[EM] Election-Methods Digest, Vol 207, Issue 9
steve bosworth
stevebosworth at hotmail.com
Tue Oct 5 21:11:45 PDT 2021
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Subject: Election-Methods Digest, Vol 207, Issue 9
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Today's Topics:
1. Re: Election-Methods Digest, Vol 207, Issue 3 (Forest Simmons)
2. Re: Better cardinal methods? (Richard Lung)
3. Re: Better cardinal methods? (Forest Simmons)
----------------------------------------------------------------------
FROM: Steve
TO: Forest
Re: Majority Judgment
Thank you for telling me about Andy Jennings' "Chiastic Approval (XA)".
However, please explain why do you say it is a "drawback" for MJ initionally to have a large number of "ties". You say this even when you also correctly say that the next steps in MJ count rationally and "cleaverly ... resolve such ties". Do you agree with me that this has the majoritarian advantage of guaranteeing that the winner is supported by at least 50% plus 1 of all the votes cast ,and is unique in both have the highest median grade and the largest number of grades equal to or above the value of this highest median grade?
Also, in what sense do you see XA as being "more robust" than MJ?
At the same time, unfortunately, XA seems to allow votes to be express merey by numbers. I understand MJ's use of word grades (Excellent,Very Good,... Reject) to be democratically superior because grades are more meaningfully and informatively expressive of the qualitative judgments that can be made by voters.
Also, correct me if I'm mistaken that XA does not guarantee that its winner will be elected with the support of a majority of all the votes (ballots) cast.
For the above reasons, I do not yet see why you said that: "The voter instructions and other features of the voter interface
environment for Jennings' method are identical to those of MJ." What do you think?
I look forward to our next dialogue.
Steve
Message: 1
Date: Tue, 5 Oct 2021 16:31:57 -0700
From: Forest Simmons <forest.simmons21 at gmail.com>
To: steve bosworth <stevebosworth at hotmail.com>
Cc: EM <Election-methods at lists.electorama.com>
Subject: Re: [EM] Election-Methods Digest, Vol 207, Issue 3
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Steve,
Great questions and suggestion!
However, in some venues not every voter has the patience to grade
potentially dozens if not hundreds of candidates as in past California
governor recall elections which were plenty cumbersome with FPTP style
ballots (which should have been voted and tallied under Approval rules). In
that context many more voters will have enough patience to vote in the
final round.
In my opinion MJ is a great improvement on most Cardinal Ratings/Score
based methods, but the certainty of tied median grades is a drawback
despite its signature clever method for resolving such ties.
A closely related but more robust method invented by Andy Jennings makes
ties vanishingly rare while preserving all of the advantages of MJ
including use of familiar, easy to understand grade style ballots with
minimal strategic incentive for grade inflation/exaggeration.
The voter instructions and other features of the voter interface
environment for Jennings' method are identical to those of MJ.
The method is called Chiastic Approval (XA) because of an X shaped (i.e.
Chi shaped) graphical interpretation showing how MJ, Approval, and XA are
related to the candidates' grade distributions.
[Those distributions are discontinuous graphs that stair step down through
the six grade levels. A vertical line through the middle of such a graph
crosses at the midrange approval cutoff point between acceptable and poor.
An horizontal line through the middle of the graph crosses it at the median
... which illustrates the ambiguity of the median, since an horizontal line
will either miss the stair stepping graph entirely, or will intersect it
along an entire line segment. On the other hand, a diagonal line of unit
slope will cross the graph at precisely one point .. at the instant it
crosses from below to above the graph. The descending distribution graph
and the ascending diagonal line (segment) form the shape of the Greek
letter chi.]
It is pleasant for election geeks to contemplate such schematic diagrams,
but the beauty will be lost on anybody else ... best to save it for those
who might appreciate it :-)
The algebraic representation will be even more of an imposition ... best to
shred any reference to it except as documentation of the software:
The distribution function F whose graph forms the descending staircase
alluded to above is defined as follows:
F(x) is the percentage of ballots that rate candidate C greater than or
equal to x ... as x increases F(x) decreases.
So the chiastic approval of candidate C is the greatest value of x such
F(x) is no greater than x.
Putting it all together we have ...
The chiastic approval for candidate C is the greatest value of x such that
x is less than or equal to the percentage of ballots that rate (i.e. grade)
candidate C at or above x.
I warned you!
How many of you understand the Huntingto-Hill method of apportionment? Yet
that is the official method for determining how many representatives each
state gets in Congress and the Electoral College. And people trust in it
unquestioningly just as they implicitly trust the medical pharmaceutical
complex.
Chiastic Approval is arguably easier to explain than MJ except perhaps at a
superficial level that avoids the tie breaking details of MJ.
Once you understand the beauty and efficiency of both Chiastic Approval and
Approval Sorted Margins it becomes apparent that no Condorcet compliant
deterministic social order (single winner order of finish) can surpass
XASM, Chiastic Approval Sorted Margins, IMHO:-)
Forest
El mar., 5 de oct. de 2021 11:33 a. m., steve bosworth <
stevebosworth at hotmail.com> escribi?:
>
> Today's Topics: Replacing Top Two primaries
>
> From: Steve Bosworth
> TO: Kevin Venzke
>
> Kevin Venzke wants to replace Top Two Primaries.
>
> Could not the objections to top two primaries be optimally satisfied by
> removing such primaries altogether, and instead electing the winner in the
> general election by using Majority Judgment (MJ)? Regardless of the
> number of candidates, MJ guarantees that the winner has received the
> highest median grade from at least 50% plus 1 of all the ballots cast. As
> you know, MJ invites each voter to judge the suitability for office of at
> least one of the candidates as either Excellent (*ideal*), Very Good,
> Good, Acceptable, Poor, or Reject (*entirely unsuitable*). Voters may
> give the same grade to any number of candidates. Each candidate who is not
> explicitly graded is counted as a ?Reject? by that voter. As a result, all
> candidates have the same number of evaluations but a different set of
> grades awarded from all voters. The MJ winner is the one who receives an
> absolute majority of all the grades equal to, or higher than, the highest *median
> grade* given to any candidate. This median grade can be found as follows:
>
> 1.
>
> Place all the grades given to each candidate, high to low, left to
> right in a row, with the name of each candidate on the left of each row.
> 2.
>
> The median grade for each candidate is in the middle of each row.
> Specifically, the middle grade for an odd number of voters, or the grade on
> the right in the middle for an even number of voters.
> 3.
>
> The winner is the candidate with the highest median grade. If more
> than one candidate has the same highest median grade, remove the current
> median grade from each tied candidate and start again at step 1 with those
> tied candidates.
>
> 4. What do you think?
> 5. Steve Bosworth (stevebosworth at hotmail.com
>
>
> ----
> Election-Methods mailing list - see https://electorama.com/em for list
> info
>
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Message: 2
Date: Wed, 6 Oct 2021 00:38:39 +0100
From: Richard Lung <voting at ukscientists.com>
To: Kristofer Munsterhjelm <km_elmet at t-online.de>
Cc: Andy Jennings <elections at jenningsstory.com>, Forest Simmons
<forest.simmons21 at gmail.com>, EM
<Election-methods at lists.electorama.com>
Subject: Re: [EM] Better cardinal methods?
Message-ID: <FB251D6D-334F-4801-8324-5635079EF76F at ukscientists.com>
Content-Type: text/plain; charset=us-ascii
Dear All,
But Elections are a statistic -- a sum of contingent choices. Votes are not in a logical relation to each other, such that there is some determinable right answer to who should be elected. Axiomatic deduction of a deterministic result is the reason why the Impossibility theorem is impossible -- it is a misconception of the nature of elections.
We can make probabilistic determinations of electing candidates, ranging from practically certain to completely indecisive. The most representative results depend on most representatively averaging the preference data. This avoids the usual social choice theory objections, that assume elections are analytic rather than synthetic.
Regards,
Richard Lung.
On 5 Oct 2021, at 10:46 pm, Kristofer Munsterhjelm <km_elmet at t-online.de> wrote:
> On 05.10.2021 04:54, Andy Jennings wrote:
> Forest,
>
> Thanks for your thoughts.
>
> I agree that there are many good ways to get cardinal information from
> voters on a valid interval scale, assuming that we don't try to compare
> intervals between voters. It seems that the cardinal information must be
> meaningful and it's a shame to throw it away (though I agree that the
> method should be invariant to affine transformations).
>
> Speaking of lottery methods, it's interesting that there is so much
> reluctance (including my gut reaction) to actually recommend a
> lottery-based method for use in real political elections. We want our
> elections to be deterministic, not influenced by chance in any way. But
> certainly there is chance in the process. Weather can influence turnout,
> as can traffic. There may be some voters that actually flip a coin in
> the voting booth. Cosmic rays have affected vote counts in the past
> (https://youtu.be/AaZ_RSt0KP8?t=44 <https://youtu.be/AaZ_RSt0KP8?t=44>).
> Websites like FiveThirtyEight report on the whole election season with
> probabilities. And sitting there watching outcomes on election night can
> definitely feel like games-of-chance-and-skill like the Olympics.
>
> So maybe we should just embrace it and try to convince people to use
> lottery methods.
If lotteries are on the table, then perhaps we should just dissolve the
electoral problem and go right to sortition. It certainly has appealing
corruption resistance properties :-)
But the problem of lotteries, I think, is that there's too much left to
chance. While every election leaves something to chance (as you've
correctly pointed out), it's not too much to destabilize the process. On
the other hand, if you have the simple random favorite lottery and 10%
of the voters vote for a dictator, then you have 10% chance of getting a
dictatorship.
One way of considering single-winner methods, I think, is that they try
to find the best outcome under the constraint of zero entropy.
Proportional representation methods might also need to compromise to
satisfy their seat limits. Perhaps it would be possible to create a
tunable entropy method where we set a maximum allowed entropy (or
variance), and it attempts to find the best outcome lottery subject to
this constraint. Such a constraint would help with the reluctance, I
think, as long as the threshold is set sufficiently low that there's no
chance of extreme upsets (like a dictator winning).
> Even if we trust the math that generates the lottery, maybe we just
> can't bring ourselves to believe that the final draw will not be rigged.
> I'm sure there are cryptographic methods for securely generating a
> random number between 0 and 1, but will the public trust them?
There was a thread about this on Reddit a while ago. There's a protocol
that goes like this:
Somehow pick a number of participants (they may be the whole electorate
or randomly chosen members of the public, or the representatives of the
previous term).
Each participant creates a sufficiently long random secret string and
publishes its cryptographic hash.
The participants (or the election officials) publish these hashes.
Once they're all published, each participant reveals his random string.
If they match their respective hashes, the strings are combined, and the
result is used as a seed for a CSPRNG.
This protocol works by forcing the participants to commit to their input
strings before they have any knowledge of the other strings. Thus they
can't adapt the inputs to fix a particular output.
Suppose there's a conspiracy to fix the output by bribing or coercing
the participants into selecting predetermined random strings. Then even
if a single member defects from the conspiracy, the chaotic nature of
the secure hash function makes the attack fail. If the combination
function is secure (e.g. a secure hash), then a conspiracy would in any
case have to use brute force to find a suitable set of strings. The
difficulty of this brute-forcing would depend on the entropy - e.g.
packing a majority of a sortition assembly of 100 would be prohibitive,
but changing the outcome of an election lottery with a few candidates
would be easier.
> Is the NIST randomness beacon trustworthy?
>
> In a small enough election, you could agree to use randomness from the
> next block mined on the bitcoin blockchain, but that runs into problems
> at the scale of a national election.
There have been proposals to use public data as entropy sources, e.g.
this one for financial data:
https://www.usenix.org/legacy/event/evtwote10/tech/full_papers/Clark.pdf
If multiple countries were to provide signed public randomness beacons,
they could be used as part of the protocol above; every country would
have to be collaborating to force the output. Number stations would
*almost* work, except they aren't signed.
-km
----
Election-Methods mailing list - see https://electorama.com/em for list info
------------------------------
Message: 3
Date: Tue, 5 Oct 2021 16:51:07 -0700
From: Forest Simmons <forest.simmons21 at gmail.com>
To: Richard Lung <voting at ukscientists.com>
Cc: Kristofer Munsterhjelm <km_elmet at t-online.de>, Andy Jennings
<elections at jenningsstory.com>, EM
<Election-methods at lists.electorama.com>
Subject: Re: [EM] Better cardinal methods?
Message-ID:
<CANUDvfq3JBvPQQxUt+yQmDorLfr-tEDdVvh7=2xQ_kHUy-Wm=w at mail.gmail.com>
Content-Type: text/plain; charset="utf-8"
Richard,
Thanks for stimulating my imagination!
Forest
El mar., 5 de oct. de 2021 4:38 p. m., Richard Lung <voting at ukscientists.com>
escribi?:
>
>
> Dear All,
>
> But Elections are a statistic -- a sum of contingent choices. Votes are
> not in a logical relation to each other, such that there is some
> determinable right answer to who should be elected. Axiomatic deduction of
> a deterministic result is the reason why the Impossibility theorem is
> impossible -- it is a misconception of the nature of elections.
>
> We can make probabilistic determinations of electing candidates, ranging
> from practically certain to completely indecisive. The most representative
> results depend on most representatively averaging the preference data. This
> avoids the usual social choice theory objections, that assume elections are
> analytic rather than synthetic.
>
> Regards,
> Richard Lung.
>
>
>
> On 5 Oct 2021, at 10:46 pm, Kristofer Munsterhjelm <km_elmet at t-online.de>
> wrote:
>
> > On 05.10.2021 04:54, Andy Jennings wrote:
> > Forest,
> >
> > Thanks for your thoughts.
> >
> > I agree that there are many good ways to get cardinal information from
> > voters on a valid interval scale, assuming that we don't try to compare
> > intervals between voters. It seems that the cardinal information must be
> > meaningful and it's a shame to throw it away (though I agree that the
> > method should be invariant to affine transformations).
> >
> > Speaking of lottery methods, it's interesting that there is so much
> > reluctance (including my gut reaction) to actually recommend a
> > lottery-based method for use in real political elections. We want our
> > elections to be deterministic, not influenced by chance in any way. But
> > certainly there is chance in the process. Weather can influence turnout,
> > as can traffic. There may be some voters that actually flip a coin in
> > the voting booth. Cosmic rays have affected vote counts in the past
> > (https://youtu.be/AaZ_RSt0KP8?t=44 <https://youtu.be/AaZ_RSt0KP8?t=44>).
> > Websites like FiveThirtyEight report on the whole election season with
> > probabilities. And sitting there watching outcomes on election night can
> > definitely feel like games-of-chance-and-skill like the Olympics.
> >
> > So maybe we should just embrace it and try to convince people to use
> > lottery methods.
>
> If lotteries are on the table, then perhaps we should just dissolve the
> electoral problem and go right to sortition. It certainly has appealing
> corruption resistance properties :-)
>
> But the problem of lotteries, I think, is that there's too much left to
> chance. While every election leaves something to chance (as you've
> correctly pointed out), it's not too much to destabilize the process. On
> the other hand, if you have the simple random favorite lottery and 10%
> of the voters vote for a dictator, then you have 10% chance of getting a
> dictatorship.
>
> One way of considering single-winner methods, I think, is that they try
> to find the best outcome under the constraint of zero entropy.
> Proportional representation methods might also need to compromise to
> satisfy their seat limits. Perhaps it would be possible to create a
> tunable entropy method where we set a maximum allowed entropy (or
> variance), and it attempts to find the best outcome lottery subject to
> this constraint. Such a constraint would help with the reluctance, I
> think, as long as the threshold is set sufficiently low that there's no
> chance of extreme upsets (like a dictator winning).
>
> > Even if we trust the math that generates the lottery, maybe we just
> > can't bring ourselves to believe that the final draw will not be rigged.
> > I'm sure there are cryptographic methods for securely generating a
> > random number between 0 and 1, but will the public trust them?
>
> There was a thread about this on Reddit a while ago. There's a protocol
> that goes like this:
>
> Somehow pick a number of participants (they may be the whole electorate
> or randomly chosen members of the public, or the representatives of the
> previous term).
>
> Each participant creates a sufficiently long random secret string and
> publishes its cryptographic hash.
>
> The participants (or the election officials) publish these hashes.
>
> Once they're all published, each participant reveals his random string.
> If they match their respective hashes, the strings are combined, and the
> result is used as a seed for a CSPRNG.
>
> This protocol works by forcing the participants to commit to their input
> strings before they have any knowledge of the other strings. Thus they
> can't adapt the inputs to fix a particular output.
>
> Suppose there's a conspiracy to fix the output by bribing or coercing
> the participants into selecting predetermined random strings. Then even
> if a single member defects from the conspiracy, the chaotic nature of
> the secure hash function makes the attack fail. If the combination
> function is secure (e.g. a secure hash), then a conspiracy would in any
> case have to use brute force to find a suitable set of strings. The
> difficulty of this brute-forcing would depend on the entropy - e.g.
> packing a majority of a sortition assembly of 100 would be prohibitive,
> but changing the outcome of an election lottery with a few candidates
> would be easier.
>
> > Is the NIST randomness beacon trustworthy?
> >
> > In a small enough election, you could agree to use randomness from the
> > next block mined on the bitcoin blockchain, but that runs into problems
> > at the scale of a national election.
>
> There have been proposals to use public data as entropy sources, e.g.
> this one for financial data:
> https://www.usenix.org/legacy/event/evtwote10/tech/full_papers/Clark.pdf
>
> If multiple countries were to provide signed public randomness beacons,
> they could be used as part of the protocol above; every country would
> have to be collaborating to force the output. Number stations would
> *almost* work, except they aren't signed.
>
> -km
> ----
> Election-Methods mailing list - see https://electorama.com/em for list
> info
>
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