Eric Sanders proposes a new quorum system

[Clay Shentrup]

He proposes scoring a no opinion as: (average score for that candidate) * (% scoring that candidate).

So your effective score is:

AX

Where:

A = average score

X = (1 + N/(Y+N))

Y = number of voters who scored you

N = number of voters who didn't score you

So holding your average constant, your strategy is to remain as unknown as possible, so as to maximize the value of X, getting it as close as possible to a maximum of 2.

Seems bad.

[Jameson Quinn]

I understand it differently. I think the proposal is that a blank counts as (average NONBLANK score for a candidate) * (% scoring that candidate)

a: average nonblank score (normalized 0-1)

y: portion of voters who scored you (0-1)

n: portion of voters who didn't score you (0-1)

score = ay + ayn = ay(1+n)

Best strategy is to maximize y.

Jameson

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[Andy Jennings]

I think you're missing a term.  Effective score should be:

A * Y * (1 + N / (Y+N))

or

A * Y * (2 - Y / (Y+N))

With that Y term in there, I've proven that it's always better to give someone the max score than not to vote for them.  And it's always worse for them to get a min score than a no vote.

I'm still evaluating it in terms of desirability.

~ Andy

--

[Andy Jennings]

Below is my analysis of 6 different quorum rules (according to criteria that I care about).

In summary, Eric's new rule meets 4 of my 5 criteria.  That's one better than the soft quorum rule.

(Still, I think I like the basic rule (highest total) best...)

~ Andy

--------------

The basic rule:  Highest total score wins

Advantages:
PARTICIPATION: "The addition of a ballot, where candidate A is strictly preferred to candidate B, to an existing tally of votes should not change the winner from candidate A to candidate B." (Wikipedia).  This sounds reasonable, but ends up being very, very selective.  Few voting systems meet it.  In score voting, this can be a non-normalized vote (e.g. A=10, B=9).  None of the other quorum rules preserve it.
NO_DARK_HORSE: (defined below)
NO_MAGIC_NUMBERS: (defined below)
EXTREME_PARTICIPATION: (defined below)

Disadvantages:
Fails DEFER_TO_OTHERS: In some cases, voters want to "let the other voters decide" on candidates they don't know much about.  Some believe that an average score of 10.0 from 90% of the electorate should beat someone with an average score of 8.5 from 100% of the electorate.  This is what motivates other quorum rules...

--------------

The average rule:  Highest average score wins

Advantages:
DEFER_TO_OTHERS
NO_MAGIC_NUMBERS
EXTREME_PARTICIPATION

Disadvantages:
Fails PARTICIPATION
Fails NO_DARK_HORSE: This rule allows a candidate with one MAX vote to win over someone with a very high (but not MAX) score from the entire electorate.  This rule fails badly if write-ins are allowed.

--------------

The hard quorum:  Highest average wins, but anyone who is not scored by at least N percent of the voters is disqualified.

Advantages:
DEFER_TO_OTHERS
NO_DARK_HORSE

Disadvantages:
Fails PARTICIPATION
Fails NO_MAGIC_NUMBERS:  What number should we choose for N?  Tunable parameters could be adjusted politically to favor certain people.
Fails EXTREME_PARTICIPATION:  Showing up and voting A=10, B=0 can actually change the winner from A to B (by bumping B over the threshold for qualification).

--------------

The soft quorum:  Highest average wins, after adding N zero votes to each candidate.

Advantages:
DEFER_TO_OTHERS
NO_DARK_HORSE
EXTREME_PARTICIPATION

Disadvantages:
Fails PARTICIPATION
Fails NO_MAGIC_NUMBERS

--------------

The Wilson rule: Lower bound of Wilson score confidence interval for a Bernoulli parameter
http://www.evanmiller.org/how-not-to-sort-by-average-rating.html

Advantages:
DEFER_TO_OTHERS
NO_DARK_HORSE  (believe, didn't prove)
EXTREME_PARTICIPATION  (believe, didn't prove)

Disadvantages:
Fails PARTICIPATION  (believe, didn't prove)
Fails NO_MAGIC_NUMBERS

Note: I don't think human rating is close enough to a Bernoulli process for this formula to be applicable.  Especially not in elections...

--------------

Eric's Sandy rule:  Fill in all the non-votes with the average vote (for that candidate) multiplied by the fraction of voters who expressed an opinion on that candidate.

Advantages:
DEFER_TO_OTHERS
NO_DARK_HORSE
EXTREME_PARTICIPATION
NO_MAGIC_NUMBERS

Disadvantages:
Fails PARTICIPATION

[Frank]

Do You have an example of Eric's rule failing the participation criterion? I came up with something similar some time back but never found such an example.

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[Andy Jennings]

On Mon, Jan 19, 2015 at 2:58 PM, Frank <frankdm...@gmail.com> wrote:

Do You have an example of Eric's rule failing the participation criterion? I came up with something similar some time back but never found such an example.

Here's one.  Using the formula F = S * (2 - Y / (Y+N))

where

F = Final score

S = Sum of all votes

Y = # of voters who voted for candidate

N = # of voters who didn't vote for candidate

Candidate A has one 10 and nine abstensions.  F = 10 * (2 - 1/10) = 19

Candidate B has two 10s and eight 0s.  F = 20 * (2 - 10/10) = 20

Candidate B wins.

Another voter shows up voting A=5, B=7 then:

A's final score is 15 * (2 - 2/11) = 27.2727...

B's final score is 26 * (2 - 11/11) = 26

A wins.

[Andy Jennings]

Another voter shows up voting A=5, B=7 then:

I meant A=5, B=6.

[Frank]

Ah, I think I see why I had trouble before. I was presuming N was the total number of Voters, in this case 11, for both calculations. The idea being its in One's interest to cast a vote of some sort for an undesirable Candidate, even if the vote is of low score. While the Winners remain the same, the approach I take has the argument of "We now have a clearer picture of the will of the Voters" to justify it.

On Tuesday, January 20, 2015, Andy Jennings <abjen...@gmail.com> wrote:

Another voter shows up voting A=5, B=7 then:

I meant A=5, B=6.

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[esand...@gmail.com]

Everyone (and especially Andy), thank you so much for evaluating my 'no opinion' scoring system. But your analysis below is inaccurate. My system does NOT fail Participation.

I've created a live Google Spreadsheet so you can play with it and see how it scores various elections. Andy, I've included your example as the default inputs:

https://docs.google.com/spreadsheets/d/1wcM95vGzbodEY6kWKEl9bd4-sjDJPJwf3ivz0t5JBDE/edit?usp=sharing

Feel free to try it out!

 

[esand...@gmail.com]

Okay, I spoke too soon. Andy, you are correct: It DOES fail Participation. I misread your original post and conflated 'abstentions' with 'zeros.' My mistake.

[Warren D Smith]

On 1/16/15, Clay Shentrup <cl...@electology.org> wrote:
> He proposes scoring a no opinion as: (average score for that candidate) *
> (% scoring that candidate).

--This proposal is the same thing as (i.e. equivalent to):
"no opinion" scores are counted as "zero."
(If by "%" you meant "fraction.")

[Andy Jennings]

On Wed, Feb 10, 2016 at 7:46 AM, Warren D Smith <warre...@gmail.com> wrote:

--This proposal is the same thing as (i.e. equivalent to):
"no opinion" scores are counted as "zero."
(If by "%" you meant "fraction.")

That's what it sounds like at first, but that's incorrect.

Suppose 90% of the voters scored a candidate and 10% abstained.  His average score (among those that actually scored him) is 6.

Then you "fill in" the abstentions with 6 * 0.9 = 5.4.

So his final score is an average of 6 * 0.9 + 5.4 * 0.1 = 5.94

[Warren D Smith]

Oho, I see claim by Andy Jennings that Eric Sanders'
proposal was different that what Clay had said, namely, allegedly:

SandersJenningsEffectiveScore
= A * Y * (1 + N / (Y+N))
= A * Y * (2 - Y / (Y+N))
= (S/V) * (2-Y)
= (S/V) * (1+N)

where
A = average nonblank score for that candidate
Y = fraction of voters who score him
N = fraction of voters who left his score blank.
Note I have used the facts that
Y+N=1 and A=S/(Y*V) where S=SumOfNonBlankScores
and V=NumberOfVoters
to produce different versions of the formula.

Andy Jennings gives an interesting discussion of possible ways
of dealing with blank scores, in terms of 5 criteria,
many somewhat-vaguely defined, he calls

DEFER_TO_OTHERS:
In some cases, voters want to "let the other voters decide" on
candidates they don't know much about. Some believe that an average
score of 10.0 from 90% of the electorate should beat someone with an
average score of 8.5 from 100% of the electorate.

NO_DARK_HORSE:
A candidate who organizes a small cult of fanatical supporters
while intentionally remaining unknown to everybody else, should not be
able to win.

EXTREME_PARTICIPATION:
Showing up and voting A=max, B=min should not be able to change the winner
from A to B. This is a very weak form of the PARTICIPATION criterion so
the word "extreme" risks deceiving the reader.

NO_MAGIC_NUMBERS:
If the scheme involves a magic number M such that, e.g. if candidate
gets more than M votes, then he's allowed to win, that's viewed as
bad. This name also risks deceiving the reader, a better name would be
"NO_MAGIC_DISCONTINUITIES"? Well, I would deny soft quorum
violates "no magic discontinuities" but Jennings claims it violates
"no magic numbers," so he evidently considers these two concepts different.

PARTICIPATION:
"The addition of a ballot, where candidate A is strictly preferred to
candidate B, to an existing tally of votes should not change the
winner from candidate A to candidate B." (Wikipedia).

Let us now consider a GENERAL scoring function F(S,Y,N)
in terms of Jennings' criteria. Sanders' particular scoring function,
at least according to Jennings, is F(S,Y,N)=S*(1+N) but we shall allow
other formulas.
"Plain sum" is F(S,Y,N)=S.
"Plain average" is F(S,Y,N)=S/(Y*V).
The "soft quorum" idea is F(S,Y,N)=(S+C)/(Y*V+K) for two pre-agreed
constants C>0,K>0.
The "hard quorum" idea is F(S,Y,N)=S/(Y*V) if Y>Q, else -infinity,
where Q>0 is a pre-agreed quorum size constant.
Wilson-Bernoulli-like ideas could be something like
F(S,Y,N)=S/(Y*V)-C*S/squareroot(Y*V)
where C>0 is a pre-agreed constant.

EXTREME_PARTICIPATION:
F(S+maxscore, Y+1/V, N-1/V) > F(s+minscore, y+1/V, n-1/V)
if F(S,Y,N)>F(s,y,n).

NO_MAGIC_DISCONTINUITIES:
Just demanding F(S,Y,N) be a continuous smooth function of its 3 arguments
(when S>0, Y>0, N>0, Y+N=1),
seems good enough.

NO_MAGIC_NUMBERS:
F(S,Y,N) is specified by a simple formula with all constants
being integers less than 10?

PARTICIPATION:
F(S+A,Y+1/V,N-1/V)>F(s+a,y+1/V,n-1/V)
if F(S,Y,N)>F(s,y,n) and minscore<=a<A<=maxscore.

DEFERS_TO_OTHERS:
F(S,Y,N) can and often should exceed F(s,y,n) even when S<s if
S/Y > s/(y*V)?
I'm not sure exactly what this should mean.
Maybe it should mean: "If we randomly erase scores for candidate X
from ballots, and do this until X has exactly 1000 scores -- and do that
for every candidate X -- then it is likely that the candidate who then
has the greatest
summed score, will be the winner using the original ballot set."

NO_DARK_HORSE:
F(s,y,n) should be less than F(S,Y,N) if y is smaller than
the largest reasonable "conspiratorial secret cult" and Y is large and
S/Y is reasonable, e.g. in the middle halfsize score interval..

In addition we would need to require, e.g. F(S,Y,N) be monotone
increasing in S with
Y,N held fixed; F(S,Y,N) be monotone increasing in Y with S held fixed
and Y+N=1.



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

[Warren D Smith]

PARTICIPATION would better be called STRONG_PARTICIPATION
and EXTREME_PARTICIPATION better name is WEAK_PARTICIPATION?

It seems to me that soft quorum should, if the parameters are chosen
right, satisfy
an intermediate-strength participation criterion.

E.g, suppose a new voter comes who scores A more than B, with score
difference at
least a fraction F of the full score range.
We then would like it to be impossible for this new voter to cause B to beat A,
whereas formerly A won.
EXTREME(WEAK)PARTICIPATION assumes F=1.
Plain (STRONG)PARTICIPATION assumes F=infinitesimal.
Intermediately, we could make F=0.3, for example.

Well, doesn't soft quorum obey an intermediate participation criterion
if its internal magic numbers are chosen right?
For example, using plain average but where each candidate gets V/10
zero score fake votes before start (V voters total), I think it is valid
to use F=0.91.

Not very impressive, I admit, but in most situations F could safely be taken
a lot smaller than 0.9, it is only certain extremely artificial
election situations
where you need large F. This could be quantified by setting up a
probability model
of voter behavior than saying participatioon failures are highly unlikely to be
possible for F-strength voters...

I also comment that the Bernoulli thing and
the soft quorum thing become pretty close to the same thing if you fiddle
the parameters right. E.g. use Z fake zero-score votes,
where Z=PositiveConstant*squareroot(#voters),
to get a soft quorum which behaves very
similarly to the Bernoulli thing.

[Andy Jennings]

On Wed, Feb 10, 2016 at 9:10 AM, Warren D Smith <warre...@gmail.com> wrote:

PARTICIPATION would better be called STRONG_PARTICIPATION
and EXTREME_PARTICIPATION better name is WEAK_PARTICIPATION?

I called it EXTREME_PARTICIPATION because the votes being added were at the extremes (MIN and MAX).  But I have no objection to it being renamed.

NO_MAGIC_NUMBERS was intended to mean, "No pre-agreed constants, at all".  Even integers below 10.  This was partially motivated by your aversion to any tunable parameters, a concern which I share.  There may be some gray area, e.g. a formula in which the integer 2 arises in a completely natural way and there is no other sane choice.

For example, in November I heard about another quorum rule: Eliminate any candidate with a total score less than half the highest total score of any candidate.  Then use the average score to choose the winner.

It fails PARTICIPATION, meets NO_DARK_HORSE, EXTREME_PARTICIPATION, and DEFER_TO_OTHERS.

I would say it fails NO_MAGIC_NUMBERS, but just barely.  "Half" is technically pulled out of nowhere and could easily be changed to any other fraction.  But it could also be claimed to be the least magical of all magic numbers.

[Andy Jennings]

Here is a rebuttal to Evan Miller's "Wilson rule" proposal:
http://planspace.org/2014/08/17/how-to-sort-by-average-rating/

Whoever that is, they end up recommending "Laplace smoothing", which is equivalent to the soft quorum rule.

[Warren D Smith]

> For example, in November I heard about another quorum rule: Eliminate any
> candidate with a total score less than half the highest total score of any
> candidate. Then use the average score to choose the winner.
>
> It fails PARTICIPATION, meets NO_DARK_HORSE, EXTREME_PARTICIPATION, and
> DEFER_TO_OTHERS.

--well, jeez, I would say it is fine re abolishing dark horses
(probably actually too good
in the sense it does not defer to others enough),
but it has an annoying magic discontinuity.

DEFER and NO_DARK_HORSE evidently somewhat conflict.

(STRONG)PARTICIPATION seems to conflict with a lot of stuff -- especially
DEFER_TO_OTHERS seems inherently impossible to reconcile with it.

I'm not sure if I share the concern about magic numbers being evilly
tunable in this application -- if the magic numbers were pre-agreed
among the candidates before election started. Unfortunately such
agreement may be impossible...

[Warren D Smith]

On 2/10/16, Warren D Smith <warre...@gmail.com> wrote:
>> For example, in November I heard about another quorum rule: Eliminate any
>> candidate with a total score less than half the highest total score of
>> any
>> candidate. Then use the average score to choose the winner.
>>
>> It fails PARTICIPATION, meets NO_DARK_HORSE, EXTREME_PARTICIPATION, and
>> DEFER_TO_OTHERS.
>
> --well, jeez, I would say it is fine re abolishing dark horses
> (probably actually too good
> in the sense it does not defer to others enough),
> but it has an annoying magic discontinuity.

Doesn't it violate extreme participation?
I mean. two candidates X & Y. With average score
X would beat Y by a lot, except he
has slightly below the quorum, say Y has 200001 scores while X has 100000.
So now a new voter comes
and scores Y=MAX, X=MIN,
Result: X wins.

[Warren D Smith]

> I'm not sure if I share the concern about magic numbers being evilly
> tunable in this application -- if the magic numbers were pre-agreed
> among the candidates before election started. Unfortunately such
> agreement may be impossible...

--here's a thought experiment about that.
Suppose we were to use score voting with the simplest kind of
soft quorum, namely adjoin N fake zero scores for each candidate
before election
starts; then use average.

Here N is a "magic number." Now suppose we asked each candidate
ahead of time to suggest the value of N>=0 they'd like,
and we used the median suggestion.
(I guess Andy would claim this scheme is magic-free?)

But we know what would happen. Assume there are 2 major party candidates and
>=3 minor-party candidates, which is the generic situation in Australia & Canada. The minors would all prefer N=0. Therefore, the median would equal 0.

Therefore, plain average is the "best" of the soft-quorum schemes,
"Q.E.D."

If however there were 2 majors and <=1 minors, which might be the generic
situation in USA today -- then they'd choose N-->infinity
as the median.

This would cause plain-sum.

[Andy Jennings]

You're right.  If MIN > 0, this can bump X over the cutoff and let him win.  I may have assumed MAX > 0 and MIN <= 0 to prove weak participation.  They seem like reasonable assumptions, though.  Maybe they should be included in the definition of weak participation.

[Warren D Smith]

>
> You're right. If MIN > 0, this can bump X over the cutoff and let him
> win. I may have assumed MAX > 0 and MIN <= 0 to prove weak participation.
> They seem like reasonable assumptions, though. Maybe they should be
> included in the definition of weak participation.

--I was intending my example to work when MIN=0.

[Andy Jennings]

Interesting thought experiment.  Having the candidates involved seems to compromise clone-proofness in a way that none of the other quorum rules do.  If this was being seriously proposed, then I could add that as a criterion...

More broadly, though, perhaps the NO_MAGIC_NUMBERS definition is not perfect, but I still feel like the fewer tunable parameters the better.  Any that come up should arise naturally.  Although I like the soft quorum rule, it bugs me that we provide so little guidance on what number of MIN scores to add to each candidate.  It's a tunable parameter that can completely change the winner!

[Andy Jennings]

Well, the rule was that any candidate with a total score (sum) less than half the highest total score (sum) of any candidate was eliminated.  So a new voter with X=0 can't bump X above the qualification threshold and cause X to win.

[Warren D Smith]

> Interesting thought experiment. Having the candidates involved seems to
> compromise clone-proofness in a way that none of the other quorum rules
> do. If this was being seriously proposed, then I could add that as a
> criterion...
>
> More broadly, though, perhaps the NO_MAGIC_NUMBERS definition is not
> perfect, but I still feel like the fewer tunable parameters the better.
> Any that come up should arise naturally. Although I like the soft quorum
> rule, it bugs me that we provide so little guidance on what number of MIN
> scores to add to each candidate. It's a tunable parameter that can
> completely change the winner!

--yah, a lot of your desiderata are pretty vague, when you try to
formalize them
they wriggle away from you. E.g. you dislike 2 but consider it the
least-magic number. Well, clearly you are ok with 0 and 1,
any formula such as A+B is really 1*A+1*B and you are ok with that.

Trouble is, 2=1+1. And 3=2+1. Therefore I just "proved" that 2 and 3
are "not magic." Some kind of information-entropy notion I guess is wanted,
but you'll never really be happy.

It's a bit like the "minimum uninteresting number."
Well, clearly, that number is interesting!

But I like your whole attempt, it's the right direction to think.

My personal feelings:
1. The whole bernoulli class of ideas is
wrong because it it is based on a probability model (independent coin
toss voters) which is not realistic for our application (organized
conspiracies of cultist voters, they are not independent).

2. The DEFER_TO_OTHERS demand seems inherently incompatible with
STRONG_PARTICIPATION. So you have to sacrifice one. I think
the lesser sacrifice in the real world will be the latter.
So then soft quorum is ok with you in all ways except for MAGIC_NUMBERS.
The trouble is, if the whole motivation of soft quorum is to protect
against cult
conspiracies, then the fact is, there really is some magic number
depending on human psychology and stuff, about the max feasible
size of a secret conspiracy. So you cannot avoid having a magic number
if your main goal is to address the cult problem, and do it well.

3. However, my personal feeling is that
plain average, with no quorum protection, will work well (at least in
large elections), because it is just an empirical fact about humans,
that a goodly fraction of them
prefer to zero-score unknown "dark horses", in fact more than the fraction who
prefer to DEFER_TO_OTHERS about scoring them. So we already were protected.
If you believe that, then: no magic numbers.

4. In view of all that, I think we're already doing fine.

[Andy Jennings]

On Fri, Feb 12, 2016 at 2:07 PM, Warren D Smith <warre...@gmail.com> wrote:

My personal feelings:
1. The whole bernoulli class of ideas is
wrong because it it is based on a probability model (independent coin
toss voters) which is not realistic for our application (organized
conspiracies of cultist voters, they are not independent).

Agree

 

2.  The DEFER_TO_OTHERS demand seems inherently incompatible with
STRONG_PARTICIPATION.  So you have to sacrifice one.   I think
the lesser sacrifice in the real world will be the latter.
So then soft quorum is ok with you in all ways except for MAGIC_NUMBERS.
The trouble is, if the whole motivation of soft quorum is to protect
against cult
conspiracies, then the fact is, there really is some magic number
depending on human psychology and stuff, about the max feasible
size of a secret conspiracy.  So you cannot avoid having a magic number
if your main goal is to address the cult problem, and do it well.

I, on the other hand, would keep strong_participation.  I've never seen a compelling example where it's obvious that deferring to others is better than plain-sum.  Should a candidate who gets a 10.0 average from 55% of the population win over someone who gets 5.0 average from 100% of the population?  I guess it's an obvious yes to some people, but it's not clear to me.

Strong_participation, on the other hand, is Score Voting's secret weapon.  It's such an obvious criterion and so few voting systems meet it.  Basically just the cardinal-summing systems (score, approval) and the positional-point systems (plurality, borda, etc.).

MJ, IRV, Condorcet... None of them meet strong_participation.

I, personally, hesitate to give it up just for defer_to_others.

 

3. However, my personal feeling is that
plain average, with no quorum protection, will work well (at least in
large elections), because it is just an empirical fact about humans,
that a goodly fraction of them
prefer to zero-score unknown "dark horses", in fact more than the fraction who
prefer to DEFER_TO_OTHERS about scoring them.  So we already were protected.
If you believe that, then: no magic numbers.

You're absolutely right, except for write-ins.  Do you disallow write-ins?  Or let voters assign a default score to every write-in they haven't explicitly scored?

Also, there's the criterion of simplicity, which is important.  No idea how to define that one.  It's related to no_magic_numbers, but I'd say that plain-avg is better than soft-quorum, which is better than Eric's Sandy rule.

[William Waugh]

On Friday, February 12, 2016 at 4:30:15 PM UTC-5, Andrew Jennings wrote:

...

  Or let voters assign a default score to every write-in they haven't explicitly scored?

...
Yes, please. Doesn't that solve everything?

[Warren D Smith]

> I, on the other hand, would keep strong_participation. I've never seen a
> compelling example where it's obvious that deferring to others is better
> than plain-sum. Should a candidate who gets a 10.0 average from 55% of the
> population win over someone who gets 5.0 average from 100% of the
> population? I guess it's an obvious yes to some people, but it's not clear
> to me.

--obvious yes to me.

Well, let's say you were trying to decide on some food.
Food A is an "amanita mushroom." Among those who ate it, 100% died
within 2 weeks.
Among those who did not eat it, i.e. the vast majority of USA population,
well, I would recommend they DEFER_TO_OTHERS,
namely those who did eat it, for the purpose of getting a better decision.
Food B is a McDonald's Big Mac with Giant Coke. Pretty unhealthy, but
it probably
won't kill you quickly. 100% of the population has tried it or at
least is familiar with it,
and they on average think it's a pretty bad food, say scoring it 3 out of 10.

More generally, look, if 50% of the population, or even merely 20%,
scores something, that's a high
reliability assessment of its average perceived worth. Accept it. You are
probably never going to get any better such assessment via anything you
ever do in your life.

[Andy Jennings]

On Fri, Feb 12, 2016 at 4:17 PM, Warren D Smith <warre...@gmail.com> wrote:

> I, on the other hand, would keep strong_participation.  I've never seen a
> compelling example where it's obvious that deferring to others is better
> than plain-sum.  Should a candidate who gets a 10.0 average from 55% of the
> population win over someone who gets 5.0 average from 100% of the
> population?  I guess it's an obvious yes to some people, but it's not clear
> to me.

--obvious yes to me.

Well, let's say you were trying to decide on some food.
Food A is an "amanita mushroom."  Among those who ate it, 100% died
within 2 weeks.
Among those who did not eat it, i.e. the vast majority of USA population,
well, I would recommend they DEFER_TO_OTHERS,
namely those who did eat it, for the purpose of getting a better decision.
Food B is a McDonald's Big Mac with Giant Coke.  Pretty unhealthy, but
it probably
won't kill you quickly.   100% of the population has tried it or at
least is familiar with it,
and they on average think it's a pretty bad food, say scoring it 3 out of 10.

Well, plain-sum is pessimistic, turning everyone who abstained from voting for the amanita mushroom into a 0 vote.  So it looks like the mushroom would get a pretty bad score and lose with plain-sum voting also.  I'm not terribly convinced by this example.

 

More generally, look, if 50% of the population, or even merely 20%,
scores something, that's a high
reliability assessment of its average perceived worth.  Accept it.   You are
probably never going to get any better such assessment via anything you
ever do in your life.

You're assuming that all voters, independent of their political philosophy, are equally likely to vote for X.  Perhaps I'm afraid that it's highly correlated with political philosophy.  If 55% of people voted for X and he got an average of 10.0, what if it's a concerted effort by one political party?

(I concede that I'm really only thinking about political elections at the moment.  Choosing a restaurant among friends is different.)

In other news, it seems I have tried to give two examples in this thread motivating DEFER_TO_OTHERS, and both are incorrect:

Jan 2015: 10.0 from 90% vs 8.5 from 100%

Feb 2016: 10.0 from 55% vs 5.0 from 100%

In both cases, the former candidate would win with plain-sum, plain-avg, and any size of soft quorum.

 

I don't mean to set up straw men.  Perhaps someone else should find a maximally convincing example...

Is there a reason you didn't answer the write-in question?

[Eric Sanders]

Highest Total Score 

If “highest total score” is an appropriate way to evaluate and compare various options, how come Yelp, Amazon, etc. don’t use highest total score to determine the ‘best’ restaurant, product, etc.? 

Instead, they use some proprietary weighted average score that takes into consideration the average rating for each option (from voters who rated it) factored by the number of voters who rated it. In this way they avoid dealing with “no opinions” entirely. 

However, in Score Voting, we cannot avoid the “no opinion” discussion. 

Non-binary utilities (scores) are not directly summable. Unlike in Approval Voting, where voters reward each option with a singular ‘yes’ vote (think of “likes” on Facebook, which can be summed), the ‘points’ in Score Voting are not singular entities which can be summed for a meaningful total. 

Approval Voting asks: How many people liked it? (quantity) 

Score Voting asks: How much did people like it? (quality) 

Since Score Voting is an evaluation of quality, our final score must indicate quality, not quantity. 

Why isn’t Highest Total Score an appropriate metric to evaluate quality? Because it treats ‘hate’ (0) and ‘no opinion’ (blank) as synonymous. On a ballot with numerous candidates, we must not assume that just because a voter leaves a candidate blank he or she ‘hates’ that candidate. To do so artificially penalizes less-scored candidates and renders the final results less than ideal. 

Imagine this election: 

Option A: 5 votes * 10 points each = 50 points 

Option B: 10 votes * 5 points each = 50 points 

Who is really the higher quality candidate here? Can we really assume that ALL 5 other voters, had they scored Option A (and not left him blank), would have given him 0’s? What is the probability of that? 

Yes, the quantity of points in the above example is the same, but the quality of these two candidates is clearly not. 

To best determine the quality of a Score Voting candidate, we need a way to estimate and incorporate the value of ‘no opinions.’ Otherwise we risk electing more-scored but lower quality candidates, the exact opposite of what Score Voting is intended to do as the (perhaps) ‘ideal’ voting method.

[Warren D Smith]

--I had in mind the opposite sign. Vote to decide on the worst of the foods.
Amanita might fail to win.

[Warren D Smith]

On 2/13/16, Eric Sanders <esand...@gmail.com> wrote:
> *Highest Total Score *

> If “highest total score” is an appropriate way to evaluate and compare
> various options, how come Yelp, Amazon, etc. don’t use highest total score
> to determine the ‘best’ restaurant, product, etc.?
>
> Instead, they use some proprietary weighted average score that takes into
> consideration the average rating for each option (from voters who rated it)

--exactly. And YouTube videos are an example where they use approval
voting, a viewer
can hit the "thumbs up" or "thumbs down" button, and it reports to
each potential viewer of a video how many so far have hit each of the
two buttons.
YouTube also tells you the total number of viewers so far of a video,
which allows you to figure out the number of "no opinion" voters too -- the
vast majority are too lazy to hit either button.

> factored by the number of voters who rated it. In this way they avoid
> dealing with “no opinions” entirely.

--well, not really -- there are plenty of raters who did not express an opinion
on that restaurant. Yelp etc simply ignore them.

> Why isn’t Highest Total Score an appropriate metric to evaluate quality?
> Because it treats ‘hate’ (0) and ‘no opinion’ (blank) as synonymous. On a
> ballot with numerous candidates, we must not assume that just because a
> voter leaves a candidate blank he or she ‘hates’ that candidate. To do so
> artificially penalizes less-scored candidates and renders the final results
> less than ideal.

--exactly; and not only that, it is the most-distortionary possible
way to treat blanks!

> Imagine this election:
>
> Option A: 5 votes * 10 points each = 50 points
> Option B: 10 votes * 5 points each = 50 points
>
> Who is really the higher quality candidate here? Can we really assume that
> ALL 5 other voters, had they scored Option A (and not left him blank),
> would have given him 0’s? What is the probability of that?

--well, it might be a reasonable probability if it were only 5 voters.
But if it
is 5000 voters, the probability becomes microscopic. With large
electorates, statistical behavior trends become certainties. And the
observed behavior is, about 1.7 times
as many honestly-ignorant voters give them zeros to "play it safe" as those who
give them "no opinion" to defer to others. So it is essentially certain
in large elections that a large number of voters, say 25-50% of the
ignorant ones, will
vote "blank" and 50-75% will vote "zero." And that is why I believe
no quorum protection is actually needed and it is safe to just use
plain average in large elections, but
quorum protection might be helpful in small elections.
It would be interesting to ask whether putting in quorum protection
will influence voters to be more honest about their ignorance.

> Yes, the *quantity* of points in the above example is the same, but the
> *quality* of these two candidates is clearly not.
>
> To best determine the *quality* of a Score Voting candidate, we need a way

> to estimate and incorporate the value of ‘no opinions.’ Otherwise we risk

> electing more-scored but *lower quality* candidates, the exact opposite of

[Warren D Smith]

> You're assuming that all voters, independent of their political philosophy,
> are equally likely to vote for X.

--I did not assume that...

> Perhaps I'm afraid that it's highly
> correlated with political philosophy. If 55% of people voted for X and he
> got an average of 10.0, what if it's a concerted effort by one political
> party?

--well, it wouldn't be. There is no way 55% of people will vote 10 for
X, because of an organized conspiracy to distort, while the other 45% will
express no opinion, in a situation where that 10 is a great exaggeration
of the average perception of X. It just would never happen.

But what some might be able to conceive happening is, up to perhaps 500
X-cultists voting X=10, while the other 9999500 voters score "no opinion" since
X is unknown. I claim this is unrealistic too, but it is not
immediately obvious it is unrealistic, you have to actually have seen
behavior data to realize a large chunk, probably
a majority, of those 9999500 will automagically score X=0 just to
"play it safe."

Now it might well be that there is a sample bias; those who know about
X are a biased
more-pro-X-than-usual set of voters. The soft quorum idea compensates for that
effect. However it is my belief that there already is
over-compensation for that effect
caused by the "zero unknowns" observed human behavior, so that in
fact, soft quorum
protection is not really needed.

> Is there a reason you didn't answer the write-in question?

--oh sorry. Write-ins.
Well, for them clearly there is a high sample bias.
And the ignorant are unable to write-in X's name since they never heard
of X, and unable to score him zero to "play it safe."

So I guess I'm not happy about the whole idea of allowing write-ins in
score voting
elections. By the way, in Canada, write-ins are forbidden.
I'd prefer if everybody was a write-in, or nobody was.
But anyhow if both are allowed, then yes I would want quorum protection.
And then it might be legitimate to treat write-ins asymmetrically
(after all, they already are asymmetrically treated just by being a
write-in candidate).

[Bruce Gilson]

On Sat, Feb 13, 2016 at 11:35 AM, Warren D Smith <warre...@gmail.com> wrote:

​[...]

By the way, in Canada, write-ins are forbidden.

​In Maryland, they have a strange rule. You can write in a candidate's name only if they have formally declared their write-in candidacy.

​

 

[Eric Sanders]

So I guess I'm not happy about the whole idea of allowing write-ins in score voting elections.  By the way, in Canada, write-ins are forbidden. I'd prefer if everybody was a write-in, or nobody was. But anyhow if both are allowed, then yes I would want quorum protection. 

Another nice thing about my 'no opinion' scoring system is that it works perfectly for write-ins too:

Since a candidate's Final Total Score = Total Score + Total Value of No Opinions 

and 

Total Value of No Opinions = # of No Opinions x Value of Each No Opinion

and

Value of Each No Opinion = % of Voters Who Scored that Candidate x Average Score Given

then

All the 'no opinions' automatically generated by voters' write-in candidates would be easily and fairly scored by my system, without resorting to arbitrary quorums.

[Eric Sanders]

Thanks, Andy. I'd like to clarify something about my scoring system: it is not a problem that it does not pass "Participation"--it is not meant to. 

As you explained, my scoring system evaluates 'no opinions' proportional to the % of voters who scored that option.

Suppose 90% of the voters scored a candidate and 10% abstained.  His average score (among those that actually scored him) is 6.
Then you "fill in" the abstentions with 6 * 0.9 = 5.4.
So his final score is an average of 6 * 0.9 + 5.4 * 0.1 = 5.94

So, in my system, the "average score" of a group always takes into consideration the relative score of the 'no opinions' (as opposed to arbitrarily assigning them as 0 or ignoring them altogether). When you add another voter to a group, that changes the relative score of the 'no opinions.' 

So "Participation" is an irrelevant criteria in this case, so long as you agree with my underlying logic and philosophy that no opinions should be evaluated proportional to the percentage of people who scored that option.

Example:

 

If a candidate has an average score of 9.0 and has been scored by 80% of voters, then the value of each of that candidate’s "No Opinions" is 9.0 x 80%, or 7.2. 

 

Now, simply multiply the value of each "No Opinion" (in this case, 7.2) by the total number of "No Opinions" for that candidate to determine the total value of that candidate's "No Opinions".

 

Lastly, add the total value of that candidate's "No Opinions" to the candidate's base total score to produce a Final Total Score and then a Final Average Score (i.e., Final Total Score / Total # of Voters).

[William Waugh]

On Sunday, February 21, 2016 at 9:00:21 AM UTC-5, Eric Sanders wrote https://groups.google.com/d/msg/electionscience/SpLDc1Z0hzE/rYdBY7vkBgAJ

What about the fascist dark horse? Is your system going to provide that a voter who doesn't know who is running as a write-in can score all such unknown candidates at zero (full opposition), so that that voter could prevent the immorality of having their ballot counted as providing any support for the election of a fascist?