Symmetrical ICT: Difference between revisions
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'''Symmetrical ICT''', short for '''Symmetrical Improved Condorcet, Top''' is a voting method designed by [[Mike Ossipoff|Michael Ossipoff]]. <!-- when? link to EM? --> It is based on Kevin Venzke's concept of "Improved Condorcet", which is a modification of pairwise comparison logic that enables methods to pass the [[favorite betrayal criterion]] at the cost of sometimes failing the [[Condorcet criterion]].
However, Symmetrical ICT doesn't actually pass the [[favorite betrayal criterion]] (as shown below).
==Definition==
(Note: This is not actually a [[Condorcet method]]. It is a Condorcet method only when using a modified definition of what a Condorcet method is.)
(X>Y) means the number of ballots ranking X over Y.
(Y>X) means the number of ballots ranking Y over X.
(X=Y)T means the number of ballots ranking X and Y in 1st place.
(X=Y)B means the number of ballots ranking X and Y at bottom, i.e. not ranking either X or Y above anyone else.
Let the partial beat relation b(X, Y) be true if (X>Y) + (X=Y)B > (Y>X) + (X=Y)T.
Then X beats Y if:
* p(X,Y) and not p(Y, X), or
* p(X,Y) and p(Y, X) and (X>Y) > (Y>X).
The winner is chosen as follows:
# If only one candidate is unbeaten, then s/he wins.
# If everyone or no one is unbeaten, then the winner is the candidate ranked in first place on the most ballots.
# If some, but not all, candidates are unbeaten, then the winner is the unbeaten candidate ranked in first place on the most ballots.
== Improved Condorcet ==
Condorcet methods usually have a low but nonzero rate of [[favorite betrayal]] failures.<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-June/114476.html|title=Measuring the risk of strict ranking|website=Election-methods mailing list archives|date=2005-06-28|last=Venzke|first=K.}}</ref> '''Improved Condorcet''' is a modification of pairwise comparisons in an otherwise Condorcet-compliant method to turn absolute Condorcet compliance and a low rate of [[FBC]] failure into absolute FBC compliance and a low rate of [[Condorcet criterion]] failures (along with absolute Majority Condorcet compliance).
Mike Ossipoff argued that improved Condorcet allows a voter who wants one of X and Y to win, and who ranks X first, to change a ranking of X>Y into X=Y without undue risk that this will change the winner from Y to someone lower ranked by that voter; and thus that it's better to satisfy the IC version of Condorcet than the actual [[Condorcet criterion]].
==History==
The tied-at-the-top rule and Improved Condorcet ideas were devised by Kevin Venzke in an effort to create a [[Minmax]] variant that passes the [[FBC]]. Then, later, Chris Benham proposed completion by top-count, to avoid the [[chicken dilemma]] and thus achieve defection-resistance.<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2012-January/094905.html|title=TTPBA//TR (a 3-slot ABE solution)|website=Election-methods mailing list archives|date=2012-01-13|last=Benham|first=C.}}</ref> Mike Ossipoff shortened the name of this method to "Improved Condordet, Top".
Mike later proposed that the ICT tied-at-the-top rule also be applied to the bottom end, to almost achieve [[later-no-help]] compliance, which then led to Symmetrical ICT.
==Criterion compliances==
Symmetrical ICT passes the [[chicken dilemma criterion]]. It fails the [[Condorcet criterion]].
It was intended to pass the [[favorite betrayal criterion]], but doesn't succeed in doing so due to the "(X>Y) > (Y>X)" term in the definition. It is possible that a voter can lower their favorite from the top and thereby make their compromise the only candidate who isn't "beaten."
=== Favorite betrayal example ===
0.389: B>A=C
0.290: A>C>B
0.241: C>B>A
0.079: A=C>B ⇒ C>A=B
In this case, the voters on the bottom row can elect a better candidate, C, by reversing their preference for A.
==Notes==
Omitting the (X=Y)B term would turn this method into ordinary ICT. In Mike's opinion, ordinary ICT has the most important properties of Symmetrical ICT, but Symmetrical ICT adds a somewhat less important improvement, consisting of simpler bottom-end strategy.
In an election with dichotomous preferences, the best ICT strategy is Approval strategy: equal-rank all approved candidates first and all unapproved candidates last. Mike considered current [[United States]] voters to have near-dichotomous preferences: that each voter has a much wider gap between acceptable candidates and unacceptable ones than between candidates of the same category.<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2011-December/094667.html|title=How to vote in IRV|website=Election-methods mailing list archives|date=2011-12-06|last=Ossipoff|first=M.}}</ref>
==References==
[[Category:Ranked voting methods]]
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