Practical Condorcet Method

3 related posts:

A basic outline of this election method. https://americarepair.home.blog/2020/12/13/brief-summary-of-practical-condorcet-election/

Discussion of this method vs IRV. https://americarepair.home.blog/2020/09/02/condorcet-is-a-better-ranked-choice/

Charts to aid in evaluation, and sample elections: https://americarepair.home.blog/condorcet-method-tips-for-evaluating-the-election/

Primary procedure first, Secondary procedure below.

(Many don’t want a primary, but many others don’t want a ballot with 20 candidates in one field. A primary, only when necessary, will be more fair to the candidates, and will improve accuracy.)

PRIMARY

A primary will only be used when there are more than 16 candidates.

The official candidates of the two largest parties will be placed in separate fields if possible. For example, Democrats in one field, and Republicans in the other. But all voters will vote on all fields.

The remaining candidates will be randomly divided (with group disparity of 1 candidate at most), and assigned to the minimum number of fields possible, each field having 7 to 11 candidates.

Primary Voting

Voters are instructed, for each field: “Rank up to 3 candidates that you would want to win.”

Votes are cast, and ballots collected.

Primary Evaluation Step 1

Each field of 7 to 11 will be reduced to the 5 candidates who have the most first-choice votes.

Primary Evaluation Step 2

The qualifying candidates will be compared in 2-candidate, head-to-head matches. The candidate ranked higher on a ballot receives that ballot’s vote, for being preferred by that voter. A candidate scores a match win by having more votes, head-to-head against one other candidate. (Match ties and losses need not be counted, only wins.)

Each candidate’s match wins are tallied.

If there are more than 5 fields (over 55 candidates): Normally, ONE candidate having the most head-to-head wins in their field will be declared the field winner, and will proceed to the secondary. If two tie for first in their field, BOTH will be declared winners. A tiebreaker will be used if more than two are tied for first in their field.

If there are 2 to 5 fields: TWO candidates having the most wins in their field will be the winners, (4 to 10 primary winners), and will proceed to the secondary. Two tied for first in their field will both be winners, but a number more than two will require a tiebreaker.

Primary Evaluation Step 3

Apply tiebreakers as needed.
(Tiebreakers are listed in step 4 of the Secondary procedure.)

SECONDARY
(Or One-Ballot, with no primary)

One field of 16 or fewer candidates.
(More than 16 possible only if there are over 176 candidates in the primary, or 166 with one tie, 155 with 2 ties, etc.)

Voting

Voters may rank 4 candidates if there are 10 or more candidates, or rank 3 candidates if there are 9 or fewer.

Voters are instructed: “Rank only the candidates that you would want to win.”

Votes are cast, and ballots collected.

Evaluation Step 1

Determine if there is a Condorcet winner: Winning head-to-head against all other candidates wins the election. (First-choice majority winners are also Condorcet winners.)

If there is no such winner, proceed to the next step.

Evaluation Step 2

Narrow the field to no fewer than five, and a maximum of eight, by eliminating candidates who have the fewest first-choice votes.

If there are six to nine candidates, reduce the field to five.
OR
If there are 10 or 11 candidates, keep six.
OR
If 12 or 13, candidates, keep seven.
OR
If there are 14 candidates or more, reduce the field to eight.

This elimination requires the winner to have a significant number of first-choice votes, and makes a hand recount less difficult. There isn’t much chance of someone in the lower half in first-choice votes winning a ranking election, so this shortcut will only very rarely burn a potential winner.

Evaluation Step 3

The candidates will be compared in 2-candidate, head-to-head matches. The candidate ranked higher on a ballot receives that ballot’s vote, for being preferred by that voter. A candidate scores a match win by having more votes, head-to-head against one other candidate. (Match ties and losses need not be counted, only wins.)

Eight candidates would make 28 matches, seven 21, six 15, five 10, four candidates would make 6 matches, three 3, and two make 1 match.

All candidates will be evaluated, and any candidate not tied for most wins will be eliminated.

Any one candidate that has the most head-to-head wins over the other remaining candidates will be declared the election winner.

Evaluation Step 4

Tiebreakers to eliminate a candidate will be performed in this order:

4A. Ties may be decided by the matches of the tied candidates, head-to-head with one another.
(If two are tied with most wins, the winner of their match prevails.)
If at least one is eliminated, go back to step 3. If not, proceed to 4B.

4B. If there is still a tie, or a multiple-way “paradox” cycle, use a round of IRV to eliminate one tied candidate (or eliminate more than one if they tied, and have fewer votes than the frontrunner).
If at least one is eliminated, go back to step 3. If not, proceed to 4C.

(IRV: “Instant Runoff Voting” method, in which more than two candidates are compared at a time, and the one having the high rank on the fewest ballots is eliminated.
Less accurate than a Condorcet method, but will do for a tiebreaker.)

4C. The candidate(s) with the fewest first-choice votes is eliminated.
If at least one is eliminated, go back to step 3. If not, proceed to 4D.

4D. Random chance.
Every remaining candidate has even odds of elimination.
Flip the same coin for every candidate. Each candidate that lands tails is eliminated, if another candidate lands heads in the same round.
Flip until at least one is eliminated, then go back to step 3.
When only one remains, that’s the winner.