[EM] Multiwinner methods with weighted votes

[steve bosworth]

Re:  Multiwinner methods with weighted votes

To Kristofer and everyone:

________________________________

From: Kristofer Munsterhjelm <km_elmet at t-online.de>
Sent: Sunday, April 2, 2017 1:00 PM>

To: steve bosworth; election-methods at lists.electorama.com;



   K:  [….]  I'd like to note a few things.

>      - You could use MJ instead of IRV. Since APR prior to weighting is
>      basically "elect candidates by IRV …”, and you've stated
>      that MJ is better than IRV, APR should be better if you replace it with
>      "elect candidates by MJ a bunch of times". All you need is another way
>     of counting which voters contributed to which candidates' election. My
>      party list-type Bucklin method will do the job, for instance.


K:  As I mentioned in the previous mail, I have constructed a multiwinner
generalization of Bucklin/MJ. It can be used both for STV-type methods
and weighted vote-type methods. See
https://github.com/kristomu/voting-scripts/tree/master/new_methods/bucklin_range.


In essence, you count the number of Excellent votes alone first. If any
candidate has more than a threshold's worth of Excellent votes alone, he
is elected with weight equal to the number of votes he got, and the
votes are removed from consideration.



You count the number of Excellent and Very good votes, and repeat the logic. You choose the
threshold to be the lowest number so that the number of elected
candidates comes out right (to 435 or whatnot).  [….]


S:  Thank you for suggesting that I consider using a form of Bucklin/MJ rather than a form of IRV for my ARP.  Please correct me if I have not fully understood your brief description of your own “multiwinner generalization of Bucklin/MJ”.  Using the USA as an example, below I will try to modify my APR proposal so that it is in line with my understanding of your Bucklin/MJ. I will call it Evaluative Associational Proportional Representation (EAPR).  Contrary to my first expectations, I see now how EARP, like ARP would allow the electorate to be represented most clearly as being composed of up to 435 groups, each enthusiastically holding a somewhat different worldview.  How does this compare with your “party list-type Bucklin method”?

Similar to APR, EAPR would also enable each citizen to guarantee that their one vote would be added to the “weighted vote” of the one congressperson they value most highly.  If no candidate she had evaluated at least as Acceptable, the EAPR ballot would allow her to require the candidate she had evaluated most highly to transfer her one vote to the congressperson he sees as the one most “fit” for the office.  If she had given more than one candidate her highest evaluation, the one that would pass her vote on in this way would be determined by lot.



Well before the general election, EAPR’s “primary election” would help to provide EAPR’s benefits. In this primary, citizens would be asked to use their “evaluations” rather than their “preferences” to help society discover the group of nationwide applicant organizations (e.g. political parties, interest groups, electoral districts, etc.) who are most valued by the electorate, i.e. the “associations” through which all voters will elect the 425 congresspersons later in the general election.  Each citizen would be asked to give one of the following “grades” to as many of the applicant organizations as they might wish:  Excellent, Very Good, Good, Acceptable, Poor, or Reject.  In this way, each citizen would record the extent to which they see each applicant organization as likely to offer a list of attractive candidate for any US voter to “grade” in the later general election.  Each organization not marked by a voter would be counted as Rejected by that voter.



Each organization that receives at least 1/435 of all the registered voters in the country as giving it their highest available evaluations would become an “association”.  At the same time, each citizen who had given their evaluation to one of these associations would become a registered voter through that association during the later general election.  If none of the organizations given a “grade” of Acceptable or above by a citizen becomes an “association” in this way, that citizen would instead automatically become a registered voter through the geographically defined “association” in which they reside (i.e. their local electoral district).



Again, these EAPR “associations” would be composed of all the most valued organizations that had received at least the above threshold of voters giving  them their highest available evaluations. The primary’s discovering of these associations would start by counting only the number of Excellents received by each applicant organization.   Any organization receiving the largest number of Excellents above the threshold number would be the first association to be discovered.  Each citizen who had evaluated this organization as Excellent would become a registered voter through this association during the later general election at their local polling station.  The total number of evaluations received by each association would help to determine the number of congresspersons which must be elected later in the general election to represent it in the House of Representatives, e.g. an association receiving 1/435 would elect one congressperson, an association receiving 2/435 would elect two.  See the Endnote for more details.



For the discovery of each succeeding association, one by one, all the remaining evaluations given to all the remaining applicant organizations by each citizen who had already become a registered voter through one of the previously discovered associations would not be used to help discover any other association.  This guarantees that each citizen’s one vote in the primary will count only once, i.e. for the association in which they become a registered voter.  Consequently, the second association to be discovered would be the one, if any, which had received the next highest number of Excellents above the threshold.  Similarly, any other organizations who had received at least the threshold of the remaining Excellents would also be one of this first group of associations to be discovered.  The second group of associations to be discovered would be composed of all those remaining organizations that had received at least the threshold but only by also adding all the remaining Very Goods they had received.  Similarly, the third group would be composed of all other organizations that had received at least the threshold but only by also adding all the remaining Goods they had received.  Similarly, the fourth group would be composed of all the other organizations that had received at least the threshold but only by also adding all the remaining Acceptables they had received.  Any citizens who had not yet become a registered voter for the general election through one of these associations as a result of the above counts would nevertheless now be added to one of these if they had given it at least an evaluation of Acceptable.  However, if none of their evaluations would allow them to become a registered voter in this way, they would instead automatically become a registered voter through their local electoral district (the geographically defined “association” in which they reside).



During the later general election of congresspersons, each citizen would be asked to evaluate as many of the candidates in the country as they might wish, i.e. giving each one of the above “grades”.  Any candidate not marked by a voter would be counted as Rejected by that voter.  Similar to the count in EARP’s primary, the first candidate in the country to be elected to the House would be the one, if any, who had received the highest number of Excellents above the threshold, i.e. at least 1/435 of all citizens in the country who have voted.  Again, to honor the principle of one-person-one-vote, all the evaluations given to other candidates by voters who have elected an earlier candidate would play no part in electing any later candidate.   Also, the next candidates to be chosen, one by one, would be the one, if any, who had received the next highest number of remaining evaluations above the threshold.  For example, the second candidate to be elected would be the one, if any, who had received the next highest number of remaining Excellents above the threshold.  All such winners would constitute the first group of congresspersons elected.



Similarly, the second group would be those that had received at least the threshold but only by also adding all the remaining Very Goods they had received.  The third group would be those that had received at least the threshold but only by also adding all the remaining Goods they had received.  The fourth group would be those that had received at least the threshold but only by also adding all the remaining Acceptables they had received.  The fifth group would be composed of the most highly evaluated candidates but those who had not received even the above threshold number of evaluations, i.e. only the number of congressperson who are still needed to complete the exact number to be elected to represent each association as previously determined by EAPR’s primary.  In any case, each congressperson would have a “weighted vote” in the House exactly equal to the total number of evaluations from citizens used to elect them.



Next, the vote of any citizen whose vote had not yet been counted toward the “weighted vote” of an elected candidate as a result of any of the above counts would now be added if possible to the “weighted vote” of the congressperson to whom she had given at least an evaluation of Acceptable.  However, if a citizen’s vote still could not be added in this way to the “weighted vote” of one of the candidates who has already been elected, EAPR’s ballot allows a citizen to require the non-elected candidate to whom she had given her highest evaluation to transfer her one vote to the ”weighted vote” of the congressperson he believes is the one most qualified for the office.  In this way, each citizen guarantees that their vote will continue fully to count within the deliberations of the House.



Finally, all the above counts must be interpreted so as to guarantee the election of the exact number of congresspersons to represent each association in the House as determined by the results of EAPR’s primary.



Endnote

When initially discovered, each “association” would immediately know the minimum number of congresspersons it would be allowed to elect, e.g. 2 if it had at least two 435ths of the nation’s registered voters, 3 if at least three 435ths, etc.  However, if together all these associations had not yet been authorized to elect all 435 representatives, the remaining number needed to complete the 435 would be distributed between these associations as follows: One by one, the right to elect an additional representative would be given sequentially to the association that currently has the “highest remainder’’.  A ‘remainder’ here is the number of electors beyond the minimum required to allow an association to elect one, two, three, or x number of representatives, as previously explained.  The second additional representative would be added to the association with the second largest remainder, and so forth.  This adding process would continue until the exact number of representatives that each association would elect as its contribution to the 435 had been discovered.

I now see EARP as superior to ARP because:

  1.  It is easier and more informative for citizens to grade candidates rather than rank them.

  2.  It does not eliminate any candidate from consideration in the count until all the winners have been discovered.

  3.  It entirely eliminates the possible occurrence of either the Condorcet or Arrow paradox.

What do you think?

Steve

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