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 EPR’s 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, EPR’s 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 EPR’s 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 winner’s 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 citizen’s 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,



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
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
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

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.
Kristofer Munsterhjelm
2018-07-20 09:30:20 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?
You're welcome.

Since you have added maximum weight limits to the EPR method, it seems
that either it is not completely free of vote-wasting, or an unweighted
method can be made free of vote-wasting as well.

Just set the maximum weight limit to (number of voters)/(number of
seats), and you will get an Asset-based method very close to BTV
(Bucklin STV) with a Hare quota. If a group of voters' favorite
candidate gets more than a Droop quota, that candidate will then decide
where the surplus goes. This is similar to, but not quite the same
thing, as the surplus redistribution step in ordinary BTV.

If this Asset BTV method (to coin a name) wastes votes, then EPR can be
slowly changed into this Asset BTV method, there must be some value of
the maximum weight restriction that turns EPR into a method that wastes
votes. Alternatively, EPR continuously approaches a vote-wasting method
as one decreases the maximum weight restriction. But in that case, since
EPR as you propose it already has a maximum weight restriction, it can't
be the minimally vote-wasting method: that method would be EPR without
any maximum weight restrictions at all.

In short: by being more strict about the maximum weight winners can get,
we can get an unweighted method. You've said unweighted methods waste
votes. It's possible to turn EPR into an unweighted method by decreasing
the max weight restriction. So somewhere along that line from no
restriction to a Hare quota restriction, EPR turns into a vote-wasting
method. But what this point is, is entirely arbitrary. Hence something
strange is going on.

Another way to pry at this is to consider normal Asset. Suppose we
instead of EPR use a method where everybody who gets one or more votes
meet up and redistribute their votes, Asset style, until only (number of
seats) of the candidates have more than zero votes. (For the sake of
simplicity, ignore the problem of scale at the moment.) Since EPR has an
Asset component yet doesn't waste votes, why would this Asset method
waste votes? If it wastes votes, something strange is going on; if it
doesn't, then EPR is not the only method that doesn't waste votes.

From a cursory look, Asset doesn't appear to waste votes quantitatively
because a voter X's vote either helps his favorite Y, or helps someone
who Y contributes asset to (who then becomes the candidate X helped
elect). It doesn't waste votes qualitatively any more than EPR does
because X's vote contributes directly to the initial assets of Y.

I suspect that the answer is that every method wastes votes somewhat,
and some are better than others. But I also imagine that it's hard to
quantify either to what degree a method wastes votes, or to what degree
it is a bad thing. This because while the grades in MJ are compared to a
common standard, that common standard might differ in different societies.

As I've understood it, a wasted vote in something like Bucklin STV
implies that either the voter's ballot has been exhausted (e.g. he only
named a favorite, nobody else, and now his vote won't count for anything
any longer), or that the method forced his vote to count towards a
compromise rather than to his favorite. Sometimes, a compromise is a
choice everybody can accept; other times, it's a choice that pleases
nobody. And those two situations differ.

If it's only properly exhausted ballots that cause trouble, the
minimally vote-wasting unweighted method could just have the otherwise
truncated ballot be completed according to the favorite's choice: the
grades not supplied by the voter would then be supplied by the default
ballot provided by the voter's favorite candidate.

On a side note, I think that redoing the method with a different initial
threshold is better than changing the initial threshold during the
process, as everybody gets to play according to the same rules. It is
also more complex, however.
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