Simmons, Forest wrote:
Here's a version that is both clone proof and monotonic:
The winner is the alternative A with the smallest number of ballots on which
alternatives that beat A pairwise are ranked in first place. [shared first
place slots are counted fractionally]
That's it.
This method satisfies the Smith Criterion, Monotonicity, and Clone Independence.
Warren Smith wrote:
this is an elegant method!
Note that it is IMMUNE to my "DH3 pathology!"
http://rangevoting.org/DH3.html
It is strategically pointless to "bury" (lower artificially) a rival
to your favorite below some non-entities, because if those nonentitites are
never
ranked top, doing so makes no difference.
And it satisfies mono-add-plump and mono-append (two Woodall criteria)!
And it is simple!
Assuming these criterion compliance claims are right , so far I am very
very impressed. Congratulations Forest!
It seems to completely dominate Schwartz,IRV which until now was one of
my favourite Condorcet methods. I am convinced that it has an
anti-burial property stronger than I suspected it was a possible for
an unadorned Condorcet method to have. One of the reasons I liked
Schwartz,IRV was that it met what I called "Dominant Mutual Third
Burial Resistance", a criterion that said that if there are three
candidates
X,Y,Z and X wins, then changing some ballots from Y>X to Y>Z can't make
Y the winner.
Well I'm quite sure this Simmons method meets "Dominant Mutual *Quarter*
Burial Resistance"!
26: A>B
25: C>A
49: B>C (sincere is B>A or B)
A>B>C>A. "Simmons" scores: A25, B26, C49. A has the lowest score and
so narrowly wins.
On top of that it has the advantage over Schwartz,IRV of meeting
mono-raise (and so isn't vulnerable to Pushover strategy), and doesn't
seem to have any disadvantage.
It definitely fails two of Steve Eppley's criteria: Minimal Defense and
"Truncation Resistance" (not ones I rate highly).
/truncation resistance/
<Proof%20MAM%20satisfies%20Minimal%20Defense%20and%20Truncation%20Resistance.htm>:
Define the "sincere top set" as the smallest subset
/ / of alternatives such that, for each alternative in the
subset, say /x/, and
/ / each alternative outside the subset, say /y/, the number of
voters who
/ / sincerely prefer /x/ over /y/ exceeds the number who
sincerely prefer /y/
over /x/. If no voter votes the reverse of any sincere
preference regarding
any pair of alternatives, and more than half of the voters
rank some /x/ in
the sincere top set over some /y/ outside the sincere top set,
then /y/ must
not be elected. (This is a strengthening of a criterion having
the same name
promoted by Mike Ossipoff, whose weaker version applies only when
the sincere top set contains only one alternative, a Condorcet
winner.)/
/
I'm not sure about his "Non-Drastic Defense" criterion, (the version)
that says that if Y is ranked no lower than equal-top on more than half
the ballots and Y
pairwise beats X, then X can't win.
It has Woodall's Symmetric Completion property, and it certainly meets
his Plurality criterion when there are three candidates (and probably
meets it period).
I'm happy with its performance in this old example:
101: A
001: B>A
101: C>B
It easily elects A. Schulze (like the other Winning Votes "defeat
dropper" methods) elects B.
It meets my "No Zero-Information Strategy" criterion, which means that
the voter with no idea how others will vote does best to simply rank
sincerely.
Chris Benham
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