[EM] Some definitions

[Michael Ossipoff]

TUC stands for "traditional unimproved Condorcet". By that, I refer to
 Condorcet methods other than Improved Condorcet methods (as defined by
 Kevin Venzke).

Of course, a Condorcet method is a method that meets the Condorcet Criterion.

Here is my general definition of the Condorcet Criterion:

Requirements:

1. The voter must be allowed to express as many mutually transitive
 pairwise-preferences as s/he wants to.

(...typically in the form of a ranking which has as many rank
 positions as that voter wants)

2. If there are one or more unbeaten candidates, then the winner
 should be an unbeaten candidate.

Traditional definition of "beat":

X beats Y iff more voters vote X over Y than vote Y over X.

Alternative definitions of "beat":

Preliminary definitions:

(X>Y) is the number of ballots ranking X over Y.

(Y>X) is the number of ballots ranking Y over X.

(X=Y)T is the number of ballots ranking X and Y at top.
 ...(not ranking anyone over either of them)

(X=Y)B is the number of ballots ranking X and Y at bottom
 ...(not ranking either of them over anyone)

Alternative definitions of "beat":

a) X beats Y iff (X>Y) > (Y>X) + (X=Y)T

b) X beats Y if (X>Y) + (X=Y)B > (Y>X) + (X=Y)T

...except that two candidates can't beat eachother. If, by the above
 beat-condition, two candidates beat eachother, then only one beats the
 other. The one that beats the other is the one who is ranked over the
 other on more ballots.

[end of general definition of Condorcet Criterion)

A Condorcet method is a method that meets the Condorcet Criterion,
 when one of the 3 above-stated definitions of "beat" is used.
 (The traditional definition of "beat", or one of the two alternative
 definitions, a) or b)  ).

A method that meets CC with the traditional "beat" definition is a
 traditional unimproved Condorcet (TUC) version.

A method that meets CC with one of the two alternative "beat"
 definitions a) or b) is an Improved Condorcet version.

Improved-Condorcet-Top (ICT) meets CC with "beat" definition a).

Symmetrical ICT  meets CC with "beat" definition b).

Definition b) is the one that best respects the preferences, intent
 and wishes of the equal-top or equal-bottom ranking voter.

Definition of Improved-Condorcet-Top (ICT):

By 'beat" definition a),

1. If exactly 1 candidate is unbeaten, then s/he wins.

2. If all or no candidates are unbeaten, then the winner is the
 candidate who is ranked at top (no one ranked over hir) on the most
 ballots.

3. If some, but not all, candidates are unbeaten, then the winner is
 the unbeaten candidate who is ranked at top on the most ballots.

[end of ICT definition]

Definition of Symmetrical iCT:

Same as ICT, except that "beat" definition b) is used.

[end of Symmetrical ICT definition]

By the way, I regard IRV much more highly than I formerly did, because:

(as I know I've already said)

1. Although, for our existing electorate, assuming the things that it
assumes, IRV is disqualified by its FBC-failure:

The only way we're going to get a better voting system for state
 and national office will be to elect a government consisting of a
 party that wants that.

The GPUS is the most winnable such party in this country, and they
 offer IRV. Any electorate that could elect the Greens by Plurality
 would be competent to make good use of IRV, despite is FBC-failure.

2. IRV meets Later-No-Harm, Later-No-Help, CD, Mutual Majority,
Clone-Independence,
 0-info Sincerity, and Weak-Participation.

Weak-Participation:

Adding a ballot shouldn't cause the defeat of the candidate whom that
 ballot votes over all the other candidates.

[end of Weak-Participation definition]

Does Weak-Participation already have another name?

IRV meets Weak-Participation. Condorcet (all versions) and
 Majority-Judgment fail Weak-Participation.

3. As I said in my post a few hours ago, IRV is much more
 count-fraud-secure than I'd formerly been saying.

Mike Ossipoff