Discussion:
[EM] EPR, Bucklin STV, & Asset
(too old to reply)
steve bosworth
2018-07-22 18:47:11 UTC
Permalink
From: Kristofer Munsterhjelm <***@t-online.de>
Sent: Friday, July 20, 2018 9:30 AM
To: steve bosworth; election-***@lists.electorama.com
Subject: Re: IRV etc. v. EPR-STEVE'S REPLY TO KRISTOFER



On 2018-07-18 11:41, steve bosworth wrote:
> ------------------------------------------------------------------------
>
> Hi Kristofer,

I’ll respond to each of you points in line:
>
S: > 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?

K: 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.



S: Below, I will again explain how EPR allows no vote to be wasted quantitatively or qualitatively. Below, I accept EPR can allow some qualitative votes to be partly wasted, but only when this is otherwise unavoidable. Immediately, however, I see unweighted methods as needlessly wasting some votes because these methods require any surplus whole or fractional votes to be transferred from a higher to a lower preference (or evaluated) candidate, i.e. when that 1st candidate is elected as result of already having received at least the chosen quota of votes. Again, these transferred votes are partly wasted qualitatively. This is also illustrated by your next sentences.

K: 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,….

S: Which it does, at least qualitatively. EPR also does this but only as a last resort, i.e. only when a voter has not evaluated any of the winners as being at least ACCEPTABLE. However, I now see that Endnote 8 in my published article does not fully explain how. Therefore, let me again add the following complete explanation which was originally included in an earlier unpublished draft. It was added at the end of the section of the article called (The EPR Algorithm):



“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. However, the above numbers of affirmed evaluations are slightly different from the following numbers of weighted votes that these s would receive as a result of the additional considerations explained in the remaining paragraphs of the section.

A-14, C-12, E-14, G-10, D-9, I-4, B-5.

“These small changes have been made by hand. Not in this sample election, but such differences might occur because of EPR’s promise to enable each citizen to guarantee that his or her vote will continue proportionately 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. Again, in the above example 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. Thus, EPR has chosen to limit 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 sample 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 “

K: …. 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.

S: Yes, but in contrast to Asset BTV, EPR minimizes this partial qualitative waste. It limits it only to any case where some citizen’s votes would otherwise be entirely wasted, or if counted, might help elect a dictatorial winner.



K: Alternatively, EPR continuously approaches a [qualitative] 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.

S: In the context of the above explanation of EPR, I characterize EPR’s ‘weight restriction’ as necessary to reduce the chances for dictatorship rather than being ‘maximal’ or minimal.

K: 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.

S: Yes, but EPR shows how all the benefits of having weighted votes can be maximized by requiring some citizen’s votes to be partly wasted qualitatively.



K: 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.



S: No, this waste starts as soon as any limit restriction is applied. However, it is justified because it helps to protect democracy. In the context of the above explanations, I think it is fair to say that EPR’s ‘vote-wasting method’ is not at all ‘arbitrary’. This is because it only helps to guarantee that each citizen’s will continue to count in the council, and at the same time it does not offering the possibility of electing a legislative dictator.

K: Another way to pry [?play??] 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 [quantitatively},



S: The only cases where EPR’s use of Asset would be clear that it is not qualitatively wasting a vote partly is when either the ‘default’ or ‘extra’ vote being transferred to a winner is going the a winner who happened also to be awarded the same evaluation by the relevant voter, i.e. the voter who had most highly valued either the relevant most valued losing candidate, or the relevant very popular winning candidate.



K: … 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.

S: By ‘normal Asset’, I take it that you are simply adding the possibility of having a public list pre-Registered Asset Electors, i.e. during the general election, giving each citizen the option of simply giving her proxy vote to one of these Electors publicly to evaluate all the candidates rather than secretly evaluating the candidates directly herself. If so, theoretically it could offer the benefits offered by simple EPR.

K: 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.
S: Yes. I see no reason to reject the addition of this Asset option, provided all the other elements of EPR remain.
K: I suspect that the answer is that every method wastes votes somewhat,
and some are better than others.

S: Yes, but only EPR (with or without the above Asset option) minimizes the partial qualitative waste.

K: 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.



S: As far as I can see, the exact amount of qualitative waste that might have occurred in any given EPR election could be counted exactly. Also, given the demand that the ideal representative democracy would not needlessly waste any citizen’s vote, any unnecessary waste is ‘bad’.

K: This because while the grades in MJ are compared to a common standard, that common standard might differ in different societies.



S: Yes and No. As I understand Balinski and Laraki, they are not asserting the obviously false claim that each voter (or each society) has the same scale of values. No, people commonly have different priorities. Correctly in my view, they are only claiming that almost every adult is able to distinguish between at least 6 different grades of valued human behavior, each according to his or her own current scale of values: EXCELLENT, VERY GOOD, GOOD, ACCEPTABLE, POOR, and REJECT.



K: 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. …



S: Yes, but such waste would be almost minimized by Bucklin STV if EPR’s two uses of Asset were added to Bucklin STV. Still, because Bucklin STV uses rankings rather than grades, it is less certain than EPR is, only to elect the winners who are most highly valued by their respective electorates.



K: Sometimes, a compromise is a choice everybody can accept; other times, it's a choice that pleases nobody. And those two situations differ.



S: Yes, but as I see it, EPR requires no compromises. Each of its features maximally foster democracy. This is because each voter can guarantee that her one vote will continue to count in the council through the member she has helped to elect and whom she sees as the one most fit for the office. At the same time, dictatorship is appropriately resisted.

K: 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.

S: Yes. But Bucklin STV would be better if it also allowed weighted votes in the council similar to those allowed by EPR. Still, EPR would be superior both because its evaluations are more meaningful, informative, and discerning than rankings; and each voter can apply the same evaluation to more than one candidate while retaining the principle of one-citizen-one-vote.


K: 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.



S: If your suggested ‘threshold’ would also limit the total number of weighted votes that a winner could retain, this would again needlessly the qualitative wasting of some votes. By contrast, the ‘number of seats/the total number of voters’ threshold of EPR does not determine the upper limit of the number of weighted votes that can be retained by an elected candidate. This threshold only determines in what round all the next lower group of remaining evaluations must be added to the currently remaining higher evaluations in order to attempt to discover the next winner. EPR’s count treats all voters according to the same set of rules.

What do you think? I look forward to your feedback.

Steve
Kristofer Munsterhjelm
2018-07-22 20:29:21 UTC
Permalink
On 2018-07-22 20:47, steve bosworth wrote:

>> K: 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.
>
> S: If your suggested ‘threshold’ would also limit the total number of
> weighted votes that a winner could retain, this would again needlessly
> the qualitative wasting of some votes. By contrast, the ‘number of
> seats/the total number of voters’ threshold of EPR does not determine
> the upper limit of the number of weighted votes that can be retained by
> an elected candidate.This threshold only determines in what round all
> the next lower group of remaining evaluations must be added to the
> currently remaining higher evaluations in order to attempt to discover
> the next winner. EPR’s count treats all voters according to the same set
> of rules.

(Rest to come later)

I'm not referring to a maximum limit on the weight of winners, but
rather to what happens in this step (quoting from jpolrisk):

> Round 7 searches for the 5th winner. However, one cannot be found even by Round 8 and even after > all the available ACCEPTABLEs have been added to the remaining
EXCELLENTs, VERY GOODs, and GOODs.
> No evaluations of POOR or REJECT must be added to help elect any candidate. Therefore, the
> remaining winners must instead be discovered by lowering the threshold of 10 iteratively by
> subtracting 1 (one-at-a-time) until the remaining winners are discovered.

What I'm saying is that a better approach is to consider that, whenever
you get to the sort of exhaustion that makes this lowering of the
threshold necessary, then instead of lowering the threshold (of 10) and
continuing the method, you should lower it and *restart* the method.

The point is that the first few winners had a higher bar to clear (the
threshold of 10), while the latter winners had a lower bar (required by
that no winners are able to clear the high bar the threshold of 10
poses). So if the bar is to be lowered, it should be lowered
consistently for all candidates, not just for those who came in last.

I'm thinking of a situation like: suppose the threshold is x voters.
Suppose there are a number of candidates who have EXCELLENT from x-1
voters each, but they don't get elected because the threshold is x. EPR
moves to the next round instead, and some candidates with X+1 number of
VERY GOODs get elected, but it's not enough to fill s seats. After this
point, the threshold gets lowered and some of the EXCELLENT candidates
get elected, filling out the council; but it would be more fair to the
voters if the count was restarted after the threshold is lowered, so
that all the X-1 EXCELLENT candidates get elected instead.
----
Election-Methods mailing list - see http://electorama.com/em for list info
steve bosworth
2018-07-24 00:28:19 UTC
Permalink
________________________________
From: steve bosworth <***@hotmail.com>
Sent: Monday, July 23, 2018 11:02 PM
To: Kristofer Munsterhjelm
Subject: Re: (3) EPR, Bucklin STV, & Asset

________________________________

From: Kristofer Munsterhjelm <***@t-online.de>
Sent: Sunday, July 22, 2018 8:29 PM
To: steve bosworth; election-***@lists.electorama.com
Subject: Re: EPR, Bucklin STV, & Asset

From Steve:

Kristofer wrote:
>> K: 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.
>
> S: If your suggested ‘threshold’ would also limit the total number of
> weighted votes that a winner could retain, this would again needlessly waste some votes qualitatively. By contrast, the ‘the total number of voters/ number of seats’ threshold of EPR does not determine the upper limit of the number of weighted votes that can be retained by
> an elected candidate. This threshold only determines in what round all
> the next lower group of remaining evaluations must be added to the
> currently remaining higher evaluations in order to attempt to discover
> the next winner. EPR’s count treats all voters [and candidates] according to the same set
> of rules.

[….]
K: I'm not referring to a maximum limit on the weight of winners, but
rather to what happens in this step (quoting from jpolrisk):

> Round 7 searches for the 5th winner. However, one cannot be found even by Round 8 and even after > all the available ACCEPTABLEs have been added to the remaining
EXCELLENTs, VERY GOODs, and GOODs.
> No evaluations of POOR or REJECT must be added to help elect any candidate. Therefore, the
> remaining winners must instead be discovered by lowering the threshold of 10 iteratively by
> subtracting 1 (one-at-a-time) until the remaining winners are discovered.

K: What I'm saying is that a better approach is to consider that, whenever
you get to the sort of exhaustion that makes this lowering of the
threshold necessary, then instead of lowering the threshold (of 10) and
continuing the method, you should lower it and *restart* the method.



S: It may be true that some other *threshold* could be use initially and would still produce the same results. However, if it were too low, counting each of the rounds could be needlessly more complicated and less revealing, e.g. round 1 might discover a large number of tied candidates, some with the same large set of EXCELLENTS, VERY GOODS, GOODS, & ACCEPTABLES; and other with different mixtures of these. Because only one can be elected during any give round, discovering this one would probably require many more uses of lot, and/or of the SCORE calculations already illustrated by the explanation in the article of how the tie is broken in Round 6:

* i.e. in Round 6, G is discovered to have 10 affirmed evaluations and is elected. Still, this is the result only after breaking the tie between G, I, and J because each has received 10 evaluations at this stage. In this case, the tie does not have to be broken by lot because G’s 10 is composed of the set of highest evaluations. That G’s are highest is discovered by counting the EXCELLENTs, VERY GOODs, and GOODs that each had received instead as SCORES, i.e. as 6, 5, and 4. Consequently, each tied candidate’s total score at this stage is G-50, I-46, and J-44.*



If so, the lower the threshold*, the more EPR would become like a Bucklin-SCORE method. If so, this in turn would needlessly prompt more citizens to vote strategically, as well as dilute the greater clarity of meaning and discernment that is offered by EPR.

In any case, we must remember that EPR aims to guarantee that each winner will have been elected only because she has been awarded the highest set of evaluations currently available from citizens. If so, this means that round 1 must start by counting only all the EXCELLENTs given to all the candidates. If at least one of the candidates receives EXCELLENTs from at least 1/7 of all the voters in a 7 seat election, it seems correct that this candidate must be seen as elected, i.e. given EPR’s above stated aim.



K: The point is that the first few winners had a higher bar to clear (the
threshold of 10), while the latter winners had a lower bar (required by [the fact]
that no [additional] winners are able to clear the high bar that the threshold of 10
poses). So if the bar is to be lowered, it should be lowered
consistently for all candidates, not just for those who came in last.



S: [Please also consider the relevant earlier response.] In this context, the threshold is not a *bar* to be elected. It is only an intuitively acceptable guide to when the group of remaining next lower evaluations must be added in order to attempt to discover the next winner.

K: I'm thinking of a situation like: suppose the threshold is x voters.
Suppose there are a number of candidates who have EXCELLENT from x-1
voters each, but they don't get elected because the threshold is x. EPR
moves to the next round instead, and some candidates with X+1 number of [EXCELLENTs plus]
VERY GOODs get elected, …



S: In any case, only one of these candidates could be elected by this round. So, the tie between them must be broken. Such ties must be broken by lot unless one of these candidate’s x+1 evaluations is composed of higher evaluations as counted by the SCORE method as already illustrated above.

K : ….but it's not enough to fill s seats.



S: For your own above example, as I understand it, the rounds that would follow using the procedure suggested by my article would go on carefully and appropriately to discover all the remaining *seats* (winners).



K: After this point, the threshold gets lowered and some of the EXCELLENT candidates
get elected, filling out the council; but it would be more fair ….



S: If EPR allows each citizen to guarantee that her vote will proportionately add to the voting power of the winner she values most, how is this unfair?



K: …. to the voters if the count was restarted after the threshold is lowered, so
that all the X-1 EXCELLENT candidates get elected instead.



S: If I understand you correctly, only if each of your tied candidate’s sets of EXCELLENTs & VERY GOODs were entirely given to him or her by entirely different sets of citizens, would each of these tied candidates certainly be elected by either using my proposed procedures, or the ones you might have in mind. However, to the extent that these tied candidates shared some citizens’ evaluations, the total number affirmed evaluations currently retained by any given formerly tied candidate could change. These changes might still allow them to be elected after all the GOODs and/or ACCEPTABLEs had been added to the count, or they might not be elected at all.

What do you think? I very much appreciate your thinking this through with me. Again, I very much look forward to your feedback.

Steve
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