[EM] proportional constraints - help needed

[Richard Fobes]

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.

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).

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.)

* 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.

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