steve bosworth
2018-07-18 09:41:15 UTC
________________________________
Hi Kristofer,
Thank you for originally telling me about MJ and helping me think that it might be possible to modify it to enable evaluative voting also to elect multi-winners. Do you see any flaws in EPR? Below, you helpfully illustrate how some varieties of voting by ranking candidates might produce somewhat similar results. However, do you agree with me that, unlike any of these varieties, EPR alone allows each voter to guarantee that her one vote will be added to the one representative whom she has helped to elect and sees as the one most fit for the office?
To be exact, it must also be explained why EPR sometimes must only represent some citizens indirectly. Too briefly, this is mentioned in Endnote 8 of the published article. The following complete explanation of this feature is not published in this version of the article but was originally added to the end of the existing section that explains how EPR can be counted by hand:
Thus, at this stage, each winner has the following number of affirmed evaluations:
A-18, C-11, E-15, G-10, D-9, I-4, B-1.
Note that this is the last type of discovery that the computer algorithm is able to make. [AC1]<file:///C:/Users/steph48/Documents/2018/Bernie/18july-Kristofer-sennet.docx#_msocom_1> [sb2]<file:///C:/Users/steph48/Documents/2018/Bernie/18july-Kristofer-sennet.docx#_msocom_2> However, the above numbers of affirmed evaluations are slightly different from the numbers of weighted votes that were reported in the previous section:
A-14, C-12, E-14, G-10, D-9, I-4, B-5.
The next several paragraphs explain why these small changes have been made by hand. Not in this case, but such differences might occur because of EPRs promise to enable each citizen to guarantee that his or her vote will continue to count in the deliberations of the council. Thus, if and when none of the evaluations of at least ACCEPTABLE by at least one voter refers to one of the elected candidates, EPRs ballot allows each voter to require the unelected candidate she had most highly valued to transfer her default vote to the total number of affirmed evaluations already received by one of the winners, i.e., this candidate must give her default vote to the member he judges to be the one most fit for the office. In this simulation, no such default votes are available.8
Instead, the differences between the above two sets of numbers results entirely from EPRs rule that removes an unlikely but theoretically possible threat to democracy: one of the elected candidates might receive enough votes to dictate to the council.[AC3]<file:///C:/Users/steph48/Documents/2018/Bernie/18july-Kristofer-sennet.docx#_msocom_3> Thus, EPR limits the total percentage of all the votes in the council that any one member can retain. For example, this limit might be set so that at least 3 members must agree before a majority decision can be made. For this election, this limit could be 20% (i.e. 14 weighted votes). Any most popular such member would be the first to be required to transfer her extra votes to one or more of her fellow councilmembers. Accordingly, in this election, member A must non-returnably give her 4 extra votes to one or more of her fellow members. Similarly, member E must transfer his extra vote.8
Of course, different but acceptable percentage limits could be adopted by different cities, states, or nations. However, using the limit of 14 votes in our example, we report that winner A transferred her 4 extra affirmed evaluations to winner B, finally giving him a weighted vote of 5 rather than 1 in the council. Also, winner E transferred his extra affirmed evaluation to winner C, giving C a weighted vote of 12 rather than 11. Again, this means that each winners final weighted vote in the council is:
A-14, C-12, E-14, G-10, D-9, I-4, B-5.
In these ways, it can be seen that each EPR citizen can guarantee that his or her vote, directly or indirectly, will continue fully to count in the deliberations of the council - no citizens vote need be wasted.
These are the ways in which EPR includes two different uses of Asset Voting, after the computer count has been completed.8
What do you think? I very much look forward to your feedback.
Thank you,
Steve
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
From: Kristofer Munsterhjelm <***@t-online.de>
Sent: Monday, July 16, 2018 7:21 PM
To: Jameson Quinn; steve bosworth
Cc: election-***@lists.electorama.com; ***@lomaxdesign.com
Subject: Re: [EM] IRV et al v. EPR
understand it), each winner has a different weight in the assembly, and
thus instead of discarding just a quota and then redistributing the
surplus, it's possible to assign more than a quota to a single winner,
who benefits from this "supermajority" by an increased weight.
To use SNTV as an example, suppose you have a Plurality election of the
type:
A: 100
B: 80
C: 30
D: 20
and three to elect. If you use ordinary SNTV, then the voters who voted
for A wasted their votes, since they voted in excess of what was
required to have A win. However, with weighted voting, it's a simple
matter of letting A have a weight of 47.6% of the total vote, B have a
weight of 38.1% and so on.
Suppose e.g. that the A- and B-voters both had D as their second
preference. Unweighted, the wasted votes for A and B deprived D of his
victory, as in SNTV, some fractions of the A- and B-voters could have
strategically voted for D instead to get him above C's count, and that's
what a better method with surplus redistribution would have done anyway.
In a weighted method, the A and B-voters get compensated for C being
elected, in the form of A and B having a greater share of power; and
this is preferable from the point of view of A- and B-voters because
they get to contribute directly to the power of their first choice
candidates instead of having that power go to their second choice.
With all that said, there's another argument that could be made in favor
of doing surplus redistribution, which is that under tactical
nomination, you could get something analogous to surplus redistribution
anyway. If the A-voters consider D to be close to A, then some of them
could vote for D, after which the fixed council size would push C off.
The benefit of reducing C's strength to zero could then make up for A's
relative power being reduced in the council.
A stronger strategy would involve cloning A into A1 and A2 and, instead
of redistributing votes to D, distributing them between A1 and A2. That
produces a more party list-like outcome -- but that strategy would also
be possible under an unweighted multiwinner system.
Hi Kristofer,
Thank you for originally telling me about MJ and helping me think that it might be possible to modify it to enable evaluative voting also to elect multi-winners. Do you see any flaws in EPR? Below, you helpfully illustrate how some varieties of voting by ranking candidates might produce somewhat similar results. However, do you agree with me that, unlike any of these varieties, EPR alone allows each voter to guarantee that her one vote will be added to the one representative whom she has helped to elect and sees as the one most fit for the office?
To be exact, it must also be explained why EPR sometimes must only represent some citizens indirectly. Too briefly, this is mentioned in Endnote 8 of the published article. The following complete explanation of this feature is not published in this version of the article but was originally added to the end of the existing section that explains how EPR can be counted by hand:
Thus, at this stage, each winner has the following number of affirmed evaluations:
A-18, C-11, E-15, G-10, D-9, I-4, B-1.
Note that this is the last type of discovery that the computer algorithm is able to make. [AC1]<file:///C:/Users/steph48/Documents/2018/Bernie/18july-Kristofer-sennet.docx#_msocom_1> [sb2]<file:///C:/Users/steph48/Documents/2018/Bernie/18july-Kristofer-sennet.docx#_msocom_2> However, the above numbers of affirmed evaluations are slightly different from the numbers of weighted votes that were reported in the previous section:
A-14, C-12, E-14, G-10, D-9, I-4, B-5.
The next several paragraphs explain why these small changes have been made by hand. Not in this case, but such differences might occur because of EPRs promise to enable each citizen to guarantee that his or her vote will continue to count in the deliberations of the council. Thus, if and when none of the evaluations of at least ACCEPTABLE by at least one voter refers to one of the elected candidates, EPRs ballot allows each voter to require the unelected candidate she had most highly valued to transfer her default vote to the total number of affirmed evaluations already received by one of the winners, i.e., this candidate must give her default vote to the member he judges to be the one most fit for the office. In this simulation, no such default votes are available.8
Instead, the differences between the above two sets of numbers results entirely from EPRs rule that removes an unlikely but theoretically possible threat to democracy: one of the elected candidates might receive enough votes to dictate to the council.[AC3]<file:///C:/Users/steph48/Documents/2018/Bernie/18july-Kristofer-sennet.docx#_msocom_3> Thus, EPR limits the total percentage of all the votes in the council that any one member can retain. For example, this limit might be set so that at least 3 members must agree before a majority decision can be made. For this election, this limit could be 20% (i.e. 14 weighted votes). Any most popular such member would be the first to be required to transfer her extra votes to one or more of her fellow councilmembers. Accordingly, in this election, member A must non-returnably give her 4 extra votes to one or more of her fellow members. Similarly, member E must transfer his extra vote.8
Of course, different but acceptable percentage limits could be adopted by different cities, states, or nations. However, using the limit of 14 votes in our example, we report that winner A transferred her 4 extra affirmed evaluations to winner B, finally giving him a weighted vote of 5 rather than 1 in the council. Also, winner E transferred his extra affirmed evaluation to winner C, giving C a weighted vote of 12 rather than 11. Again, this means that each winners final weighted vote in the council is:
A-14, C-12, E-14, G-10, D-9, I-4, B-5.
In these ways, it can be seen that each EPR citizen can guarantee that his or her vote, directly or indirectly, will continue fully to count in the deliberations of the council - no citizens vote need be wasted.
These are the ways in which EPR includes two different uses of Asset Voting, after the computer count has been completed.8
What do you think? I very much look forward to your feedback.
Thank you,
Steve
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
From: Kristofer Munsterhjelm <***@t-online.de>
Sent: Monday, July 16, 2018 7:21 PM
To: Jameson Quinn; steve bosworth
Cc: election-***@lists.electorama.com; ***@lomaxdesign.com
Subject: Re: [EM] IRV et al v. EPR
This system as described is very close to being an excellent
"Proportional Majority Judgment" method, but has one key flaw. When a
candidate is elected with more than 1 quota of support, all of their
supporting ballots are marked as used. To give a proportional method and
to minimize strategic incentives, only 1 quota of supporting ballots
should be marked as used. This could be done through some ordering
criterion (highest support for winner/lowest support for others), by
proportionally reweighting ballots, or by using up randomly-chosen
ballots; the differences between these three options would be relatively
minor.
This reflects the basic way to transform any single-winner method into a
proportional multi-winner method: find single winners sequentially, and
then for each of those winners, "use up" the one quota of ballots that
"contributed most" to making that candidate the winner. There's room for
judgment calls in defining "contributed most", but other than that this
is a general template that IMO gives an optimal combination of good and
practical from methods as varied as IRV (which becomes STV), MJ, STAR,
Score, approval, Condorcet... in short, almost any single-winner method.
Most of those multiwinner methods have unweighted winners. In EPR (as I"Proportional Majority Judgment" method, but has one key flaw. When a
candidate is elected with more than 1 quota of support, all of their
supporting ballots are marked as used. To give a proportional method and
to minimize strategic incentives, only 1 quota of supporting ballots
should be marked as used. This could be done through some ordering
criterion (highest support for winner/lowest support for others), by
proportionally reweighting ballots, or by using up randomly-chosen
ballots; the differences between these three options would be relatively
minor.
This reflects the basic way to transform any single-winner method into a
proportional multi-winner method: find single winners sequentially, and
then for each of those winners, "use up" the one quota of ballots that
"contributed most" to making that candidate the winner. There's room for
judgment calls in defining "contributed most", but other than that this
is a general template that IMO gives an optimal combination of good and
practical from methods as varied as IRV (which becomes STV), MJ, STAR,
Score, approval, Condorcet... in short, almost any single-winner method.
understand it), each winner has a different weight in the assembly, and
thus instead of discarding just a quota and then redistributing the
surplus, it's possible to assign more than a quota to a single winner,
who benefits from this "supermajority" by an increased weight.
To use SNTV as an example, suppose you have a Plurality election of the
type:
A: 100
B: 80
C: 30
D: 20
and three to elect. If you use ordinary SNTV, then the voters who voted
for A wasted their votes, since they voted in excess of what was
required to have A win. However, with weighted voting, it's a simple
matter of letting A have a weight of 47.6% of the total vote, B have a
weight of 38.1% and so on.
Suppose e.g. that the A- and B-voters both had D as their second
preference. Unweighted, the wasted votes for A and B deprived D of his
victory, as in SNTV, some fractions of the A- and B-voters could have
strategically voted for D instead to get him above C's count, and that's
what a better method with surplus redistribution would have done anyway.
In a weighted method, the A and B-voters get compensated for C being
elected, in the form of A and B having a greater share of power; and
this is preferable from the point of view of A- and B-voters because
they get to contribute directly to the power of their first choice
candidates instead of having that power go to their second choice.
With all that said, there's another argument that could be made in favor
of doing surplus redistribution, which is that under tactical
nomination, you could get something analogous to surplus redistribution
anyway. If the A-voters consider D to be close to A, then some of them
could vote for D, after which the fixed council size would push C off.
The benefit of reducing C's strength to zero could then make up for A's
relative power being reduced in the council.
A stronger strategy would involve cloning A into A1 and A2 and, instead
of redistributing votes to D, distributing them between A1 and A2. That
produces a more party list-like outcome -- but that strategy would also
be possible under an unweighted multiwinner system.