Chris Benham wrote:
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.*
To have any point a criterion must be met by some method.
It is met by my recently proposed SMD,TR method, which I introduced
as "3-slot SMD,FPP(w)":
*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.*
[snip examples of methods failing the criterion]
You have some examples showing that RP/Schulze/"etc" fail the criterion.
Do they show that Condorcet and UM is incompatible? Or have they just
been constructed on basis of some Condorcet methods, with differing
methods for each?
I think I remember that you said Condorcet implies some vulnerability to
burial. Is that sufficient to make it fail UM? I wouldn't be surprised
if it is, seeing that you have examples for a very broad range of
election methods.
93: A
09: B>A
78: B
14: C>B
02: C>A
04: C
200 ballots
B>A 101-95, B>C 87-20, A>C 102-20.
All Condorcet methods, plus MDD,X and MAMPO and ICA elect B.
B has a majority-strength pairwise win against A, but say 82 of the 93A
change to
A>C thus:
82: A>C
11: A
09: B>A
78: B
14: C>B
02: C>A
04: C
B>A 101-95, C>B 102-87, A>C 102-20
Approvals: A104, B101, C102
TR scores: A93, B87, C 20
Now MDD,A and MDD,TR and MAMPO and ICA and Schulze/RP/MinMax etc. using
WV or Margins elect A. So all those methods fail the UM criterion.
I did a bit of calculation and it seems my FPC (first preference
Copeland) variant elects B here, as should plain FPC. Since it's
nonmonotonic, it's vulnerable to Pushover, though, and I'm not sure
whether that can be fixed at all.
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