Symmetrical ICT

Symmetrical ICT, short for Symmetrical Improved Condorcet, Top is a voting method designed by Michael Ossipoff. 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.

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:


 * 1) If only one candidate is unbeaten, then s/he wins.
 * 2) If everyone or no one is unbeaten, then the winner is the candidate ranked in first place on the most ballots.
 * 3) 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. 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.

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. 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."