[EM] proportional constraints - help needed

[Peter Zbornik]

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