A couple questions for D. Smith if you are willing.

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stvforc...@gmail.com

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Jan 5, 2017, 7:27:22 PM1/5/17
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We're debating IRV and AV, and your regret came up.  I had a few questions about it if you are willing to elaborate for me.

1) My programming knowledge is limited.  However with the few CS classes I have taken, I know that when writing programs such as the one you have, you need to set variables.  I am aware that you have the final score set up as the difference between perfect and the result of the voter.  However how do you define perfect utility?  In your code, what did you use as the variables for utility/scores?  What did you consider to be a "positive" utility factor, or a "negative" utility factor?

2) It appears that the results are all seemingly linear or parabolic in nature as we go along right up until you included "infinite issues".  Then the numbers jump massive standard deviations from the mean.  The results are usually in violation of the previous patterns as well.  For example a line of scores might be decreasing from 2 candidates to 5, and further decreasing from zero issues to four.  But then infinite is tossed in, the trend is completely reversed, and we are given rather outlandish numbers that don't match with the rest of the system.  It is the equivalent of using a domain of all real numbers with formula Y=(X^3)((X-5)^4)+3 and we are looking at values where X>2.  It decreases linearly, but then reverses and skyrockets to infinity.  Now most mathematicians and statisticians would never include any part of the infinite exposition in their data.  They would restrict the domain to 2<X<5 so as to obtain meaningful data.  But you did not.  Why did you include "infinite" data points when these points were ALWAYS odd balls, sometimes extreme outliers, and so very different from the patterns and numbers you obtained everywhere else?  Wouldn't a statistician have eliminated and excluded these from your end results?

3) Why did you opt to use Australia style rules for IRV instead of the much more common Ireland/main/US methods?  Given that Australia's mandatory voting rules, and mandatory full ballot rules would force individuals to rank (and thus support) candidates they did not actually support, doesn't this arrive at a different result than you would have had you used an IRV style where candidates could stop supporting candidates at their own threshold?

4) This is also linked to the infinite issues I mentioned above.  I notice that Range voting is treated very favorably by this factor.  In almost all cases infinite issues with any level of voter ignorance causes the range voting score to plummet, even if it was building from 2 issues to 4. This reversal does not agree with your other data points.  Do you have an explanation for this regularly occurring phenomenon?

Thanks in advance!

Chris 

William Waugh

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Jan 5, 2017, 7:54:04 PM1/5/17
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Maybe I can save him some typing by answering the first question.

On Thursday, January 5, 2017 at 7:27:22 PM UTC-5, stvforc...@gmail.com wrote:
...
1) ...  I am aware that you have the final score set up as the difference between perfect and the result of the voter.  However how do you define perfect utility?  In your code, what did you use as the variables for utility/scores?  What did you consider to be a "positive" utility factor, or a "negative" utility factor?

I think what he does is this. He starts with some more or less random assumption about valuations placed by a bunch of hypothetical voters on the various candidates' winning (the candidates are also hypothetical). The social utility of someone winning is taken to be the sum over the voters' valuations of that candidate winning. The "magical" best choice is the candidate whose winning that would maximize that utility. Regret is the difference between the utility of the winner chosen by the voting system under test and the utility of the magical best winner. This exercise is repeated many times with different random numbers controlling the cases, and some statistical measures are then applied to the results.

Warren D Smith

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Jan 5, 2017, 8:37:56 PM1/5/17
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On 1/5/17, stvforc...@gmail.com <stvforc...@gmail.com> wrote:
> We're debating IRV and AV, and your regret came up. I had a few questions
> about it if you are willing to elaborate for me.
>
> 1) My programming knowledge is limited. However with the few CS classes I
> have taken, I know that when writing programs such as the one you have, you
>
> need to set variables. I am aware that you have the final score set up as
> the difference between perfect and the result of the voter. However how do
>
> you define perfect utility? In your code, what did you use as the
> variables for utility/scores? What did you consider to be a "positive"
> utility factor, or a "negative" utility factor?

--umm. First of all, maybe your questions are answered
already on one of these web pages:

http://rangevoting.org/BayRegDum.html
http://rangevoting.org/BRmulti.html

voters somehow have utilities for election of each candidate.
These numbers can be regarded as input to the BR calculator.

There also was a paper:
http://rangevoting.org/WarrenSmithPages/homepage/works.html
see #56

> 2) It appears that the results are all seemingly linear or parabolic in
> nature as we go along right up until you included "infinite issues".

--I have no idea what "as we go along right up" or "the results" mean.

> Then
> the numbers jump massive standard deviations from the mean.

--What numbers? Mean of what?

> The results
> are usually in violation of the previous patterns as well. For example a
> line of scores might be decreasing from 2 candidates to 5, and further
> decreasing from zero issues to four. But then infinite is tossed in, the
> trend is completely reversed, and we are given rather outlandish numbers
> that don't match with the rest of the system. It is the equivalent of
> using a domain of all real numbers with formula Y=(X^3)((X-5)^4)+3 and we
> are looking at values where X>2. It decreases linearly, but then reverses
> and skyrockets to infinity. Now most mathematicians and statisticians
> would never include any part of the infinite exposition in their data.
> They would restrict the domain to 2<X<5 so as to obtain meaningful data.
> But you did not. Why did you include "infinite" data points when these
> points were ALWAYS odd balls, sometimes extreme outliers, and so very
> different from the patterns and numbers you obtained everywhere else?
> Wouldn't a statistician have eliminated and excluded these from your end
> results?

--not sure what you are talking about.

> 3) Why did you opt to use Australia style rules for IRV instead of the much
>
> more common Ireland/main/US methods?

--"more common" and "outside Australia"
are two contradictory phrases. You just contradicted yourself.
Australia has held more IRV elections than the rest of the world combined.
Also, you seem to be under the impression there are some sort
of standard US rules for IRV. There are not. In my BR codes I
used IRV with full rank orderings.

> Given that Australia's mandatory
> voting rules, and mandatory full ballot rules would force individuals to
> rank (and thus support) candidates they did not actually support, doesn't
> this arrive at a different result than you would have had you used an IRV
> style where candidates could stop supporting candidates at their own
> threshold?

--quite probably IRV with full orderings, and IRV with
truncated orderings (several possible truncation flavors) would
indeed yield different BRs.
The BR code could be redone to also allow the latter kind(s)
of IRV as yet another competing voting method, which first
would require defining voter "honest" and "strategic" behaviors
for that kind of ballot. Nobody ever suggested those
2 definitions, which was why I did not do that. My guess, and it
is only a guess, is that usually IRV will perform better
(smaller BR) if voters provide full orderings rather than truncating,
because they then provide more information, which presumably on
average will help provide better election results. However it
could be counterargued that if each voter always truncated
at the "optimal" place (whatever that means for that voter)
including not truncating at all as an option,
we ought to do better than "never truncate"
and the ballots will actually provide MORE information.
But bad ways of truncating are a lot more common than
good ways of truncating, so I suspect
truncation usually will hurt, but perhaps with enough wisdom and
tuning of the truncation location (and decision whether
to truncate) IRV could be improved. Needless to say, nobody has ever,
anywhere in the literature that I am aware of, ever analysed
what the "optimum truncation strategy" might be. If you can find
such an analysis anywhere please let me know.

> 4) This is also linked to the infinite issues I mentioned above. I notice
> that Range voting is treated very favorably by this factor.

--"factor"?

> In almost all
> cases infinite issues with any level of voter ignorance causes the range
> voting score to plummet, even if it was building from 2 issues to 4. This
> reversal does not agree with your other data points. Do you have an
> explanation for this regularly occurring phenomenon?

--Sorry for my cluelessness, but
I do not know what you are talking about.

> Thanks in advance!
>
> Chris
>
> --
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--
Warren D. Smith
http://RangeVoting.org <-- add your endorsement (by clicking
"endorse" as 1st step)

Warren D Smith

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Jan 5, 2017, 8:43:03 PM1/5/17
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Also I should remark that most IRV proponents, such as FairVote, generally
recommend that voters always provide full orderings, and try to
encourage that and discourage IRV ballot truncation.

Now if those same proponents at the same time would like
to argue that I have unfairly hurt IRV's evaluation by forcing its
voters to provide
full orderings -- since IRV would have performed better if they had truncated
-- well, that would be a surprise since then those IRV proponents would
be massively contradicting themselves.

(Which they often have done, historically, but this would be an additional such
contradiction.)

stvforc...@gmail.com

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Jan 6, 2017, 9:49:31 AM1/6/17
to The Center for Election Science
For #1 - Thank you.  I will look at those sites.  I did a quick search prior to writing, but I couldn't find it easily thus I just decided to ask directly.


#2 - Allow me to simply copy and paste from your data then.  For clarity sake, I'm going to only continue one point #2 leaving point 3 and 4 aside for the moment.  It will help keep the conversation on track.

Your data has some rather drastic abnormalities and it happens exclusively when you shift from a numerical value for issues, to infinite issues.  Here are some examples:


200 voters, 1 issue, 99 ignorance:
10 |  1.14353   1.73402   2.11705   2.40098   
11 |  1.14353   1.73841   2.12829   2.42353   
12 |  1.14323   1.79825   2.22756   2.52766   
13 |  1.30423   1.95194   2.37133   2.67611   
14 |  1.31709   1.97563   2.39908   2.71050   
15 |  2.63451   3.95035   4.79655   5.41547   
16 |  1.14353   1.69885   2.06326   2.33086   
17 |  1.14353   1.72265   2.08869   2.36298

200 voters, 2 issues, 99 ignorance
10 |  0.88038   1.32844   1.63188   1.84345   
11 |  0.88038   1.33585   1.63582   1.84912   
12 |  0.87997   1.36885   1.68600   1.91402   
13 |  0.96744   1.45804   1.76898   1.99551   
14 |  0.97695   1.47021   1.78572   2.01165   
15 |  1.95559   2.93559   3.57001   4.02250   
16 |  0.88038   1.30893   1.59450   1.80465   
17 |  0.88038   1.32445   1.60826   1.81970

   

200 voters, 4 issues, 99 ignorance
10 |  0.64469   0.97340   1.18606   1.34317
11 |  0.64469   0.97512   1.18676   1.34773   
12 |  0.64487   0.99196   1.21658   1.37956   
13 |  0.68870   1.03447   1.25808   1.41969   
14 |  0.69462   1.04192   1.26548   1.42748   
15 |  1.38734   2.08346   2.53237   2.85406   
16 |  0.64469   0.96335   1.17169   1.32409   
17 |  0.64469   0.96780   1.17622   1.33184

Notice how as the number of issues increases, the overall "score" for every category trends downwards (Meaning increase in overall utility).  This trend is universal in your data.  However when you jump from 4 issues to "infinite" issues, we see this downward trend reverse drastically. . .


10 |  1.62043   3.12970   4.45909   5.57267   
11 |  1.62043   3.25451   4.70978   5.97823   

12 |  1.62330   5.61193   8.21399  10.06463   

13 |  7.41816  11.10125  13.50752  15.28285   

14 |  7.97718  11.94536  14.52958  16.42629   

15 | 15.94065  23.92663  29.11791  32.86929   

16 |  1.62043   1.84531   2.38968   2.83686   

17 |  1.62043   2.64512   3.36122   3.89010


16 |  1.62043   1.84531   2.38968   2.83686   

17 |  1.62043   2.64512   3.36122   3.89010   

18 |  1.62043   2.64512   3.34779   3.88619   

26 |  1.62043   8.79597  11.38676  13.24482

So my question is this, if the data is trending downwards regularly and without exception, and all the points as you move from 1, to 2, to 3 to 4 are close to one another (within 1 standard deviation), why did you choose to include "infinite issues" when that data point clearly bucks the trend of the others, and suddenly we have points so far away from the mean of the previous points that it is almost 10 SD away?  In statistics the 68, 95, 99 rule states that 99% of the data with normal distribution should lie within 3 SD from mean.  Anything outside of this is considered to be an outlier data point and is ignored.  Yet you opted to include this in your results.

I'm curious as to your reason for this choice as it clearly and dramatically affects the outcome of your test.



Part 2 - on a related note, range voting does something very odd when you move from any integer (n : N is an element of the Reals), to n being infinite.  Range voting's score increases slightly as you proceed from two candidates, to three, to four regardless of the value of n so long as n is an element of the reals.  But when you switch to n being infinite, the range voting score decreases from candidates moving from 2, to 3, to 4, to 5.

Examples:

Issue Based Utilities (4 Issues). IgnoranceQ=0.99. (Identical.) 200 voters.

system|2 canddts 3 canddts 4 canddts 5 canddts
------+--------- --------- --------- ---------
    0 |  0.64469   0.95884   1.16057   1.30883

Random-Normal(0,1) Utilities (infinite issue limit). IgnoranceQ=0.99. (Identical.) 200 voters.

system|2 canddts 3 canddts 4 canddts 5 canddts
------+--------- --------- --------- ---------
    0 |  1.62043   1.36920   1.17042   1.03423


You opted to include this data in every one of your examples, and in your results yet the general trend of the data is completely the reverse of the previous established pattern.  With any numerical value of issues where n = element of reals, range voting's score increases.  With infinite issues, it suddenly reverses and decreases. 

My question for part 2 is the same as part one.  Clearly your data is altered, not just in scope, but in direction and orientation as well.  Thus the infinite data point isn't useful in measuring against the other numerical data points.  Based on this data, my best guess for the mathematical function of your program is that it behaves in some fashion like the graph Y = (X^3)((X-5)^4)+3 in so much as it gives good data within a small domain (2<X<5) but after this point it increases exponentially and in the opposite direction to the trend.  Most mathematicians and statisticians know not to use data from this end point as it is a statistical outlier and will drastically skew their results.  You opted to keep it in.  I'm curious as to your reasoning for this decision.


stvforc...@gmail.com

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Jan 6, 2017, 10:06:12 AM1/6/17
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RE: topic #1 - Thank you for the links but I'm afraid they did not answer my question.  They did however provide me with an example I can show you to illustrate my question.  You wrote, "The sum over all voters V of their utility for X, maximized over all candidates X, is the "optimum societal utility" which would have been achieved if the election system had magically chosen the societally best candidate. "

 My question is how is this "best" candidate achieved in the program?  Is there criteria that they scored 100 on?  hmm . . . I'm trying to figure out how to word it to make my question clear.  In short, you have a philosophy of truth (for you).  This philosophy is described by you on this forum thusly:

"Many of my sims do include mild versions of utility monsters where, say, some 1 guy has 3X the utility of some other guy.  That is pretty common. As a matter of philosophy unrelated to reality I guess I would say that if any utility monster really existed then he/she really should have and should deserve to have, a huge affect on elections, and all of society should dedicate itself toward making that one guy very very happy.    And in fact, that does happen in the natural world, the utility monster is the queen bee, and all the other bees care intensely about the queen.  In bee elections the queen does not vote (because she has no information) but the other bees, to the extent they have feelings and thoughts and a system of morality, I am sure devote a great amount of them toward the queen."

Now to be clear I am not debating the validity or error of this philosophy.  What I am asking is while you were deriving and writing this program, was this the philosophy you used as guidelines for designing the "societally best candidate"? What would the program say would be the best type of candidate?  Perhaps I am asking the wrong question and if so please feel free to explain.  As I said, my knowledge of CS is limited.

stvforc...@gmail.com

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Jan 6, 2017, 10:23:53 AM1/6/17
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I have included a photo of the graph of Y= (X^3)((X-5)^4)+3.  For some reason it is hidden under the first "show quoted text" in that post.  I will try and attach it here as well.

stvforc...@gmail.com

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Jan 6, 2017, 12:53:55 PM1/6/17
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Sorry, I just keep on posting.  I spoke at length with others about your reply to point 3, and I think I understand.  IRV with a full ballot vs IRV with a truncated ballot, given pure mathematics, the full ballot, and the model of the utility makes sense.  Where I was having issues was that for me, being forced to fill out a full ballot and "support" candidates I did not like would give me "negative" happiness.  It was annoy me and piss me off.  But there is no way to measure this in your model.  It is the "human" element, which is impossible to quantify.  Hence why this model of yours strikes me as having errors with regard to the IRV component.  It would also exclude the "Anti-utility" of voters who desired a majority supported candidate but did not get that regardless of the placement of THEIR candidate on the ballot as we are currently seeing with Hillary V Trump and the whole popular vote/electoral college debacle.  In short, the manner in which you have measured utility is very precise mathematically, but excludes factors, which I fully acknowledge, are impossible to program.

I just wanted to let you know I really did think about your response to #3, and I have a much better understanding now.  Thank you.  I am looking forward to hearing about point 2 in similar detail.

PS - I also think I understand the answer to question 1 now as well so feel free to ignore it.




On Thursday, January 5, 2017 at 6:37:56 PM UTC-7, Warren D. Smith (CRV cofounder, http://RangeVoting.org) wrote:

Warren D Smith

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Jan 6, 2017, 3:19:08 PM1/6/17
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On 1/6/17, stvforc...@gmail.com <stvforc...@gmail.com> wrote:
> For #1 - Thank you. I will look at those sites. I did a quick search
> prior to writing, but I couldn't find it easily thus I just decided to ask
> directly.


--I'm not fully sure I understand, but let's take a stab.
The "infinite number of issues" case actually is equivalent to
random normal utilities, i.e. that each voter's utility for each candidate,
is an i.i.d. random normal. There kind of are no issues anymore
even though it is equiv. to infinite number of them.
This is (due to central limit
theorem) if all utility contributions from the issues,
sum and are independent -- which is true for some spatial politics
models but not others. E.g. it would NOT be true if utility is
an generic arbitrary function of voter-candidate distance. But it
is true if utility is L2 distance itself, or is voter-candidate dot-product.

Any trend you see for 1,2,3,4 issues... is not necessarily meaning much
when we get to infinity. For example you had mentioned linear or
quadratic extrapolation as (I presume) a function of the number
of issues. Well, of course, almost any linear or quadratic would predict
+-infinity. But of course, the truth is finite. Therefore, you know a priori
that any attempt to make such an extrapolation, is going to be total garbage.
If you then find that the infinite issues result does not meet naive
expectations, this is therefore not a surprise.

Also, if regrets have been normalized so that "random winner" has regret=1
always (I did not check whether that was the case for the tables you cite),
that's another thing.

Anyhow, so there seem to be two possible explanations:

(a) the infinite-issues result just does not obey naive expectations,
which if so does not seem a big surprise to me, nor should it to you;

(b) I was wrong to call this the infinite-issues limit, because I
mis-applied (or too quickly without enough thinking applied) the
central limit theorem. Which might have happened, in the sense
I might have done it right, but later changed the software to use
a different function of distance, or something, at which point
it was no longer true to call it the infinite issues limit. This is
definitely the case in later versions of the software which went beyond
my original paper by using more general kinds of utility, i.e. which
indeed permitted arbitrary functions of distance.

OK, checking my paper
http://rangevoting.org/WarrenSmithPages/homepage/rangevote.pdf
page 18,
it sounds like I did it right re (b) so the presumed answer is (a).

> Your data has some rather drastic abnormalities and it happens exclusively
> when you shift from a numerical value for issues, to infinite issues. Here
> are some examples:

--well, why is it a surprise to get a drastic change when we go from 4 to
infinite number of issues? I mean, that sounds drastic to me.

> In statistics the 68, 95, 99
> rule states that 99% of the data with normal distribution should lie within
> 3 SD from mean. Anything outside of this is considered to be an outlier
> data point and is ignored. Yet you opted to include this in your
> results.

--huh? There is no normal distribution, if I understand you aright.
We have numbers. They are not from a normal distribution, they are from
a voting simulator. If one foolishly regarded them all as randoms from
a normal distrib, then you'd get crazy notions. So: Not a surprise,
that this is exactly what happens.

stvforc...@gmail.com

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Jan 7, 2017, 10:12:32 AM1/7/17
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So my first and foremost question still remains.

If you are making the case, as it seems you are, that the infinite numbers have nothing to do with cases 1-4 (I can accept this) . . . why did you bother including them in your data?

I happen to agree with you when you wrote," But of course, the truth is finite.  Therefore, you know a priori
that any attempt to make such an extrapolation, is going to be total garbage."


But if we are concerned about the finite truth, and real possibilities in life, why did you include the infinite data at all, especially as you agree that the infinite issues creates "Drastic change" from the other finite numbers you used?

Why did you include infinite numbers as almost 20% of your data?  If the numbers are impossible in real life, and the results are a "drastic change", why are they included?  Why not stick with actual numbers which could happen?

Warren D Smith

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Jan 7, 2017, 4:56:27 PM1/7/17
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On 1/7/17, stvforc...@gmail.com <stvforc...@gmail.com> wrote:
> So my first and foremost question still remains.
>
> If you are making the case, as it seems you are, that the infinite numbers
> have nothing to do with cases 1-4 (I can accept this) . . . why did you
> bother including them in your data?

--well, I thought they were interesting.
I however do not think it is best to regard them foremost as
"infinite number of issues limit"
(even though this technically does seem a valid interpretation)
because that can risk distracting you.

For practical purposes they are best regarded
as "each voter has an independent random-normal utility for each candidate."
When one puts it that way, it seems like that is a simple
model of some genuine interest.

If we then say "...and this happens to be equivalent to the
infinite-issues limit," that sounds cute, but really, who directly cares?
Because it seems unlikely this infinite-issues limit actually matters
much for real life as such?

But
(a) maybe it does matter, so it is worth at least mentioning
this additional interpretation;
(b) if I give you data for 1,2,3,4 and infinity issues, that
allows you at least to try to draw a curve that fits thru those
5 data points, thus allowing you to at least dream you know
roughly what happens for any other number (say 9) of
issues.
If I had not given you the infinity datapoint then as you yourself
said, you would have been more likely to have
gotten wrong impressions about the behavior for (say) 9.

-------

Of course, another possibility looming over all this always is,
my program has bugs and some result or subset of
my results was just wrong. Well, I tend to doubt it
had too many bugs... it isn't all that complicated...
and I did years later write a followup
redone expanded version of the program (IEVS, available public source)
and when I did so I found only 1 bug, which did not matter for
the present purpose (it was factor-2 error...)...
and there have been others who independently wrote similar programs
finding similar results... but there seems no way I can provide
perfect confidence in the validity of my or their computer programs...

Abd ul-Rahman Lomax

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Jan 7, 2017, 6:47:13 PM1/7/17
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At 12:53 PM 1/6/2017, stvforc...@gmail.com wrote:
>Sorry, I just keep on posting. I spoke at
>length with others about your reply to point 3,
>and I think I understand. IRV with a full
>ballot vs IRV with a truncated ballot, given
>pure mathematics, the full ballot, and the model
>of the utility makes sense. Where I was having
>issues was that for me, being forced to fill out
>a full ballot and "support" candidates I did not
>like would give me "negative" happiness. It
>was annoy me and piss me off. But there is no
>way to measure this in your model. It is the
>"human" element, which is impossible to
>quantify. Hence why this model of yours
>strikes me as having errors with regard to the
>IRV component. It would also exclude the
>"Anti-utility" of voters who desired a majority
>supported candidate but did not get that
>regardless of the placement of THEIR candidate
>on the ballot as we are currently seeing with
>Hillary V Trump and the whole popular
>vote/electoral college debacle. In short, the
>manner in which you have measured utility is
>very precise mathematically, but excludes
>factors, which I fully acknowledge, are impossible to program.

There is a series of issues raised. Ballot design
is not what Warren studied in his Bayesian regret
work, though he may have made assumptions about
how voters would fill out ballots. I.e., he did a
study with full rank ordering. This could be
compared with other studies where there was
truncation. It is a characteristic of the real
worled that actions have effects. If a voting
system creates some loss of "happiness" for the
voter if they vote a certain way, they may be
"pissed off," but they might also be pissed off
about the weather and how long it takes for the
sun to rise. And it's just about as useful.

Consider IRV: if you have no preference among the
less-preferred candidates, it does you no harm to
truncate, unless the voting system requires you
to rank all candidates, which is true in some
places in Australia, not all. I consider that
rude and coercive and a Bad Idea. That Warren
used full ranking is simply studying how the
system works if voters are all ranked. If outcome
is worsened by full ranking, something is very
odd about the system. I do know of one situation
where full ranking, when there is no preference, causes harm.

Under Robert's Rules of Order's suggested
Preferential Voting System -- which is basically
IRV, but with one difference from most
implementations -- if a candidate does not
receive a majority of all votes cast -- and
"vote" means, under those rules, a ballot with
any kind of mark on it -- then the candidate
cannot be elected. If no candidate receives at
least a majority, then the election fails and
must be repeated. FairVote touts the Roberts
Rules suggestion -- it is not actually a
recommendation -- but ignores (and tried to
suppress) information that shows a fundamental
difference. After all, IRV is sold on the basis
that a repeated election is not needed. It was
also sold as supporting "majority results," but
majority of what? Majority of ballots containing
votes for the candidates remaining in the last
round counted. Not of all voters. And so IRV can
elect candidates not supported by a majority!

However, if the rules require a true majority,
then IRV is just a little less dangerous.

Warren's approach to the study of voting system
performance is the only relatively objective
analysis I know. So what is this "infinite"
business? I think there is some misunderstanding
here. Let's start with utility, and specifically
the utility outcome for a single person.

In real life, there is no clear definition of
utility. I prefer to think of preference
strength, which is always a comparison. Ranked
voting systems assume a "preference order," and
equate the steps in it, which neglects something
crucial in real life, preference strength.
Preference without any measure of strength can lead to some weird results.

Consider the type of election that the Borda
supporter suggested showed some kind of Bad Results from Score:

99: A,0 B,99 C,100
1: A,0 B,100, C,0

B wins in straight Score because, because the
strong preference for B by that single voter
(slightly) outweighs the very weak preference of
all the other voters. That was considered some
sort of terrible outcome, but nobody would
actualy be distressed by the outcome. A
preference of 100:99 is quite weak. Unless A is
truly awful, like a Hell result, distorting the
election badly. That is a candidate set problem.
But what if the election is just B and C? This is
the problem. In the real world, preference
strength does matter. It determines who shows up
to vote. If those utilities invented in that
example were real and proportional and
commensurable, B is actually, slightly, the best
outcome. B is well-supported by everyone, whereas
C leaves one out in the cold. Then we make up
stories about that single voter being a liar and a strategic voter.

However, these are just simulated utilities.
There are many models. One way to look at the
simulated utilities is to imagine an auction.
What would a voter pay for the election of a
candidate, compared to a lottery among all the candidates?

Should the utilities for candidates be limited in
range? Well, realistically, they must be. If
there were an infinite preference held by a
single voter, that would determine the election.
Infinite preference occurs to me as a kind of insanity.

In studying voting systems, the first level of
study will properly, my opinion, assume that we
have an electorate that wants a fair election,
that this is a value to them. They actually do
want the greatest good for the greatest number,
not solely their own benefit. (This is normal for
humans, in spite of what we sometimes think.)

We will then, setting up simulated utilities,
consider a Heaven-Hell scale where most
candidates will fall in the middle. This is not
how they will vote, rather they will normalize,
at least to some degree, so that they may express
preferences and exercise voting power. Yet if
everyone were to vote on a Score ballot that
allowed that kind of preference statement, with
true utilities, it's fairly obvious that the
election would maximize overall satisfaction. I
would have raw utilities be on a Heaven-Hell
scale. A more sophisticated system would have
different voters havin actually differing full
preference strengths. Remember, this is not a
voting system yet, it is a device for studying
overall social utility. Real people have
differing levels of political involvement and for
some, it is quite rational to not vote at all.

Indeed, one of the reasons why ordinary top-two
runoff voting flips results in about a third of
runoffs (from the top two based on the first
ballot, which is single-vote) is that many voters
don't have a strong preference between the top
two, so they don't show, leaving an electorate
with stronger preferences, and thus this actually
pushes results toward *sincere score,* since
whether or not voters show up is, absent
coercion, a sincere voting practice in the U.S.
And a good reason why coerced voting and full
ranking is a poor idea, probably damaging real results.

So we have a set of preferences. Now, what kind
of scale do we use for this. Apparently Warren
uses real numbers in a range, and does not
specifically limit the resolution to some small
value. This, then, allows more refined study of
preference strength, which he assumes will be
distributed, not just coarse. This allows the
similated voters to have preferences that do not
represent a large jump in preference strength. As
long as the preference is distinguishable, this
increases the reality of the simulation.

There is a limit to that, but it is at no
specific and clear place. My sense is that in
ordinary elections, the difference between, say,
67% of full range and 68% would be
indistinguishable. It might vary from day to day,
easily, if I have to make a choice. In a coarse
system, I would probably want to rate or rank
these equally, because that would be closer to a
true expression. I really don't care which is
elected. However, if there are only two
candidates, and I do show up and vote -- for
unrelated reasons -- would I rate them 67/100 and
68/100? It has often been said that this is bad,
somehow. What it is, in fact, in a contested election, is a partial abstention.

In any case, once a set of simulated utilities is
chosen, and the more it is set up to match what
we might want to optimize in the real world, the
better -- this requires not using a very coarse
scale, like utilities from 0 to 5 -- we can then
use the utilities to run a simulated election.
Warren does at least two kinds of simulations for
voting systems. He does a fully-sincere study
first. In Score Voting, voters just vote their
closest rating for each candidate, without
consideration of strategy. In this voting, the
vote for each candidate is independent of the candidate set.

In real elections, of course, this is not going
to happen. If there is a truly bad candidate whom
I detest, I may shove the ratings of all other
candidates up. To make this easier, I would
actually have a score ballot with ratings of -N
to +N, with a postive number indicating approval
of the candidates, at least to a minimal degree,
0 indifference, and negative votes disapproval.
(It is possible then to require majority
approval, or alternatively, majority approval
including the 0 votes. This would really mean the
absence of majority *disapproval.*)

In ranked systems, strategy becomes more
important. Failure to applyl strategy in Score
voting might possibly cause harm, sometimes, but,
practically by definition *not much harm.* In
ranked systems, it can cause much more harm.
Consider an IRV ballot with a lot of candidates.
You only approve of one or two. So you vote for
those. Unfortunately, all IRV systems I have seen
lock out equal ranking. Why? ... But one
candidate you detest. This, then, forces you to
rank all the candidates! Even though you have no
preference among all those intermediate candidates.

Bayesian Regret analysis allows the study of
voting systems under conditions that can simulate
real voting to a degree. What we have seen from a
study of strategic voting is that strategic
voting may help the individual voter, but harm
overall social benefit. So we think strategic
voting is bad. It is not. It is a voter using the
system-as-it-is to as an expression of power.
Strategic voting in range is almost an oxymoron,
because, while it can seem to cause a benefit in
some way or other, it can also cause harm. If you
actually prefer A>B>C with equal preference
strength, but vote max score for A and min for B
and C, as a "strategic vote," you risk a loss to
C because you failed to express your preference
for B over C. If your preferences actually are
equally distributed, that is, according to my
study, the optimal zero-knowledge vote. But we
don't have zero knowledge, so we adjust the
utilities to put preference strength where we
think it will make a difference. This, then, is
voting, not absolute utilities, but Von
Neumann-Morganstern utilities, modified by
expectations. And that was shown to be the only
system that beats Arrow's theorem.

(if utilities are truncated into a narrow range
or have coarse resolution, this must create error in the system.)

To my mind, the whole exercise is academic,
because there are far better systems for creating
consensus governance, at least in theory. They
have not been shown, yet, to function as formal
systems on a large scale, though they resemble
informal social structures that are known to
work. I suggested that those interested in voting
systems use these methods for internal
decision-making, to study how they work in actual
practice. Asset Voting is one such technique. It
would revolutionize how human organizations are created and function.



stvforc...@gmail.com

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Jan 11, 2017, 1:11:17 PM1/11/17
to The Center for Election Science
Mr. Smith, thank you.  The more I read your pages, the higher my opinion of you.

A new question if I may . . . what exactly does line 26. Strategic Borda II (1 frontrunner max, 1 min vote, rest honest) mean in terms of voter behavior?  I see that almost all IRV strategic voting methods refer back to this line.  Thus I am curious what it means?

Second question, which may be the same answer:  How do you define strategic voting under IRV?  What line measures it in your regret study?


Thank you so much for your insight.  You are helping me understand your work.

Chris

Warren D Smith

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Jan 11, 2017, 3:49:22 PM1/11/17
to electio...@googlegroups.com
In the original regret study "strategic voting" meant something
I called the "moving average strategy".
Which was this:

As a voter: Start with as input
(i) your utilities for each candidate;
(ii) a decreasing ordering, supplied by "God" of the presumed likelihoods
each candidate will win.
Then:
1. Go thru the ordering, each time giving that
candidate the MAX or MIN allowed score (constrained by the
rules of that voting system and the scores you already decided on)
2. depending on whether his utility EXCEEDS or falls BELOW
the average utility among the preceding candidates.
3. Except that for the first 2 (the 2 most likely to win) candidates, you
always give them either MIN-MAX or MAX-MIN
whichever is most honest.

(This strategy actually is best under a certain somewhat extreme
set of assumptions and for a certain subset of voting systems...)
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Clay Shentrup

unread,
Jan 12, 2017, 12:38:20 AM1/12/17
to The Center for Election Science
On Wednesday, January 11, 2017 at 12:49:22 PM UTC-8, Warren D. Smith (CRV cofounder, http://RangeVoting.org) wrote:
(ii) a decreasing ordering, supplied by "God" of the presumed likelihoods
each candidate will win.

I'm skeptical about the fact that this isn't based on the actual opinions of other voters. I'd prefer a two-pass where the first round was honest and the second was somehow based on a probability derived from the closeness of those actual totals. Perhaps this has its own problems? 

Jameson Quinn

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Jan 12, 2017, 7:32:06 AM1/12/17
to electionsciencefoundation
I'm currently getting Voter Satisfaction Efficiency numbers (VSE; that is, essentially, Bayesian Regret scaled onto -100% to 100%) using a procedure that builds on Warren's original procedure in several ways:

- I have various voter models, including some that I think are more realistic than Warren's "impartial culture" and "n-dimensional ideology".
- As with Warren, strategy is based on a commonly-known ordering of candidates; but unlike the case with Warren, that ordering is not purely arbitrary. In my system, it can either be ordering for the method under consideration with honest voting, or some "media" function of that ordering which can add noise and/or bias in favor of or against certain candidates. (This goes to Clay's point.)
- The strategic ballot for each system is based on more realistic game theory, and for some systems there are various levels of strategy.
- Voters are not necessarily intrinsically honest or strategic, but can decide whether to be strategic based on circumstances. For instance, there can be "one-sided strategy" in which voters only strategize if they prefer the runner-up over the winner, or "zealot strategy" in which they only strategize if the runner up and winner are not consecutive in their honest preference order.

I'm looking at other improvements as well.

As I've told Mark Frohnmayer, I plan to have an initial write-up of my findings by the end of the month, and a paper draft suitable for academic peer review a couple of weeks after that.

One initial piece of the writeup, in which I try to explain what I'm doing for a technically intermediate audience, is here. Comments there are welcome.

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William Waugh

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Jan 12, 2017, 11:20:06 AM1/12/17
to The Center for Election Science
Are you publishing the source code?

On Thursday, January 12, 2017 at 7:32:06 AM UTC-5, Jameson Quinn wrote:

Jameson Quinn

unread,
Jan 12, 2017, 11:36:59 AM1/12/17
to electionsciencefoundation

Leon Smith

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Jan 15, 2017, 4:05:05 AM1/15/17
to electio...@googlegroups.com


On Jan 12, 2017 11:37 AM, "Jameson Quinn" <jameso...@gmail.com> wrote:
>
> https://github.com/The-Center-for-Election-Science/vse-sim
>

By the way, https://github.com/electology is a thing.   Jameson, if you want access, I would be more than happy to provide it.

Best,
Leon

> 2017-01-12 11:20 GMT-05:00 William Waugh <2knuw...@snkmail.com>:
>>
>> Are you publishing the source code?
>>
>> On Thursday, January 12, 2017 at 7:32:06 AM UTC-5, Jameson Quinn wrote:
>>>
>>> https://groups.google.com/d/msg/electionscience/do8-1wQLXB4/uMPksH8qAQAJ
>>
>> --
>> You received this message because you are subscribed to the Google Groups "The Center for Election Science" group.

>> To unsubscribe from this group and stop receiving emails from it, send an email to electionscien...@googlegroups.com.


>> For more options, visit https://groups.google.com/d/optout.
>
>

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stvforc...@gmail.com

unread,
Jan 28, 2017, 8:30:54 PM1/28/17
to The Center for Election Science
You all are the CS people so I will ask you.

What methods did you employ that account for totally illogical voters?


1) I am conducting a survey and in it I am asking about voting methods.  The main point aside, I am finding that better than 1/3 of voters, when ranking choices, are putting Trump/Hillary or "Hillary Trump".  They are also "approving" Hillary and Trump.  I saw one score vote with both at 100%, and everyone else at zero.

Now . . .given my limited understanding of your computer model, the "Hillary" and "Trump" candidates would have drastically different utility placements.  As you trend towards one, you trend away from the other.  I'm curious if your model had anything to offer about how you "programed" this particular set of "utilities"?

Hmmm . . . I don't like how that is worded.

Let me try again.

2) There are some VASTLY illogical voters out there in the world.  They practically vote at random it seems.  How does your computer model take this into account?  Or does it?

I read from Mr. Smith .  .

""The trouble with humans is that you can't easily measure "utility" of different election alternatives for them. Why? Because there are no tangible, commonly agreed units (like "money") for measuring "utility" or human "happiness." And even if the units were there, you still could not measure it."

And

"Because our Bayesian regret computer simulations employed thus-logical strategic voters (in those sims involving strategic voters) the BR measurements were unable to see this whole problem (or only saw a small effect from it). "

http://rangevoting.org/BurrSummary.html

Does your computer model hold if the whole public or a good portion of the public vote in ways which seem a paradox for their "happiness"?  As I'm thinking about this . . . I am having a thought.  I'd better break this up.



3) My thought - your computer model assumes that "voters" become "happier" as they approach one candidate and it maps voting accordingly. But voters change their minds in illogical ways.  I asked Clay about Obamacare for example.  In the 1990s, it was the GOP dream, yet just 10 years later, it is the hated topic and must be repealed.  Now, focusing on ONLY the illogical nature of this flip . . . does your computer model account for this tendency in human behavior?

You write, "The trouble with humans is that you can't easily measure "utility" of different election alternatives for them. Why? Because there are no tangible, commonly agreed units (like "money") for measuring "utility" or human "happiness." And even if the units were there, you still could not measure it. And if you ask humans, they lie to you (or don't even know their own utilities). How do you distinguish the utility-lies from the utility-truth? And imagine the controversies we'd get into if we said something like "Electing Chirac clearly would have been better for the people of France, by 765 utility units." This would not be "science." It would be "a mess." . . .

Computers don't have those problems. We can make artificial "candidates" and "voters" inside our computer. We can read their "minds" without any possible lies to determine their exact happiness values in agreed-upon units. There is no controversy and any data you get has an exactly known meaning and is valid for all future time. The expense is tiny and the speed is huge, so we can gather enormous amounts of data. "


But in real life, humans change their minds based on the hour of the day, how much sleep they got, and if they had a good breakfast.  There are people who have two minds about an issue.  They have not even decided within themselves how they feel about something.

How does your computer model account for this human flaw?  From what I can read, it doesn't.  I assumes some sort of baseline of logic, when clearly this is far from accurate in reality.




4)  With every scientific experiment, we try and apply it to the real world to make sure it works according to our model.  If the real world results don't match the model, we change the model.

Now given that AV in particular has had a couple trial runs, and each time (with the one exception of the UN Sec. Gen, Approval voters ended up NOT voting in accordance with the model, (IE, bullet voting, split voting, and ultimately repealing AV), doesn't this indicate, under SCIENTIFIC principles, that there is something off with the model, and therefore it should be subject to review?

To add context, I am referring to Dartmouth where AV was repealed and they cited a lot of bullet voting, and discord, the IVN poll done where out of 4 candidates and 32K votes, the average number of votes cast was 1.25, and the bucklin system of the early 1900s which was repealed for again, bullet voting (as well as confusion).  (Your own page:  https://electology.org/bucklin-voting  )

If AV leads to overall voter happiness . . . what is going on with it's implementation that it renders 82% of users so angry with it, they repeal it in a landslide?  Wouldn't this indicate a problem with your model as well?
 

Warren D Smith

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Jan 28, 2017, 11:29:51 PM1/28/17
to electio...@googlegroups.com
> What methods did you employ that account for totally illogical voters?
>
>
> 1) I am conducting a survey and in it I am asking about voting methods.
> The main point aside, I am finding that better than 1/3 of voters, when
> ranking choices, are putting Trump/Hillary or "Hillary Trump".

--meaning what? They think there is a candidate named "HIllary Trump"?
I have no idea what you are trying to say here.

> They are
> also "approving" Hillary and Trump. I saw one score vote with both at
> 100%, and everyone else at zero.

--well, that perhaps is a legitimate expression of that voter's opinion.

> Now . . .given my limited understanding of your computer model, the
> "Hillary" and "Trump" candidates would have drastically different utility
> placements. As you trend towards one, you trend away from the other.

--not necessarily. Maybe that voter thinks both are desirable
hence both have high utility for that voter.

> I'm
> curious if your model had anything to offer about how you "programed" this
> particular set of "utilities"?
>
> Hmmm . . . I don't like how that is worded.
>
> Let me try again.
>
> 2) There are some VASTLY illogical voters out there in the world. They
> practically vote at random it seems. How does your computer model take
> this into account? Or does it?

--In my old (1999-2000) sims, we could
make the voters be honest. Or we could make them be strategically
dishonest. Also, we could add "ignorance" which is, their
utilities were added to an adjustable amount of random noise,
thus creating "confused utilities" and the voters would
act (i.e. vote) either honestly or strategically based on
their confused utilities, not their real utilities.

> I read from Mr. Smith . .
>
> ""The *trouble with humans* is that you can't easily measure "utility" of
> different election alternatives for them. Why? Because there are no
> tangible, commonly agreed units (like "money") for measuring "utility" or
> human "happiness." And even if the units were there, you still could not
> measure it."
>
> And
>
> "Because our *Bayesian regret* <http://rangevoting.org/BayRegDum.html>
> computer simulations employed thus-logical strategic voters (in those sims
> involving strategic voters) the BR measurements were unable to see this
> whole problem (or only saw a small effect from it). "
>
> http://rangevoting.org/BurrSummary.html
>
> Does your computer model hold if the whole public or a good portion of the
> public vote in ways which seem a paradox for their "happiness"? As I'm
> thinking about this . . . I am having a thought. I'd better break this up.

--well, the "ignorance" factor in my sims could cause voters to
act illogically, yes. However, because that ignorance consisted of
added random noise,
it tended to cancel out. That is, with 1000 voters all highly
influenced by random
ignorance, their ignorances tended to all be random and different,
thus averaging
out to something resembling actual knowledge.

That may have been unrealistic: In the USA 2016 election there was
an intentional effort mounted by somebody to create "fake news" stories which
were pro-Trump and/or anti-Hillary. These fake news stories
are known to have had comparable readership
(by various metrics) to the genuine election-related news
stories. Therefore the ignorance in USA 2016
(or at least, that fraction of it created by "fake news") did not tend
to act in a random and largely self-cancelling fashion.
It acted unidirectionally.

I actually personally encountered a rather rabid Trump supporter who
informed me I would be crazy to vote for Hillary because she was a secret
lesbian. I mean, he was literally yelling, hardly able to control himself.
Did he say that because of some fake news story telling it to him?
(I have no idea what input was flowing into his brain, whether
he was typical voter or not, or what. I just thought that experience
was pretty damn strange. I personally care little or not at all if Hillary
is a secret lesbian, that is way low on the list of
things I care about, plus anyhow I am unaware of any
reason to believe it.)

> 3) My thought - your computer model assumes that "voters" become "happier"
> as they approach one candidate and it maps voting accordingly.

--voters get different happiness values if different candidates win.
("approach"? Huh?)

> But voters
> change their minds in illogical ways. I asked Clay about Obamacare for
> example. In the 1990s, it was the GOP dream, yet just 10 years later, it
> is the hated topic and must be repealed. Now, focusing on ONLY the
> illogical nature of this flip . . . does your computer model account for
> this tendency in human behavior?

--well, that flip-flop was not necessarily a matter of illogical voters, likely
more a matter of illogical politicians. Or obeying some higher logic
that is not immediately obvious.
Anyhow, certainly some republicans and conservatives supported,
e.g. RomneyCare, I do not know about all of them. And certainly many
of them flipped on this and other things.

> But in real life, humans change their minds based on the hour of the day,
> how much sleep they got, and if they had a good breakfast. There are
> people who have two minds about an issue. They have not even decided
> within themselves how they feel about something.

--well something like that would act very much like random noise hence
would be simulated by the "ignorance knob" I already had
on the simulator.

> Now given that AV in particular has had a couple trial runs, and each time
> (with the one exception of the UN Sec. Gen, Approval voters ended up
> NOT voting in accordance with the model, (IE, bullet voting, split voting,
> and ultimately repealing AV), doesn't this indicate, under SCIENTIFIC
> principles, that there is something off with the model, and therefore it
> should be subject to review?

--uh, maybe. If I had the slightest idea what you were talking about.
There have been many "trial runs" and also many genuine runs, of
approval and score voting. Here is some info about various studies:
http://rangevoting.org/FrenchStudy.html
http://rangevoting.org/GermanApprovalStudies.html
http://rangevoting.org/OrsayTable.html
http://rangevoting.org/French2007studies.html
http://www.rangevoting.org/France2012.html
Here is info about various elections thru history vis-a-vis different voting
systems:
http://www.rangevoting.org/FunnyElections.html
Here is analysis of Australian 2007 IRV elections vis-a-vis other systems:
http://www.rangevoting.org/Aus07.html
For approval and/or score voting used in real major stakes government elections,
see
http://www.rangevoting.org/Sparta.html
http://www.rangevoting.org/SovietApp.html
http://www.rangevoting.org/GreekApproval.html (unfinished page;
help solicited)
http://www.rangevoting.org/UNsecyGen.html
http://www.rangevoting.org/PopeApprovalSystem.html
Re the myth about approval "bullet voting" see
http://www.rangevoting.org/BulletBugaboo.html

> To add context, I am referring to Dartmouth where AV was repealed and they
> cited a lot of bullet voting, and discord, the IVN poll done where out of 4
>
> candidates and 32K votes, the average number of votes cast was 1.25, and
> the bucklin system of the early 1900s which was repealed for again, bullet
> voting (as well as confusion). (Your own page:
> https://electology.org/bucklin-voting )

--I did not write that page. Concerning Dartmouth, I have some info
on that which may or
may not be what you had in mind, see
http://rangevoting.org/DartmouthBack.html
http://rangevoting.org/RichieOnApproval.html

> If AV leads to overall voter happiness . . . what is going on with it's
> implementation that it renders 82% of users so angry with it, they repeal
> it in a landslide? Wouldn't this indicate a problem with your model as
> well?

--can you provide more info?
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