[EM] VoteFair representation ranking

Richard Fobes ElectionMethods at VoteFair.org
Fri Mar 1 00:08:58 PST 2013

Peter Zbornik ~

Here are answers to your questions (which are copied below).

In VoteFair representation ranking, the winner of position # 1 is 
identified using VoteFair _popularity_ ranking, which is equivalent to 
the Condorcet-Kemeny method.  That single-seat algorithm is explained in 

Chapter 15 of "Ending the Hidden Unfairness in U.S. Elections" explains 
(step-by-step) how VoteFair _representation_ ranking identifies the 
winner of the seat in position # 2.  The explanation includes a specific 
example.  Here is a link to a PDF file that contains just that chapter:


The example in that chapter is presented graphically.  Below are the 
same ballot preferences expressed using a more familiar syntax (for this 
forum).  There are 100 ballots, and each group of 10 ballots have the 
same ranking.

A=Aletha, E=Elliot, M=Meridith, R=Roland, S=Seldon, W=Walter

S, E, M, W, R, A x10
S, E, M, W, A, R x10
S, E, W, M, A, R x10
S, M, W, E, R, A x10
S, M, E, A, W, R x10
S, M, E, W, R, A x10
S, M, E, W, A, R x10
A, W, R, S, M, E x10
R, A, W, M, S, E x10
R, W, A, M, E, S x10

In this example S (Seldon) wins position # 1, and W (Walter) wins 
position # 2.

Notice that W would not win the second position if overall popularity 
were being calculated.  (That would be M or E, depending on the method 

Also note that -- unlike STV (and IRV) -- the calculations do not look 
at just the currently-considered top-ranked candidate.  Instead, the 
calculations look "deep" into the ballot ("looking" all the way to the 
bottom of each ballot if necessary).

In conventional terms, S is the most popular "majority" candidate, and W 
is the most popular "opposition" candidate.

Expressed another way, W is not the second-most "popular" among all the 
voters.  Instead, W is the most popular among the voters who are not 
well-represented by the first-position winner (S).

Additional consideration is given to the "majority" voters if they 
amount to more than just 51% (or so).  For example, if a majority of 70% 
of the voters have the same preferences, their secondary preferences are 
"squeezed" into 20% (the amount beyond 50%) when they are combined with 
the remaining not-yet-represented 30% of the voters.

The supplied chapter explains yet another consideration that ensures 
that the majority cannot rank a variety of minor (unpopular) candidates 
at the top of their ballot to make it look like they are unrepresented 
by the first-position winner.

The details are explained, step by step, in the supplied PDF-format chapter.

One organization that uses VoteFair ranking to elect its officials has 
two locations for its members.  VoteFair representation nicely ensures 
that neither location outvotes the other location.  So far the results 
I've seen give the same results for both VoteFair popularity ranking and 
VoteFair representation ranking, so their membership is not as divided 
as it might otherwise seem.  The organization has been very happy with 
the results.  There is a testimonial on the VoteFair site.

More broadly, in the many cases where VoteFair ranking is used, the 
winner of position #2 is often the same as the second-most popular 
according to VoteFair popularity ranking (equivalent to Condorcet-Kemeny).

Yet I have also seen numerous cases where VoteFair representation 
ranking does produce a result that is different (in the second position) 
from VoteFair popularity ranking.  Such results reveal a significant 
"split" in the voter preferences.  Specifically the method has been 
successful in identifying who deserves to win the second-most 
representative position when the second-most popular (according to 
VoteFair popularity ranking) is not the right choice (because that would 
allow the same majority to fill both positions).

Regarding positions # 3 and # 4 and beyond, VoteFair representation 
continues the ranking process by repeating the 
"majority-versus-opposition" algorithm for each pair of next-most 
representative positions.

When I designed it I assumed that in many cases only the top two most 
representative candidates would need to be identified.  That's because 
other methods can be used to fill other seats.  For example, different 
districts can be used to fill other seats in a legislature, and VoteFair 
party ranking can fill seats on a PR or PR-like basis (which requires 
that party preferences be marked on the ballot).

In your situation the winners are filling an (open) party list, and you 
do not know how many party-list seats will be won.  You have said that 
you expect that the number might be 1, 2, 3, 4, or 5 seats.  For this 
purpose VoteFair representation ranking would fill position # 1 with the 
overall most popular "majority" candidate, and would fill position # 2 
with the overall most popular "opposition" candidate, and would fill 
position # 3 with the next-most popular "majority" candidate, and would 
fill position # 4 with the next-most popular "opposition" candidate.

The code that implements VoteFair representation ranking is open source 
code, so "a complete and exhaustive description of the algorithm" is the 
code itself, which is well-commented:


(The code also handles "ties," which is necessary for an "exhaustive 
description of the algorithm."  The explanation in the supplied chapter 
is also quite complete, although it does not deal with how to handle 

Although the code is written in Perl, it uses a subset of Perl that 
makes it straightforward to port the code to the "C" language.

(The code just handles numbers because the Vote-Info-Split-Join (VISJ) 
software is available to handle text, such as the names of the candidates.)

Getting back to the VoteFair ranking algorithm, if you would like to see 
details about the calculations without downloading and running the 
software, please supply me with a specific example (in the above format 
if there are more than just a few ballots), and I can run the VoteFair 
ranking software and have it produce a "log" that I can post here.

In your party-list situation, when you reach the point where 
gender-based quotas are no longer likely to displace any of the 
candidates who -- without the quota adjustments -- would win positions # 
1, # 2, # 3, and # 4, then I can add code (for "VoteFair party-list 
ranking") that better calculates the winner of position # 5 and beyond. 
  In that case you can think of position # 5 as being filled by a 
candidate who represents 20 percent of the voters who are not 
well-represented by the winners of the first 4 positions.  That 
enhancement would amount to moving a portion of the VoteFair 
_negotiation_ ranking code into the VoteFair ranking code that is on 
GitHub.  For that purpose it would be necessary to specify a threshold 
to determine at what seat/position a minority is large enough to win a 

In summary, the result of using VoteFair representation ranking, 
combined with shifting the most-popular women into positions # 2 and/or 
# 5 if necessary (to meet that quota), would meet your desire for a 
method "which allows quoted seats to be proportionally distributed, in 
order to avoid that the same voters get all quoted seats."

If the algorithm for VoteFair representation ranking still isn't clear 
after reading the supplied chapter (in PDF format), please ask questions.

Thank you for your interest.

Richard Fobes

On 2/28/2013 11:37 AM, Peter Zbornik wrote:
> Dear Richard,
> sorry for not getting to your reply earlier than now.
> Comments to your email in the text below.
> 2013/2/17 Richard Fobes<ElectionMethods at votefair.org>:
>> On 2/17/2013 12:17 AM, Peter Zbornik wrote:
>>> 2013/2/16 Kristofer Munsterhjelm<km_elmet at lavabit.com>:
>>>> On 02/14/2013 07:07 PM, Richard Fobes wrote:
>>>>   ...
>>>>>> ... as in
>>>>>> the top-down method of Otten?
>>>>> ...
>>>> ... perhaps Peter meant this one?
>>>> http://www.votingmatters.org.uk/ISSUE13/P3.HTM
>>> yes, that's the method I was thinking of. Thanks Kristofer.
>> The approach specified in this article by Joseph Otten involves identifying
>> "doomed" candidates and "guarded" candidates.
>> No, VoteFair representation ranking does not use that approach.
>> VoteFair representation ranking uses a more advanced approach that looks
>> deeper into the ballots.
>> Specifically, after the first-position winner has been chosen, VoteFair
>> _representation_ ranking starts by identifying the ballots that do not rank
>> that candidate as their first choice, and using those ballots it identifies
>> which (remaining) candidate is most popular.  Then, it looks at the relative
>> ranking between those two candidates.
>> Obviously the ballots that rank the first-position winner higher are
>> well-represented.  The other ballots -- that rank the second tentatively
>> popular candidate above the first-position winner -- are not represented by
>> the first-position winner, so those ballots get full influence.  The
>> well-represented ballots get only a small influence, specifically to the
>> extent that the first winner had the support of _more_ _than_ half the
>> voters (the amount beyond 50%).  Then the second-position winner is
>> identified.
> I don't understand votefair ranking neither from the description above
> nor from the web pages.
> Don't you have a worked example and a complete and exhaustive
> description of the algorithm?
>> Note that the second-position winner might be, or might not be, the
>> tentatively identified candidate.
>> This approach precludes the strategy of a majority of voters putting
>> unpopular candidates at the top of their ballot (with different voters using
>> different unpopular candidates) as an attempt to fool the algorithm into
>> thinking they are not well-represented by the first-position winner.
>> This approach avoids the weakness of STV (and IRV), which focuses attention
>> on the top-ranked candidate on each ballot, and only looking at lower-ranked
>> candidates on an as-needed basis.
>>>> Possibly combined in some way with
>>>> http://www.votingmatters.org.uk/issue9/p5.htm .
>>> Maybe, I don't know.
>> The key paragraph from this second article is:
>> "Were we to know in advance that we would win, say, n seats in a region,
>> then it would be straightforward to use STV to select n candidates from the
>> potential candidates and put them in the top n places in our list. If we
>> don't know n in advance (which we don't!) then we can perform this operation
>> for every possible n, i.e. from 1 up to the number of seats available in the
>> region, and attempt to construct a list whose top n candidates are those
>> victorious in the nth selection ballot. (There is really only 1 ballot - the
>> division into n ballots is notional.)"
>> It says what I said earlier: that STV needs to know in advance how many
>> seats will be won.
>> I did not quickly understand how Joseph Otten proposes combining the
>> different lists (one for each value of "n") into a single list, and I'm not
>> in the academic world so I would not get paid to spend time figuring that
>> out, and since Peter says it may not be relevant, I'll leave this level of
>> detail unresolved.
>> Getting to the point of answering Peter's question, no, VoteFair
>> representation ranking also does not use this second-article approach.
>> Shifting perspective here, there is an important difference between STV and
>> VoteFair representation ranking.
>> STV has the same weakness as IRV, namely it puts all of its focus on the
>> top-ranked candidate on each ballot.
>> In contrast, VoteFair representation ranking looks much deeper into each
>> ballot to identify whether the ballot is from  a voter who is (or is not)
>> well-represented by which candidates have won the earlier seats (in the
>> party list).
> Well I don't understand what "looking deeper" means.
>> As I've indicated before, if a party list needs to be longer than about five
>> positions, it's possible to get even better proportionality in the later
>> seats by using an algorithm used in VoteFair _negotiation_ ranking.
>> The algorithm behind VoteFair _negotiation_ ranking could calculate a full
>> party-list ranking, and then if the ranking violates the gender-based rules,
>> then an administrator can indicate an "incompatibility" that adjusts the
>> ranking to meet the gender-based quota (expressed as an incompatibility).
>> There are two reasons why I haven't proposed using VoteFair negotiation
>> ranking for use in a party-list election:
>> * It is not designed to handle thousands of voters, which would be needed
>> for party-list voting.  (It's designed for a group of people working in a
>> collaborative situation.)
> Party list voting will have max 500 voters, typically less than 100.
>> * It is designed in a way that regards the different party-list positions as
>> distinct "proposals" (such as filling cabinet positions) rather than as
>> somewhat-equivalent seats being filled.
>> Yet, as I've indicated, the advanced adjustment capabilities of VoteFair
>> _negotiation_ ranking can be combined with VoteFair _representation_
>> ranking.  That would create a "VoteFair party-list ranking" algorithm.
>> However, combined with the need for gender adjustments in up to two
>> positions, that algorithm would only start having significantly different
>> results starting at about the fifth seat.  That makes it not worthwhile for
>> this situation that involves five seats, with a high likelihood that the
>> fifth-position winner will be displaced to fulfill a gender-based quota
>> requirement.
> As I mentioned, I am looking for an algorithm, which allows qouted
> seats to be proportionally distributed, in order to avoid that the
> same voters get all quoted seats.
>> In the future when longer party lists are needed, adjustments can be made
>> starting at about the fifth seat to provide representation for small --
>> although not tiny -- minorities.
>> If we expect the party to win only 1, 2, 3, 4, or 5 seats, the first four
>> positions need to be filled by:
>> 1: The overall most popular "majority" candidate
>> 2: The overall most popular "opposition" candidate
>> 3: The next-most popular "majority" candidate
>> 4: The next-most popular "opposition" candidate
>> That's what VoteFair representation ranking calculates -- in a way that
>> deeply looks into the ballots to ensure representation for
>> not-yet-represented voters.
>> Richard Fobes
> Best regards
> Peter Zborník

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