Y>A

Approvals:   A51,  B52,  Y3,   X0
Max. AO:    A49,  B48,  Y52, X52
Top Ratings: A48, B49,   Y3,  X0

As before only X and Y are disqualified, but now B has the highest Top Ratings
score.

I will soon post more on the subject of  which methods meet or fail the (newly
amended)  Unmanipulable Majority criterion.

Chris Benham


      Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=other&p2=au&p3=tagline
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20081201/feb8a32f/attachment.htm>