[EM] VoteFair representation ranking recommended for Czech Green Party

[VoteFair at SolutionsCreative.com]

From: Peter Zbornik:
>>> I would appreciate if Votefair ranking would have some mathematical
>>> description and at least well described and discussed in some
>>> peer-reviewed paper.
...

From: Raph Frank [mailto:raphfrk at gmail.com] 
> Can you put on a clear description of the method (single seat and PR
> version) on your website and ideally link it from the front page.

On the front page of VoteFair.org is a tab named "Government elections", and
when that is clicked there is a second row of tabs that includes "Board
members".  Here is the URL for that page:

http://www.votefair.org/board.html

On that page is a description of VoteFair ranking that best matches what I
recommend for the Czech Green party council elections.  For convenience,
below is the content of that page.  I have not yet edited it for this
specific situation.  The paragraph titled "Second-most representative
candidate" is the one that describes the basis of VoteFair representation
ranking.

--------------- beginning of extracted content -----------------

    Introduction: Members of the City Council [or Board of Directors] shall
be elected as described herein.  Candidates for non-equivalent city-council
[or board-member] seats must compete in separate races.  Candidates for
equivalent city-council [or board-member] seats must compete together in the
same race.

    Order-of-preference ballots: Each registered [or authorized] voter shall
be allowed to indicate his or her first preference, second preference, third
preference, and so on, for all the candidates competing in the same race.  A
voter shall be allowed to indicate a different preference level for each
candidate in the race.  A voter shall be allowed to indicate ties among any
candidates.  In each race the name of a candidate can appear only once in
the list of candidates.

    Write-in candidates: Write-in candidates are allowed in elections for
city-council [or board] members.  If a voter writes in the name of a
candidate then the voter shall be allowed to indicate the preference level
for that write-in candidate.  If a voter writes in the name of a write-in
candidate, all the other ballots on which that candidate's name is not
written shall be interpreted as if the write-in candidate is at the
preference level below all the candidate names that do appear on the ballot,
and tied with any other write-in candidate names that do not appear.

    Interpretation of preference marks If a voter assigns the same candidate
to more than one preference level, the highest indicated preference level
for that candidate shall be used.  If a voter does not assign a candidate to
any preference level, the lowest preference level, below the preference
levels of all the assigned candidates, shall be used.  On any ballot or any
combination of ballots the skipping of preference levels and the shifting of
candidates to higher or lower preference levels without changing the
relative preferences shall have no affect on the outcome of the election.
Valid preference information shall not be ignored because of incorrect
markings elsewhere on the ballot.

    VoteFair tally table: As needed for VoteFair popularity and
representation ranking, specified preference information obtained from the
order-of-preference ballots shall be combined into a VoteFair tally table as
follows.  The VoteFair tally table shall list every possible combination of
two candidates.  For each combination of two candidates, the VoteFair tally
table shall indicate the number of specified voters who prefer the first of
the two candidates over the second candidate, the number of specified voters
who indicate no preference between the two candidates, and the number of
specified voters who prefer the second of the two candidates over the first
candidate.  The sum of the three numbers that apply to each pair of
candidates shall equal the equivalent sum of numbers for each other
combination of two candidates.

    VoteFair popularity ranking: The overall order of preference for each
specified group of candidates shall be calculated using VoteFair popularity
ranking, which is described as follows.  Based on the numbers in the
specified VoteFair tally table, every possible sequence of candidates shall
be considered and a score shall be calculated for each such sequence.  The
score for a sequence shall equal the sum of the applicable tally numbers for
each pair combination, which means that if there are three choices labeled
A, B, and C, the score for the sequence of B being the first overall
preference, C being the second overall preference, and A being the third
overall preference equals the number of voters who prefer B over C, plus the
number of voters who prefer B over A, plus the number of voters who prefer C
over A.  The sequence that has the highest score shall indicate the overall
order of preference expressed by the voters.  If more than one sequence has
the same highest score, the overall order of preference contains at least
one tie and the tied choices and their preference levels shall be
identified.  The overall order of preference for each race shall be made
available to the public [or voters].

    First-most representative candidate: Within each race the first-most
representative candidate shall be the candidate who is most preferred
according to VoteFair popularity ranking.

    Second-most representative candidate: Within each race the second-most
representative candidate shall be identified using the following steps.
First, identify the ballots on which the first-most representative candidate
is ranked as the voter's first choice.  Second, using only the ballots that
are not identified in the first step, and excluding preference information
about the candidate identified as the first-most representative candidate,
use VoteFair popularity ranking to identify a new most-preferred candidate.
Third, again consider all the ballots.  Fourth, identify the ballots on
which the first-most representative candidate is preferred over the
candidate identified in the second step.  (This step identifies the ballots
of voters who are already well-represented by the first-most representative
candidate.) Fifth, calculate a number equal to the number of ballots
identified in the fourth step minus half the total number of ballots.
Sixth, calculate a reduced-influence scale number that is equal to the
number calculated in the fifth step divided by the number of ballots
identified in the fourth step, and retain all significant digits.  Seventh,
again consider all the ballots.  Eighth, for each ballot identified in the
fourth step use a partial vote equal to the reduced-influence scale number,
and for each ballot not identified in the fourth step use one full vote.
Ninth, based on the reduction of influence of some ballots as described in
the eighth step, and using a corresponding adjustment in the total number of
ballots, and excluding the first-most representative candidate from
consideration, use VoteFair popularity ranking to identify a new
most-preferred candidate.  Finally, regard this new most-preferred candidate
as the second-most representative candidate.

    Successively representative candidates: The third-most, fifth-most, and
seventh-most representative candidates shall be identified using VoteFair
popularity ranking except that the candidates already identified as more
representative shall be removed from consideration and only the remaining
voter preferences shall be considered.  The fourth-most, sixth-most, and
eighth-most representative candidates shall be identified using the same
method used to identify the second-most representative candidate except that
the candidates already identified as more representative shall be removed
from consideration and the next-most representative candidate shall take the
place of the first-most representative candidate when identifying which
ballots shall have reduced influence.

    Within each race the candidate who is first-most representative
according to VoteFair representation ranking shall be elected to the first
seat among the equivalent seats, the candidate who is second-most
representative according to VoteFair representation ranking shall be elected
to the second seat among the equivalent seats, and each available successive
most-representative candidate according to VoteFair representation ranking
shall be elected to each successive seat.

    Ties: If any ranking calculation involves a tie that affects the
results, the court that has jurisdiction over the election shall have
jurisdiction over the recounting and checking of the votes.  If a tie
persists, the same court shall resolve the tie by randomly generating and
introducing into the appropriate VoteFair tally table a single
order-of-preference vote that contains no ties and does not alter the
overall order of preference except to eliminate all ties at that stage in
the calculations.


--------------- end of extracted content -----------------


> For example:

> "Q:  In VoteFair ranking, how are all the votes combined into one
> overall sequence?

> A:  The best way to see how the calculations are done is to try it! "

> This is totally not true (at least for me).  You are asking someone to
> reverse engineer your method.  Just explain how it works (it could
> just be a link).

> It is hard for us to comment if you don't describe the method completely.

See above.  Also, based on this comment I've added three links to this
answer in the FAQ.

Previously I had presumed that election-method experts would go to the pages
that contain the rigorous descriptions (as above).  I had intended the FAQ
for average folks (who run away from mathematics and even too many numbers).

> Anyway, based on what I can determine by searching for info about the
> method, is this an accurate description?

> Single seat Votefair is equivalent to the Condorcet-Kemeny system.

Yes.  I call this VoteFair popularity ranking.  (Only after giving it this
name did I learn about its academic name.)

> VoteFair representation ranking works like reweighted range voting.

I looked up reweighted range voting and there is a similarity, but only for
filling the second seat.

> You use a single seat method and then elect candidates in rounds and
> deweight ballots after each step.

There is one election step where the ballot weighting changes, but then the
weighting is returned to 1 for filling the third (and other odd-numbered)
seat(s).  (See below.)

> The process is:

> 1) Voters cast a ranked ballot

> 2) All ballots start with a weighting of 1

> 3) Determine the Vote Fair winner (W).  This candidate is considered
elected.

> 4) For next step, ignore all ballots which rank W first choice

> 5) Work out the new Vote Fair winner (S).  This candidate is the 2nd
> place for this round.

> 6) All ballots that rank W over S are considered to support W.

> 7) The weight for every ballot which supports W is multiplied by a
> value (k).  k is selected so that the total weight drops by half.

> 8) If there are more seats to fill goto 3)

A good start, but step 8 needs to jump back to step 2, not step 3.

Also, there should be a step 7.5 that uses Condorcet-Kemeny (VoteFair
popularity ranking) to fill each even-numbered seat.

In terms of wording refinements, in step 3, "VoteFair winner" should be
changed to "most popular choice using VoteFair popularity ranking" (or "the
Condorcet-Kemeny winner").  This is because the name "VoteFair ranking" (in
this context) refers to the entire set of methods described in my book (only
some of which we are discussing here).

> ...

> It seems like a faction with >1/3 of the voters could guarantee to get
> a seat in a 2 seat election.  They would just need to place their
> candidate first choice.  If the lose the first round, their ballots
> won't be deweighted (as their candidate is ranked first), so they will
> take the 2nd seat.  ...

Yes.

> I think this method might be proportional even when electing more than
> 2 candidates.  Does it meet Droop proportionality?

The method does not get repeatedly used the way other methods keep reducing
the weight of each voter's ballot.  In what I recommend, all ballots return
to full weight after each two successive candidates are chosen.

For choosing more than two choices in the manner you imply, I've created an
algorithm that is used at NegotiationTool.com, but that algorithm is not
relevant here.

> Also, is it guaranteed that the number from 6) is always more than 50%
> of the remaining ballot weight?  If not, then k could be negative :).
> In most cases, it would be OK, since W must be a condorcet winner.

You have the general idea, but I'd have to look at the code to remind myself
about all possible edge cases.

> However, if there is a condorcet tie, then S might be one of the
> candidates which defeats W pairwise.

I'm not sure what you are saying here.

As with any method, there has to be some tie-breaking technique to handle
ties.

Thank you for taking the time to help me clarify VoteFair ranking!

(I apologize for the delay in replying; my life is currently quite busy.)

Richard Fobes