C.Benham

2014-04-25 18:40:53 UTC

This is my new idea for a Condorcet method that meets Mono-raise and

Chicken Dilemma and is relatively resistant

to Burial strategy.

*Voters rank from the top however many candidates they wish Truncation

and equal-ranking is allowed.

A pairwise matrix is created, giving normal gross scores except that

ballots that explicitly equal rank (not truncate) any two

candidates X and Y give a whole vote to each in that pairwise contest.

Using this information, give each alternative a score that equals the

smallest number of votes it received in a pairwise loss.

Henceforth we are only concerned with the direction of the pairwise

defeats and these individual candidate scores.

Use the Schulze algorithm, weighing each pairwise "defeat" by the

absolute margin of difference between the two candidates'

scores. (Or use Ranked Pairs or River in the same way if you prefer).

Or use the candidate scores for the Margins Sort algorithm.*

This method uses the same type of pairwise matrix as a Schulze (Losing

Votes) variant I suggested earlier. I think this is much

better.

46 A

44 B>C (sincere is B or B>A)

05 C>A

05 C>B

A>B 51-49, B>C 44-10, C>A 54-46. MinMax (Losing Votes) scores:

B49, A46, C10.

The method I suggested earlier elects the buriers' candidate B, but my

new method elects A (the "sincere CW").

The Margins Sort version begins with the MM(LV) order B>A>C, then

notices that the two adjacent candidates with the two most

similar scores are B and A and that A pairwise beats B, so flips that

order and then considers A>B>C and then sees that there for each

pair of adjacent candidates, the one higher in the order pairwise beats

the one lower in the order and so is content and elects the now

highest-ordered candidate.

The other versions look at the pairwise results weighted thus: A > B

(46-49 = -3) B>C (49-10 = 39) C>A (10-46 = -36).

A's pairwise defeat score (negative 36) is by far the lowest so A wins.

Chris Benham

----

Election-Methods mailing list - see http://electorama.com/em for list info

Chicken Dilemma and is relatively resistant

to Burial strategy.

*Voters rank from the top however many candidates they wish Truncation

and equal-ranking is allowed.

A pairwise matrix is created, giving normal gross scores except that

ballots that explicitly equal rank (not truncate) any two

candidates X and Y give a whole vote to each in that pairwise contest.

Using this information, give each alternative a score that equals the

smallest number of votes it received in a pairwise loss.

Henceforth we are only concerned with the direction of the pairwise

defeats and these individual candidate scores.

Use the Schulze algorithm, weighing each pairwise "defeat" by the

absolute margin of difference between the two candidates'

scores. (Or use Ranked Pairs or River in the same way if you prefer).

Or use the candidate scores for the Margins Sort algorithm.*

This method uses the same type of pairwise matrix as a Schulze (Losing

Votes) variant I suggested earlier. I think this is much

better.

46 A

44 B>C (sincere is B or B>A)

05 C>A

05 C>B

A>B 51-49, B>C 44-10, C>A 54-46. MinMax (Losing Votes) scores:

B49, A46, C10.

The method I suggested earlier elects the buriers' candidate B, but my

new method elects A (the "sincere CW").

The Margins Sort version begins with the MM(LV) order B>A>C, then

notices that the two adjacent candidates with the two most

similar scores are B and A and that A pairwise beats B, so flips that

order and then considers A>B>C and then sees that there for each

pair of adjacent candidates, the one higher in the order pairwise beats

the one lower in the order and so is content and elects the now

highest-ordered candidate.

The other versions look at the pairwise results weighted thus: A > B

(46-49 = -3) B>C (49-10 = 39) C>A (10-46 = -36).

A's pairwise defeat score (negative 36) is by far the lowest so A wins.

Chris Benham

----

Election-Methods mailing list - see http://electorama.com/em for list info