Definite Majority Choice

I'm just throwing something up here to get this page started. Edit as appropriate --Araucaria 15:09, 18 Mar 2005 (PST)

Voters can grade their choices from favorite (A) to least preferred (ungraded), and give some or all of their graded choices a "passing grade", which signifies approval.

Graded rankings added into a Round-Robin array, and the approval scores of each candidate are tabulated as well.

To determine the winner:

Eliminate any candidate that is defeated in a one-to-one match with any other higher-approved candidate. So by 2 different measures, a definite majority agrees that candidate should be eliminated.
If more than one candidate remains, the winner is the single candidate that defeats all others in one-to-one (pairwise)contests.

One implementation of Definite Majority Choice might use a Graded Ballot with a Lowest Passing Grade option:

            A    B    C    D    E    F    G

      X1   ( )  ( )  ( )  ( )  ( )  ( )  ( )

      X2   ( )  ( )  ( )  ( )  ( )  ( )  ( )

      X3   ( )  ( )  ( )  ( )  ( )  ( )  ( )

      X3   ( )  ( )  ( )  ( )  ( )  ( )  ( )

   Lowest  ( )  ( )  ( )  ( )  ( )  ( )  ( )
   Passing
   Grade
   (optional)

You can give the same grade to more than one candidate. By default, each graded candidate gets a "passing grade" and one Approval point.

Ungraded candidates are graded below all others and get no Approval points.

Optionally, a voter can specify a Lowest Passing Grade (LPG), which means that any graded candidates with lower grades get no approval points.

If this were a vote for president, one could compare the LPG selection to Gerald Ford. One might disagree whether he was a good or bad president, but anybody better than him would be a good president, and anybody worse than him would be bad.

The main reason to grade candidates below the "Gerald Ford" mark would be if you're not optimistic about the chances for your higher-ranked favorite and compromise candidates. Grading candidate X below the LPG mark gives you a chance to say "I don't like X and don't want him to win, but of all the alternatives, he would make the fewest changes in the wrong direction. I won't give him a passing grade because I want him to have as small a mandate as possible." Then you have some say in the outcome, instead of leaving the choice among the alternatives to the most vocal and extreme parts of other factions.

Handling Ties and Near Ties

In ordinary DMC, the winner is the candidate in Forest Simmon's P set, the set of candidates which are not approval-consistently defeated.

But in the event of a tie or near tie (say, margin within 0.01%), there may be no clear winner.

In that case, form the superset P*, the union of all sets P that result from all possible combinations of reversed ties or near-ties. Then choose the winner using Random Ballot Order.