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After this description and definition of Symmetrical ICT, I'll say a few words of what it implies for the compatibility of FBC and Condorcet's Criterion.
ICT stands for "Improved-Condorcet-Top". The idea for Improved Condorcet is from Kevin Venzke. Improved Condorcet meets FBC. Then, later, Chris Benham proposed completion by top-count, to achieve "defection-resistance", avoidance of the Chicken[[chicken Dilemmadilemma]]. Chris had a long name for his method, but I called it "Improved-Condorcet-Top", in keeping with Kevin's naming.
I later proposed that the Improved Condorcet improvement be done at bottom-end as well, to almost achieve compliance with Later-No-Help, which would achieve additional easing and simplification of strategy need.
X beats Y iff (X>Y) + (X=Y)B > (Y>X) + (X=Y)T
...except that two candidates can't beat eachother. If the above beat condition statement says that two candidates beat eachothereach other, then only one of them beats the other. The one that beats the other is the one that is ranked over the other on more ballots than vice-versa.
Likewise, then, it can be said that FBC and the Condorcet Criterion are compatible, contrary to popular belief.
Symmetrical ICT, like ordinary ICT, automatically avoids the chicken dilemma. Here is a criterion that measures for that property:▼Though it's defined elsewhere in electowiki, under its own name, I'd like to state my definition of FBC here. This definition is also linked to at the FBC article in electowiki, as an alternative definition of FBC. But it's the FBC definition that I now prefer, and it's what I now mean when I say FBC.
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== Favorite-Burial Criterion (FBC) ==
A candidate is top-voted, and at top, on a ballot if that ballot doesn't vote anyone over that candidate.
If no one who is not at top on your ballot wins, then moving an additional candidate to top on your ballot shouldn't cause to win anyone who isn't then at top on your ballot.
[end of FBC definition]
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▲Symmetrical ICT, like ordinary ICT, automatically avoids the chicken dilemma. Here is a criterion that measures for that property:
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== The Chicken Dilemma Criterion: ==
The Chicken Dilemma Criterion (CD):
'''Supporting definitions:'''
1. The A voters are the voters who prefer candidate A to every other
candidate. The B voters are the voters who prefer candidate B to every
other candidate.
2. The "other candidates" are the candidates other than A and B.
3. A particular voter votes sincerely if s/he doesn't falsify a
preference, or fail to vote a felt preference that the balloting
system in use would have allowed hir to vote in addition to the
preferences that s/he actually votes.
'''Premise:'''
1. The A voters and the B voters, combined, add up to more than half
of the voters in the election.
2. The A voters and the B voters all prefer both A and B to the other
candidates.
3. The A voters are more numerous than are the B voters.
4. Voting is sincere, except that the B voters refuse to vote A over anyone.
5. Candidate A would be the unique winner under sincere voting (...in
other words, if the B voters voted sincerely, as do all the other
voters).
'''Requirement:'''
B doesn't win.
[end of CD definition]
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'''A few improved properties of ICT and Symmetrical ICT:'''
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