[EM] Definite Majority Choice, first round public proposal (draft)

[Araucaria Araucana]

Below is a draft of a first round proposal for a single
general-election voting method replacement.  Comments humbly
requested.  Could the explanation be made any clearer?

As discussed previously, Definite Majority Choice (hat-tip to Forest
for the name) is just another name for Ranked Approval Voting (RAV),
Approval Runoff Condorcet (ARC), and finds the same winner as Pairwise
Sorted Approval.  I believe that it finds the same winner as both
Ranked Pairs and Beatpath when defeat strength is measured by the
Approval of the pairwise winner.  Among non-eliminated candidates,
there are no pairwise cycles, thus removing the biggest objection of
IRV advocates to Condorcet methods.

Note that Pairwise Sorting on a previously seeded ordering is also
known as Local Kemenization and is used in Rank Aggregation methods --
see, e.g., http://www10.org/cdrom/papers/577/.  So if all else fails,
you could say that DMC finds the Google winner!

Credits: Forest Simmons, Jobst Heitzig, Russ Paielli, Chris Benham,
         Kevin Venzke, and of course Steve Eppley, Markus Schulze and
         Mike Ossipoff.  Anybody else I should cite?  Who first
         proposed Graded Ballots?  Adam Tarr?

-- Ted

,----[ definite-majority-choice-graded-ballot ]
| Definite Majority Choice:
| 
| Voters can grade their choices from favorite (A) to least preferred
| (ungraded), and give some or all of their graded choices a "passing
| grade", signifying approval.
| 
| Ranked ballots are added into a Round-Robin array, and the approval
| scores of each candidate are also tabulated.
| 
| 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.
| 
| How to vote:
| 
| Graded ballot:
| 
|             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 candidates get 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."  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.
`----

-- 
araucaria dot araucana at gmail dot com