Thank you, Daniel.  Both suggested changes look pretty good.Geez, i love this group.  Much better tha the Reddit thing.Powered by Cricket Wireless------ Original message------From: Daniel CarreraDate: Tue, Sep 21, 2021 1:03 PMTo: robert bristow-johnson;Cc: EM;Subject:Re: [EM] Can anyone help with straight-ahead Condorcet language?On Tue, Sep 21, 2021 at 10:38 AM robert bristow-johnson rbj@audioimagination.com wrote: Here is Bottom-Two Runoff:

All elections of [office] shall be by ballot, using a system of ranked-choice voting without a separate runoff election. The presiding election officer shall implement a ranked-choice voting protocol according to these guidelines:
  (1) The ballot shall give voters the option of ranking candidates in order of preference. Lower ordinal preference shall be considered higher rank and the candidate marked as first preference is considered ranked highest. Equal ranking of candidates shall not be allowed. Any candidate not marked with a preference shall be considered as ranked lower than every candidate marked with a preference.
  (2) If a candidate receives a majority (over 50 percent) of first preferences, that candidate is elected.
  (3) If no candidate receives a majority of first preferences, an instant runoff retabulation shall be performed by the presiding election officer. The instant runoff retabulation shall be conducted in sequential rounds. A "continuing candidate" is defined as a candidate that has not been defeated in any previous round. Initially, no candidate is defeated and all candidates begin as continuing candidates.
  (4) In each round, every ballot shall count as a single vote for whichever continuing candidate the voter has ranked highest. The two candidates with the fewest votes in a round, herein denoted as "A" and "B", shall contend in a runoff in which the candidate, A or B, with lesser voter support shall be defeated in the current round. If the number of ballots ranking A higher than B exceeds the number of ballots ranking B higher than A, then B has lesser voter support, B is defeated, and A continues to the following round. Likewise, if the number of ballots ranking B higher than A exceeds the number of ballots ranking A higher than B, then A has lesser voter support, A is defeated, and B continues to the following round. In the case that the aforementioned measures of voter support of A and B are tied, then the candidate with fewest votes is defeated in the current round.
  (5) The aforementioned instant runoff retabulation, eliminating one candidate each round, shall be repeated until only two candidates remain. The remaining candidate then receiving the greatest number of votes is elected.
  (6) The [governing jurisdiction] may adopt additional regulations consistent with this subsection to implement these standards.

If step (4) above can be made better, I would be interested in seeing it.You can reuse the ordinal system to simplify (4):(4) In each round, every ballot shall count as a single vote for whichever continuing candidate the voter has ranked highest. The two candidates with the fewest votes in a round, herein denoted as "runoff candidates", shall contend in a runoff. In each runoff, every ballot shall count as a single vote for whichever runoff candidate the voter has ranked highest. The candidate with the fewest votes is defeated in the current round. 
Here is straight-ahead Condorcet (version 1, most like Daniel's):

All elections of [office] shall be by ballot, using a system of ranked-choice voting without a separate runoff election. The presiding election officer shall implement a ranked-choice voting protocol according to these guidelines:
  (1) The ballot shall give voters the option of ranking candidates in order of preference. Lower ordinal preference shall be considered higher rank and the candidate marked as first preference is considered ranked highest. Equal ranking of candidates shall be allowed. Any candidate not marked with a preference shall be considered as ranked lower than every candidate marked with a preference.
  (2) If a candidate receives a majority (over 50 percent) of first preferences, that candidate is elected.
  (3) If no candidate receives a majority of first preferences, a Condorcet-consistent retabulation shall be performed by the presiding election officer. The candidate, who is the Condorcet winner, is elected if the rankings on all of the ballots indicate that this one candidate defeats, with a simple majority of voter preferences, every other candidate when compared in turn with each other individual candidate. A selected candidate defeats another candidate by a simple majority when the number of ballots marked ranking the selected candidate higher than the other candidate exceeds the number of ballots marked to the contrary.
  (4) If no Condorcet winner exists in step (3), then the candidate with the plurality of first preferences is elected.
  (5) The [governing jurisdiction] may adopt additional regulations consistent with this subsection to implement these standards.

Here is another straight-ahead Condorcet (version 2):

All elections of [office] shall be by ballot, using a system of ranked-choice voting without a separate runoff election. The presiding election officer shall implement a ranked-choice voting protocol according to these guidelines:
  (1) The ballot shall give voters the option of ranking candidates in order of preference. Lower ordinal preference shall be considered higher rank and the candidate marked as first preference is considered ranked highest. Equal ranking of candidates shall be allowed. Any candidate not marked with a preference shall be considered as ranked lower than every candidate marked with a preference.
  (2) If a candidate receives a majority (over 50 percent) of first preferences, that candidate is elected.
  (3) If no candidate receives a majority of first preferences, a Condorcet-consistent retabulation shall be performed by the presiding election officer. The retabulation shall examine each possible pairing of candidates. If N is the number of candidates, including combined Write-In, then the number of possible pairings of candidates is N(N-1)/2. For each possible pairing of candidates, if fewer ballots are marked preferring a selected candidate over the other candidate than the number of ballots marked to the contrary, then the selected candidate is marked as defeated. After all candidate pairs are examined, the candidate who remains unmarked as defeated is the Condorcet winner and is elected.
  (4) If no Condorcet winner exists in step (3), then the candidate with the plurality of first preferences is elected.
  (5) The [governing jurisdiction] may adopt additional regulations consistent with this subsection to implement these standards.

In the last two, I want to keep all of the steps the way they are, but if step (3) can be made better, that is what I am groping for.

Concise is good, but it must be complete and clear in normal usage of the American English language.Here is a more concise rewrite of your first version:(3) If no candidate receives a majority of first preferences, the presiding officer shall perform a series of two-candidate runoffs where every candidate has a runoff with every other candidate. Each runoff between two candidates is won by the candidate that is ranked higher by a majority of ballots. A candidate that wins all of their runoffs is the Condorcet winner and is elected.Cheers,-- Dr. Daniel CarreraPostdoctoral Research AssociateIowa State University

I have doubts about this line: “Each runoff between two candidates is won by the candidate that is ranked higher by a majority of ballots.”  A candidate can win a majority of the ballots that express a preference in that pairing without winning a majority of the overall ballots cast.  Here I think Robert’s “more than marked otherwise” phrasing is more verbose, but less ambiguous.

--pH

From: Election-Methods election-methods-bounces@lists.electorama.com On Behalf Of robert bristow-johnson
Sent: Tuesday, September 21, 2021 12:31 PM
To: Daniel Carrera dcarrera@gmail.com
Cc: EM Election-methods@lists.electorama.com
Subject: Re: [EM] Can anyone help with straight-ahead Condorcet language?

Thank you, Daniel.  Both suggested changes look pretty good.

Geez, i love this group.  Much better tha the Reddit thing.

Powered by Cricket Wireless

------ Original message------
From: Daniel Carrera
Date: Tue, Sep 21, 2021 1:03 PM
To: robert bristow-johnson;
Cc: EM;
Subject:Re: [EM] Can anyone help with straight-ahead Condorcet language?

On Tue, Sep 21, 2021 at 10:38 AM robert bristow-johnson <rbj@audioimagination.commailto:rbj@audioimagination.com> wrote:

Here is Bottom-Two Runoff:

All elections of [office] shall be by ballot, using a system of ranked-choice voting without a separate runoff election. The presiding election officer shall implement a ranked-choice voting protocol according to these guidelines:
(1) The ballot shall give voters the option of ranking candidates in order of preference. Lower ordinal preference shall be considered higher rank and the candidate marked as first preference is considered ranked highest. Equal ranking of candidates shall not be allowed. Any candidate not marked with a preference shall be considered as ranked lower than every candidate marked with a preference.
(2) If a candidate receives a majority (over 50 percent) of first preferences, that candidate is elected.
(3) If no candidate receives a majority of first preferences, an instant runoff retabulation shall be performed by the presiding election officer. The instant runoff retabulation shall be conducted in sequential rounds. A "continuing candidate" is defined as a candidate that has not been defeated in any previous round. Initially, no candidate is defeated and all candidates begin as continuing candidates.
(4) In each round, every ballot shall count as a single vote for whichever continuing candidate the voter has ranked highest. The two candidates with the fewest votes in a round, herein denoted as "A" and "B", shall contend in a runoff in which the candidate, A or B, with lesser voter support shall be defeated in the current round. If the number of ballots ranking A higher than B exceeds the number of ballots ranking B higher than A, then B has lesser voter support, B is defeated, and A continues to the following round. Likewise, if the number of ballots ranking B higher than A exceeds the number of ballots ranking A higher than B, then A has lesser voter support, A is defeated, and B continues to the following round. In the case that the aforementioned measures of voter support of A and B are tied, then the candidate with fewest votes is defeated in the current round.
(5) The aforementioned instant runoff retabulation, eliminating one candidate each round, shall be repeated until only two candidates remain. The remaining candidate then receiving the greatest number of votes is elected.
(6) The [governing jurisdiction] may adopt additional regulations consistent with this subsection to implement these standards.

If step (4) above can be made better, I would be interested in seeing it.

You can reuse the ordinal system to simplify (4):

(4) In each round, every ballot shall count as a single vote for whichever continuing candidate the voter has ranked highest. The two candidates with the fewest votes in a round, herein denoted as "runoff candidates", shall contend in a runoff. In each runoff, every ballot shall count as a single vote for whichever runoff candidate the voter has ranked highest. The candidate with the fewest votes is defeated in the current round.

Here is straight-ahead Condorcet (version 1, most like Daniel's):

All elections of [office] shall be by ballot, using a system of ranked-choice voting without a separate runoff election. The presiding election officer shall implement a ranked-choice voting protocol according to these guidelines:
(1) The ballot shall give voters the option of ranking candidates in order of preference. Lower ordinal preference shall be considered higher rank and the candidate marked as first preference is considered ranked highest. Equal ranking of candidates shall be allowed. Any candidate not marked with a preference shall be considered as ranked lower than every candidate marked with a preference.
(2) If a candidate receives a majority (over 50 percent) of first preferences, that candidate is elected.
(3) If no candidate receives a majority of first preferences, a Condorcet-consistent retabulation shall be performed by the presiding election officer. The candidate, who is the Condorcet winner, is elected if the rankings on all of the ballots indicate that this one candidate defeats, with a simple majority of voter preferences, every other candidate when compared in turn with each other individual candidate. A selected candidate defeats another candidate by a simple majority when the number of ballots marked ranking the selected candidate higher than the other candidate exceeds the number of ballots marked to the contrary.
(4) If no Condorcet winner exists in step (3), then the candidate with the plurality of first preferences is elected.
(5) The [governing jurisdiction] may adopt additional regulations consistent with this subsection to implement these standards.

Here is another straight-ahead Condorcet (version 2):

All elections of [office] shall be by ballot, using a system of ranked-choice voting without a separate runoff election. The presiding election officer shall implement a ranked-choice voting protocol according to these guidelines:
(1) The ballot shall give voters the option of ranking candidates in order of preference. Lower ordinal preference shall be considered higher rank and the candidate marked as first preference is considered ranked highest. Equal ranking of candidates shall be allowed. Any candidate not marked with a preference shall be considered as ranked lower than every candidate marked with a preference.
(2) If a candidate receives a majority (over 50 percent) of first preferences, that candidate is elected.
(3) If no candidate receives a majority of first preferences, a Condorcet-consistent retabulation shall be performed by the presiding election officer. The retabulation shall examine each possible pairing of candidates. If N is the number of candidates, including combined Write-In, then the number of possible pairings of candidates is N(N-1)/2. For each possible pairing of candidates, if fewer ballots are marked preferring a selected candidate over the other candidate than the number of ballots marked to the contrary, then the selected candidate is marked as defeated. After all candidate pairs are examined, the candidate who remains unmarked as defeated is the Condorcet winner and is elected.
(4) If no Condorcet winner exists in step (3), then the candidate with the plurality of first preferences is elected.
(5) The [governing jurisdiction] may adopt additional regulations consistent with this subsection to implement these standards.

In the last two, I want to keep all of the steps the way they are, but if step (3) can be made better, that is what I am groping for.

Concise is good, but it must be complete and clear in normal usage of the American English language.

Here is a more concise rewrite of your first version:

(3) If no candidate receives a majority of first preferences, the presiding officer shall perform a series of two-candidate runoffs where every candidate has a runoff with every other candidate. Each runoff between two candidates is won by the candidate that is ranked higher by a majority of ballots. A candidate that wins all of their runoffs is the Condorcet winner and is elected.

Cheers,

Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University