What Voters Want — Negative Vote?

[Clay Shentrup]

The guy advocating for Negative Vote (one vote for or against one candidate) saw the What Voters Want page and wants to know what voters would think of Negative Vote.

https://www.facebook.com/groups/NegativeVote/1004626816286041/?comment_id=1005558166192906

I'm just speculating they'd dislike it, because it's so much less expressive. But it would be great to have some data.

[William Waugh]

I signed up to join the group so I can argue against their stupid proposal of a plurality/antiplurality alternative at the voter's choice.

[Warren D Smith]

I cannot read that facebook page.
The "negative vote" was invented by Boehm in an unpublished manuscript,
and was a mental predecessor of approval voting, which is regarded by
pretty much everybody as having obsoleted it.

(Assuming by "negative vote" they mean the same thing Boehm did.)

Even later it was realized that approval voting is not actually a new
concept, it was known
centuries ago but forgotten.

https://frozengarlic.wordpress.com/2015/03/05/negative-voting/

has considerable discussion by me and 2 Taiwanese guys who seem to be
ignoring me,
but anyhow, it's a good start.


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

[William Waugh]

A point brought out in the comments to the posting on Wordpress, which may are may not be mentioned within the Facebook group, is that if no candidate gets a net positive vote, NOTA should be regarded as having won, and the campaign should be restarted with the original candidates disqualified. So that changes the semantics. However, the descriptions are consistent to the degree that both say that a voter only gets to weigh in on one candidate at most.

On Monday, August 24, 2015 at 11:42:46 AM UTC-4, Warren D. Smith (CRV cofounder, http://RangeVoting.org) wrote:

I cannot read that facebook page.

...

https://frozengarlic.wordpress.com/2015/03/05/negative-voting/

has considerable discussion by me and 2 Taiwanese guys who seem to be
ignoring me,
but anyhow, it's a good start.

...

[William Waugh]

I repeat here a couple of comments I posted on the Spacebook discussion area dedicated to Negative Voting.

First comment:

I live in the United States of America. I strongly advocate voting-system reform (or revolution) here. One of my main concerns with the politics of the US is that a two-party system prevails. The parties spar with one another on various social questions in order to distract the public, but they agree on an aggressive foreign policy and on continued burning of fossil fuels. Both major parties accept campaign money from interests that run contrary to the public interest. So I would like a new voting system to be adopted here that would offer voters a possible strategy to break the entrenchment of the two-party system. I don't know whether Taiwanese voting-system activists have the same concern with the two-party system as I think applies in the US. And I don't know whether any of the participants in this discussion group think that the plurality/antiplurality Negative Vote system is appropriate for the US. If so, please show yourself so I can argue against your position.

Second comment:

Congratulations on having found the courage to campaign for voting-system reform. Given that you have chosen to contribute to the social work involved in convincing others for reform, why do you not want to permit voters to weigh in on all the candidates when they cast their vote? Wouldn't that provide them more freedom of expression?

What do you think of the argument by Mark Frohnmayer that voting systems should meet a test of balance?
http://v.gd/uOOS6M

[Clay Shentrup]

On Monday, August 24, 2015 at 8:16:02 AM UTC-7, William Waugh wrote:

I signed up to join the group so I can argue against their stupid proposal of a plurality/antiplurality alternative at the voter's choice.

I've Skyped with one of the lead dudes. He's ineducable. Seemingly intelligent, but incredibly resistant to any kind of factual analysis. 

[William Waugh]

It just struck me, that in fact Negative Vote does meet Frohnmayer balance. I think it must be the worst system that does.

[William Waugh]

Geometrically, the range of freedom of a voter under Range Voting (including Approval) is a cube, but with Negative Vote, it's a spiky shape.

[William Waugh]

Using Facebook, I brought the attention of Mark Frohnmayer to Negative Vote. I asked him: In the past, you have suggested that reasoning can be found to explain why certain voting systems would tend to support two-party entrenchment whereas certain others, in contrast, would permit multiparty situations and/or success by independent candidates. Where do you think "Negative Vote" stands with respect to such reasoning?

[Paul Cohen]

You claim it is much less less expressive, but you don't say what you are comparing it to.  What you call negative voting (and I would call balanced or perhaps symmetric voting) is more expressive than the plurality system of voting that we are accustomed to.  It is more expressive because it measures both opposition to candidates and support in a balanced way. 

The system you describe is actually only one of many voting system that provide this balance - measuring support and opposition equally and in fact it might be termed <i>the balanced form of plurality voting</i>.  Just as plurality voting allows for full expression when there are only two candidates, this system allows for full expression when there are only three. 

But a central objective of balanced voting is to encourage there to be many candidates and if there are many candidates then a more expressive system will be needed.  Some time ago I wrote <a href = "http://www.opednews.com/Series/Balanced-Voting-by-Paul-Cohen-140521-562.html"> on balanced voting that address balanced voting generally, but specifically describe balanced versions of plurality voting, IRV and approval voting.  In each instance, the balanced version is shown to be more expressive than the non-balanced version of these systems.  Just as important however, in each instance the balanced system will do more to reduce polarization by better encouraging there to be participation by more candidates.

[William Waugh]

"You claim it is much less less expressive, but you don't say what you are comparing it to." -- Obviously we're comparing it to systems that allow the voter to weigh in on all the candidacies, not just one.

[Warren D Smith]

If I understand what you mean,
"balanced voting" is more expressive than plurality,
but not tremendously. Counts of the number of possible nontrivial ballots
you could cast:

Plurality = N
Balanced = 2*N
Approval = 2^N - 2
Full Rank Order = N!
Score with L levels = L^N - L

Boehm invented balanced in the early 1970s (called it "negative voting") but
most voting people soon after that came to the conclusion approval
obsoletes the
balanced system, whereupon the latter was pretty much discarded.
Later, apparently some people unaware of that history
re-invented balanced.

Plurality is neither the least expressive nor the worst voting system --
you can certainly invent even worse systems if you try -- but it certainly
is a strong contender for that title among methods seriously proposed...

[Paul Cohen]

As I tried to say, balanced voting is not just a single voting system but a characteristic of a voting system - and in my opinion a very desirable characteristic because it necessitates measuring both negative and positive sentiment (just as polls often do).  The simplest system of balanced voting which you call "negative voting" is pretty expressive when there are three or fewer candidates since a voter can fully express how he or she would rank the candidates - including the ability to distinguish between actively disliking a candidate and not caring one way or the other about that candidate. 

But when there is a larger number of candidates then obviously a more complicated system would be needed to allow the voters adequate expression.  My own preference would be to use balanced approval voting, but IRBV would be another alternative for a wide range of candidates.  That preference is not a theoretical one but mostly a matter of preferring a simpler voting system over a more complicated one. 

[Paul Cohen]

I just published an article on Op Ed News related to this discussion. If the link does not work for some reason, here is the URL:

http://www.opednews.com/articles/Neither-Positive-nor-Negat-by-Paul-Cohen-Alternative-Voting-Systems_Systems_Voting_Voting-Laws-State-151021-661.html

On Monday, August 24, 2015 at 10:25:59 AM UTC-4, Clay Shentrup wrote:

The guy advocating for Negative Vote (one vote for or against one candidate) saw the What Voters Want page and wants to know what voters would think of Negative Vote...

[William Waugh]

As an addendum to your definition of balanced voting, you add that "In a balanced voting system, the votes of two voters who feel exactly the opposite about the candidates will simply cancel one another." You don't assert the converse, that any system in which the votes of two voters who feel the opposite about the candidates will cancel one another is a balanced system. If you did, and if you made the addendum statement and its converse the definition of the term "balanced voting", then you would be defining the term the same way Mark Frohnmayer does.

So let's go back to how you do define it.

"I defined a balanced voting system as any voting system that gives voters an equal opportunity to vote for or against any particular candidate; balance does not come simply from allowing a negative vote but by allowing equal (balanced) opportunity to express a negative or positive attitude towards a candidate.", you write.

A voting system consists of two mathematical objects. The first object is a constraint that says what freedom the voter has in filling out a ballot. The second object is a function that takes as input, the ballots, and as output, identifies the winner(s) and may give some additional information about how well the losers did.

(I assume the discussion you present in your articles concerns only single-winner systems, and I am commenting in that context.)

It's not clear to me that your definition implies a procedure that just anybody could execute mechanically, without inserting any judgment of their own, to determine whether a given voting system meets your definition.

What does it mean to say that a voter has an opportunity to vote for or against any particular candidate?

If your vote could swing the election from electing candidate A to rejecting A and electing someone else, does that mean you have an opportunity to vote against A?

In [1], you state that Approval Voting is not balanced. However, a voter in that system gets to approve or disapprove each candidate. If I approve every candidate except A and disapprove A, I can cost A the election. In fact I could cost A the election by approving one other candidate besides A and disapproving A and the others. Have I not then voted against A? Did I not therefore have the opportunity to do so? This seems to prove that Approval meets your definition of "balanced". But you go on to deny that, so I must be failing to understand the meaning of the definition you give. Please specify out your definition so anyone who knows math[2] could apply it.

[1] http://www.opednews.com/articles/What-Might-be-the-Best-Vot-by-Paul-Cohen-Polarization_Voting-Laws-State_Voting-Reform-140529-132.html

[2] "maths" if you are not from the US.

[Paul Cohen]

On Thursday, October 22, 2015 at 11:36:25 PM UTC-4, William Waugh wrote:

As an addendum to your definition of balanced voting, you add that "In a balanced voting system, the votes of two voters who feel exactly the opposite about the candidates will simply cancel one another." You don't assert the converse, that any system in which the votes of two voters who feel the opposite about the candidates will cancel one another is a balanced system. If you did, and if you made the addendum statement and its converse the definition of the term "balanced voting", then you would be defining the term the same way Mark Frohnmayer does.

I'm afraid I've never found Mark Frohnmayer define the term "balanced voting", but if that is his definition I agree with him; it is a good definition. 

I would note that it is longstanding practice by people doing mathematics to not explicitly state the converse of a definition - the converse is assumed in a definition. 

 

[Paul Cohen]

In [1], you state that Approval Voting is not balanced. However, a voter in that system gets to approve or disapprove each candidate. If I approve every candidate except A and disapprove A, I can cost A the election. In fact I could cost A the election by approving one other candidate besides A and disapproving A and the others. Have I not then voted against A? Did I not therefore have the opportunity to do so? This seems to prove that Approval meets your definition of "balanced". But you go on to deny that, so I must be failing to understand the meaning of the definition you give. Please specify out your definition so anyone who knows math[2] could apply it.

Although my academic training was as a mathematician, much of my life I worked as an engineer and I probably have been approaching the voting issue more as an engineer than as a mathematician - though there was a bit of each that came to bear on the problem.  In particular I have been thinking of voters as people who actually vote in real elections and how that process might be improved - not so much as mathematical objects to serve a subjects for proving theorems.  Your point seems valid though and perhaps I should give the definition of "balanced" a bit more thought from the perspective of a mathematician in order to get a precise definition.  But as I explain below, I tend to think that some additional concept is what is lacking. 

But first, at the risk of seeming too much of an engineer, let me make clear where I find a problem with approval voting.  Let us suppose a (female) voter goes to the polls to vote in an election with ten candidates running for office.  Probably that voter has a few candidates she likes and a few that she dislikes - for the sake of the example, lets say there are three of each.  Now there are four remaining candidates she is ambivalent about; perhaps she has never before even heard the names of a couple of them and the other two she is simply undecided about.  With approval voting, how would she vote?   Probably she would vote for the three candidates she likes - leaving the voting system uninformed about the three she dislikes because, with her vote she cannot distinguish between them and the four she feels ambivalent about.   Or perhaps she might find some creative way to vote strategically in an attempt to make the distinction - perhaps voting for all seven of the candidates she does not actively dislike. 

On the other hand, with what I called "balanced approval voting" she would vote for the three candidates she likes and against the three candidates she dislikes.  The voting system is clearly informed about the three different categories.  


Returning to the problem of modeling this mathematically, through careful definitions, I'm not really sure how to proceed.  Probably it would require some time and effort trying to formulate and prove some theorems to see what definitions are actually needed for logical arguments.  My immediate impression is that it would be best to add some additional concept - like expressiveness to be used along with balance.  

[Bruce Gilson]

On Sat, Oct 24, 2015 at 8:52 AM, Paul Cohen <pec...@fairpoint.net> wrote:

​[

.

​.​

.

​]​

 

But first, at the risk of seeming too much of an engineer,

let me make clear where I find a problem with approval voting.  Let us suppose a (female) voter goes to the polls to vote in an election with ten candidates running for office.  Probably that voter has a few candidates she likes and a few that she dislikes - for the sake of the example, lets say there are three of each.  Now there are four remaining candidates she is ambivalent about; perhaps she has never before even heard the names of a couple of them and the other two she is simply undecided about.  With approval voting, how would she vote?   Probably she would vote for the three candidates she likes - leaving the voting system uninformed about the three she dislikes because, with her vote she cannot distinguish between them and the four she feels ambivalent about.   Or perhaps she might find some creative way to vote strategically in an attempt to make the distinction - perhaps voting for all seven of the candidates she does not actively dislike. 

On the other hand, with what I called "balanced approval voting" she would vote for the three candidates she likes and against the three candidates she dislikes.  The voting system is clearly informed about the three different categories. 

​You are here expressing a point which I have been trying to get across many times. There are people on this mailing list who refuse to accept my criticism of approval voting as valid, so I applaud your making this point.

​

 

Returning to the problem of modeling this mathematically, through careful definitions, I'm not really sure how to proceed.  Probably it would require some time and effort trying to formulate and prove some theorems to see what definitions are actually needed for logical arguments.  My immediate impression is that it would be best to add some additional concept - like expressiveness to be used along with balance.  

​Please continue in this direction. You seem to be one of the few on this list who shares my point of view.​

[Andy Jennings]

On Sat, Oct 24, 2015 at 7:13 AM, Bruce Gilson <brg...@gmail.com> wrote:

You are here expressing a point which I have been trying to get across many times. There are people on this mailing list who refuse to accept my criticism of approval voting as valid, so I applaud your making this point.

Bruce, I know you've made this argument several times.  I've been listening.  I concede that some voters will be frustrated that Approval Voting forces them to approve or disapprove everyone.  They would be happier with more levels of evaluation.

I, for one, would like to see us eventually get to an evaluative system with somewhere between 3 and 100 levels.  I think most here would agree.

But many of us believe that approval voting is still the best first step, especially for large political elections.  If it is done with "mark all that you approve, leave the rest blank," (instead of "mark the approve column or the disapprove column for each candidate") then it has these advantages:

- It works with all existing voting machines.

- Ballot looks the same to people as the current ballot.

- Voters who don't understand the system has changed can do what they did before, just mark one.

- It's much better than what we have now.

- Voter satisfaction (Bayesian Regret) in simulations is still quite good with approval.

- It could serve as a bridge to evaluative voting with more levels.

Sophisticated voters like you could use one of the following methods to vote:

- Gap method: Rate all the candidates on a 0-9 scale, then look for the biggest gap in the ratings.  Put your approval cutoff there.

- Probabilistic method:  Rate all the candidates on a -1, 0, +1 scale.  Then flip a coin.  If it's heads, then approve the top two grades.  If it's tails, then approve only the top grade.  If a large number of voters do this, then the outcome will be the same as -1/0/+1 score voting.  (Or use seven levels and a die.)

I realize neither of these is a completely satisfying voting experience for voters who think like you.  I was in New Hampshire two weeks ago running the RLC straw poll.  There were some high-information voters who really liked score voting.  They really appreciated being able to evaluate on a six-level scale.  I get it.

But there are also a lot of low-information voters out there who will be very confused by score voting.  There were many who took our straw poll who just bullet voted 5 for one candidate and left.  Others rolled their eyes when I told them to rate every candidate because it was too much work.

If you have ideas for research we can do to show that it's feasible to jump straight to a fine-grained evaluative system, then feel free to suggest it to the CES and find some donors to help fund the research.  I'd love to see that be true.

But for now, we're doing what we can with what we know...

[Bruce Gilson]

On Sat, Oct 24, 2015 at 2:20 PM, Andy Jennings <abjen...@gmail.com> wrote:

​[...]

But many of us believe that approval voting is still the best first step, especially for large political elections.  If it is done with "mark all that you approve, leave the rest blank," (instead of

​​

"mark the approve column or the disapprove column for each candidate") then it has these advantages:

​​

- It works with all existing voting machines.

​ 

​

[...]​

​But if you simply go with ​

​

"mark the approve column or the disapprove column for each candidate" the voter can simply abstain from marking either column to express a neutral vote. And this works on any voting machine that permits "yes/no" votes on referenda, which I suspect is every machine in existence.

[Jameson Quinn]

Bruce, the reason some of us are wary of any proposal that imputes neutral votes by default is that this would probably lead to some groups of voters having systematically lower voting power than others. Or at least, that's how I feel.

I think score(-1,0,1) is a good system, and using those ratings for a median system would be even better. But if it's being used for score voting, I don't like using 0 as the default option.

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[Andy Jennings]

I'll give you two more arguments for that ballot format:

1) "mark all that you approve and leave the rest blank" makes it easier to tamper with ballots (add approvals).  With "mark approve or disapprove", you could spoil ballots, but hopefully the high spoilage rates would be suspicious.

2) We should make the ballot _not_ look similar to the old ballot so people don't think it's the same old voting system.

If you're going to have columns, though, I think you might as well make it three +1/0/-1.  Like Jameson, I would prefer neutral to be explicit.

Still, for me, (1) and (2) above don't seem to outweigh the advantages of "mark all that you approve and leave the rest blank."

Arizona counting machines can't do columns.  The evaluation options would have to be rows.  Each candidate would take up as much space as a ballot initiative does now.  The ballot would be like 5 times larger.  I'm not sure about other places.

[William Waugh]

Paul Cohen, you describe what you call "balanced approval voting" and you say you like it better than approval voting. Let me offer you a clue about what balanced approval voting is equivalent to.

When I call two descriptions of voting systems "equivalent", I mean that there is a two-way mapping (bijection) between possible votes in the one system and possible votes in the other system, so that if every vote in any possible election were mapped through that mapping from one system to the other, then the systems would elect the same candidate.

Balanced approval voting is equivalent to score voting with three equally-spaced values in the offered range. You could write it as {1, 0, -1}; you could equivalently write it as {102, 101, 100} if you wanted. However, another part of the definition of one of these systems is to say what happens if a voter leaves a candidate unmentioned when filling in the ballot (which is particularly likely if write-ins are allowed and the voter has never heard of the candidate). If I understand right your description of balanced approval voting, it will rate such an unmentioned candidate in the _middle_ of the scale. I want to rate them at the _bottom_ because of fear of the _Westboro Baptist Church_ scenario, a horror story that runs through my mind in connection with default-middle systems.

Consider for example an election with write-ins allowed. Suppose a very high proportion of the voters want to bullet vote, because of their stances with regard to the candidacies listed on the ballot. Say there are three candidates on the ballot who are popular with one or another bloc of bullet voters. Under this scenario, each of the popular candidates may have an average score from the voters falling below the middle mark of the range. This could happen if about one third of the voters are giving the candidate the maximum score and two thirds are giving the candidate the bottom score. However, with your tallying system, the church candidate, unknown to any voters other than her 100 supporters, gets an average above the middle, because you have coerced your voters into giving her a middle level of support. Multiply the average score for each candidate by the count of voters, and you get the total for that candidate. So the church candidate wins the election.

A solution might be to add on the ballot, an option for the voter to specify how to treat write-in candidates that that voter doesn't write in. Personally, I would rate them at the bottom. Someone I don't know could be worse than anyone I have heard of.

On Saturday, October 24, 2015 at 8:52:34 AM UTC-4, Paul Cohen wrote https://groups.google.com/d/msg/electionscience/KbddzUQz56Y/tBAU9z6FBQAJ

[Bruce Gilson]

On Sat, Oct 24, 2015 at 4:37 PM, Jameson Quinn <jameso...@gmail.com> wrote:

Bruce, the reason some of us are wary of any proposal that imputes neutral votes by default is that this would probably lead to some groups of voters having systematically lower voting power than others. Or at least, that's how I feel.

​I do not understand this point. The decision to abstain from approving or disapproving a candidate is a conscious one, not something that is forced upon a particular group.​

 

I think score(-1,0,1) is a good system, and using those ratings for a median system would be even better. But if it's being used for score voting, I don't like using 0 as the default option.

​I have an open mind on the question of mean- vs. median-based systems. Until I see them tried in practice, all the advantages I see for one vs. the other seem to be theoretical, and how the systems work in practice remains to be seen. But I feel strongly the opposite of your position on 0 not being default in a -1 to +1 range. If I do not know anything about a candidate,​ that means I still prefer him to anyone whose positions are known to be diametrically opposite to mine.

 

​I would sooner vote for Bozo the Clown than for (say) Bernie Sanders, an admitted socialist. ​

[Andy Jennings]

On Sat, Oct 24, 2015 at 4:20 PM, Bruce Gilson <brg...@gmail.com> wrote:

But I feel strongly the opposite of your position on 0 not being default in a -1 to +1 range. If I do not know anything about a candidate,​ that means I still prefer him to anyone whose positions are known to be diametrically opposite to mine.

 

​I would sooner vote for Bozo the Clown than for (say) Bernie Sanders, an admitted socialist. ​

But isn't it feasible that there is an election with two strong candidates and an electorate almost perfectly divided, where the main candidates end up with a -0.01 and -0.02 average?  Then a write-in would have an average of 0.00001 and win.  I guess there would probably be many write-ins and there would be voters who write people in just to give them -1, too.  It just seems like a really fragile system.

Would you not allow write-ins?

[Paul Cohen]

I agree.  This equivalence was discussed in the comments of one of my articles at OEN and I made much the same point (using different terminology) was in an article I published there a couple years earlier.   

[Paul Cohen]

I should probably add for clarification that in my articles on OEN, I was in no way building up to an attack on approval voting or to claim balanced approval voting was something new and unique - although at the time I discovered it I did think it might be a new idea.  The history of my thinking on the subject goes back to around 2010 or 2011 when the only alternative to our voting system that seemed to be under discussion was IRV.  An article I read about experiences with IRV indicated problems, mostly related to its perceived complexity and the problems with educating voters.  It seemed to me that with only the few candidates we usually have in our elections, IRV might be overkill - so I came up with the idea of balanced voting as a simplification of IRV suitable for use when there are only a few candidates.  In further developing the idea of balanced voting I came up with the idea of what I now call "balanced approval voting".  I did not have a name for it at first, but when a comment to my article suggested I learn about approval voting I adopted the name.  In turn, that made me consider IRV and whether that might be improved by adding balance.  

The point is, that I was not particularly trying to criticize other systems that people may favor; I was thinking about the idea of balance and what its implications were.  In the OEN articles I was describing what I had discovered following this line of thinking.  

On Saturday, October 24, 2015 at 5:54:21 PM UTC-4, William Waugh wrote:

[Paul Cohen]

First of all, let me agree with an earlier comment that we really need to try out some of these systems and get some real-world experience with the different proposals; we would no doubt learn quite a lot.  The trials don't have to be at a governmental level, but should attempt to get a cross-section of ordinary people, not just a cross-section say, of mathematicians.  Perhaps some public high-schools could be enlisted to try some of the different methods for electing class president. 

You make an interesting point about vote tampering, but to me that is a peripheral - though very important - issue that should not govern the selection of a voting method.  There likely are technological countermeasures possible for any new vote-tampering scheme and that would seem to be the right approach for the problem.  I would hope that getting away from our two-party duopoly would reduce cheating at elections or at least make it more difficult.  The polarization of two-party politics seems to be a big motivator for cheating.  And of course I have been arguing that balance voting systems will lead naturally to more political parties.

But voter education is a very important issue that, if you are concerned about actual adoption of a voting system, is important.  In this context, I think having two columns, "for" and "against" has a considerable advantage even over a three-column -1, 0, 1 ballot but certainly over the 0, 1, 2 approach, even though these three different ballot designs are for (abstractly) the same system of voting.  If you are talking to mathematicians of course it will be apparent to them that there is no real difference - but this level of abstraction will be a hard sell with the general public.  Think, for example, about which ballot you would like to explain to your 85 year-old grandmother.  

[Paul Cohen]

Write-in candidates would seem to present this problem whenever voters can vote on multiple candidates.  One solution would be as you suggest, another would be to use a median scoring system and yet another would be to not allow write-in voting.  I would tend to favor the last option, accompanied with a nomination system that makes it easy for names to be placed on the ballot - perhaps a petition with a few signatures from 0.1% of the voters. 

On Saturday, October 24, 2015 at 5:54:21 PM UTC-4, William Waugh wrote:

[William Waugh]

On Saturday, October 24, 2015 at 7:20:31 PM UTC-4, Bruce R. Gilson wrote:

... If I do not know anything about a candidate,​ that means I still prefer him to anyone whose positions are known to be diametrically opposite to mine.

 

​I would sooner vote for Bozo the Clown than for (say) Bernie Sanders, an admitted socialist. ​

So then on a normalized scale of your political power from 0 to 1, you'd give 0 to Sanders and 1/2 to Hitler.

How about this, as I already mentioned in this thread? Allow each voter to give a rating to apply to "all others", i. e. any candidates not specifically rated on that voter's ballot? Then you could give the unknowns the medium level of support that you prefer, and I as a voter could give them the bottom level of support, as I prefer.

[Bruce Gilson]

On Sun, Oct 25, 2015 at 8:46 PM, William Waugh <2knuw...@snkmail.com> wrote:

On Saturday, October 24, 2015 at 7:20:31 PM UTC-4, Bruce R. Gilson wrote:

... If I do not know anything about a candidate,​ that means I still prefer him to anyone whose positions are known to be diametrically opposite to mine.

 

​I would sooner vote for Bozo the Clown than for (say) Bernie Sanders, an admitted socialist. ​

So then on a normalized scale of your political power from 0 to 1, you'd give 0 to Sanders and 1/2 to Hitler.

​No. I know who Hitler is, so he doesn't get the 1/2. I specifically referred to candidates about which I know nothing.

​

 

How about this, as I already mentioned in this thread? Allow each voter to give a rating to apply to "all others", i. e. any candidates not specifically rated on that voter's ballot? Then you could give the unknowns the medium level of support that you prefer, and I as a voter could give them the bottom level of support, as I prefer.

​No problem. I'd be absolutely willing to go with this plan.​

 

[William Waugh]

http://www.opednews.com/articles/Instant-Runoff-Balanced-Vo-by-Paul-Cohen-Alternative-Voting-Systems_Approval-Voting_Election-Instant-Runoff-Voting_Election-Voting-Issues-140603-488.html

1. The last paragraph asks for a comparison between a multiwinner voting system and a single-winner system; that's apples-to-oranges and does not make sense.

2. The system is still very similar to IRV and so I would want to see some kind of evidence or argument that it wouldn't exhibit the same pathological behavior as is shown for IRV in http://zesty.ca/voting/sim/ particularly at and below the heading "Shattered".

Have you heard of Reweighted Range Voting (RRV)?

[Paul Cohen]

1. Whether an election is single-winner or multi-winner would seem to be largely independent of the voting system though some systems would be inappropriate for choosing multiple winners.  It would seem that approval voting, balanced or not, could be used for choosing either a single winner or several. I've always thought of IRV as for use in choosing a single winner, but it would not be at all difficult to use IRV (or IRBV) for multiple winners. 

2. When time permits, I'll take a look at the example you link to for pathological behavior of IRV, but let me say that, as I suggest in my article, I am not particularly an advocate of IRV or IRBV though I do think IRBV is a significant improvement over IRV.  I thought it appropriate to write the article about IRV and IRBV not as an advocate but only because there is such widespread interest in IRV.  There is a ballot initiative in Maine to adopt IRV and most discussions that I've seen are by people who seem to think that IRV is the only possible alternative to plurality voting.  IRV would probably be an improvement but IRBV would be even more of an improvement.  That said, I'm sure there is no perfect system that has no flaws.

No, I'm not familiar with RRV voting - again, as time permits .... 

[Warren D Smith]

RRV:

http://RangeVoting.org/RRV.html

[Paul Cohen]

With regard to the issue of write-ins it occurs to me that another alternative would be to insist that for a write-in to be considered in the voting, some minimum percentage of voters might be required to have shown interest in the candidate.  In other words, a candidate could be dropped from the running unless (for example) 10% of the voters chose to vote either approval or disapproval for that candidate. 

On Saturday, October 24, 2015 at 5:54:21 PM UTC-4, William Waugh wrote:

Consider for example an election with write-ins allowed.

[Brian Goldman]

 In other words, a candidate could be dropped from the running unless (for example) 10% of the voters chose to vote either approval or disapproval for that candidate. 

This creates a participation failure. Consider a candidate which wins with exactly 10% of the voters expressing an opinion. Anyone who voted negatively for that candidate was actually hurt by doing so, as if they had not that candidate would not have won.

​

[Paul Cohen]

Your point that balanced approval voting is equivalent to a set of range voting schemes suggests that all objections to balanced approval voting should be considered with regard to range voting as well.  For example, how should abstentions be handled for write-in candidates when range voting is used?

In your example, {102, 101, 100}, presumably if this is identical to balanced voting then an abstention with regard to any candidate should be treated the same as a 101.  But for the reasons you suggest, what should be done for write-in candidates?  

More generally, for range {6, 5, 4, 3, 2, 1} how should an abstention be handled?  Presumably in the case {5, 4, 3, 2, 1} it should be treated the same as a 3.

Let me say that I do think range voting is a good approach, whatever range is selected.  However, I think the one I call balanced voting is particularly intuitive and easy to explain and I see that as particularly important when dealing with the general public.

On Saturday, October 24, 2015 at 5:54:21 PM UTC-4, William Waugh wrote:

[William Waugh]

I don't think an election should offer a voter an option to abstain on some but not all candidates. The election should offer the voter the opportunity to support whichever candidates the voter chooses to support. So the options would be maximum support vs. no support with possible intermediate degrees of partial support. Another writer in this thread wants the option to give a middle level of support to unknown candidates. In the interest of getting improved voting systems into place, I am willing to concede that writer that option. However, I think it is not a good option for a voter to take. Someone willing to carry out his public responsibility would not give political support (even partial) to an unknown candidate, in my opinion.

The system you describe under the name "balanced approval voting" (although all approval voting is balanced in the sense that every possible vote has its opposite), falsely presents an option to "abstain". I say falsely, on the grounds that your tallying method treats the "abstention" as 50% support. Giving a middle level of support is not properly described as an abstention.

You could offer abstention by averaging a candidate's scores instead of summing them. But that leads to the horror story of a small group supporting an unknown candidate. 100% of those who don't "abstain" from weighing in on that candidacy support the election of that candidate, so that candidate wins. Unless the tallying treats non-mention of the candidate as full opposition instead of as abstention.

On Wednesday, October 28, 2015 at 9:45:31 AM UTC-4, Paul Cohen wrote https://groups.google.com/d/msg/electionscience/KbddzUQz56Y/xaN55lF0CAAJ

[William Waugh]

>> 1. Whether an election is single-winner or multi-winner would seem to be largely independent of the voting system ...

No. People describe or prescribe or identify or define or indicate voting systems for specifically the single-winner case or the multi-winner case. The definition for a multiwinner system has to specify how to identify the second and subsequent winners. A multiwinner system can be made based on approval ballots by tallying them as Reweighted Range Voting (RRV). If you simply take the top N candidates, yes, that's some kind of multiwinner system, but it does not yield proportional representation; it has a winner-take-all tendency. A majority party can force all the winners to come from itself.

>> ... I've always thought of IRV as for use in choosing a single winner, but it would not be at all difficult to use IRV (or IRBV) for multiple winners.

In fact IRV is the degenerate case of a multi-winner system, the Single Transferrable Vote.

Single-winner voting systems have been studied mathematically more thoroughly than multiwinner systems have.

[Bruce Gilson]

On Wed, Oct 28, 2015 at 11:59 AM, William Waugh <2knuw...@snkmail.com> wrote:

I don't think an election should offer a voter an option to abstain on some but not all candidates. The election should offer the voter the opportunity to support whichever candidates the voter chooses to support. So the options would be maximum support vs. no support with possible intermediate degrees of partial support. Another writer in this thread wants the option to give a middle level of support to unknown candidates. In the interest of getting improved voting systems into place, I am willing to concede that writer that option. However, I think it is not a good option for a voter to take. Someone willing to carry out his public responsibility would not give political support (even partial) to an unknown candidate, in my opinion.

​I presume that I am the "other writer in this thread." And I think the problem I have with your ideas is that I see an election as not only an opportunity to give support ​to (one or more) candidate(s) but also to oppose

​

 (one or more) candidate(s)

. Therefore I want the opportunity to abstain because I feel that if I don't know anything about a candidate, I don't want to have my vote treated in the same way as a conscious ​

​

​desire to oppose that candidate. A totally unknown candidate means I'm willing to take a chance on him if the alternative is electing someone about whom all I know is he's opposed to everything I stand for.​

The system you describe under the name "balanced approval voting" (although all approval voting is balanced in the sense that every possible vote has its opposite), falsely presents an option to "abstain". I say falsely, on the grounds that your tallying method treats the "abstention" as 50% support. Giving a middle level of support is not properly described as an abstention.

​I disagree. But this is a result of the fact that I consider the opposite of giving full support to a candidate is not giving him 0% support -- it is rather giving him 100% opposition. So the abstention is not being given 50% support, but rather giving him neither any support nor any opposition.​

 

[Paul Cohen]

I have been considering only single-winner systems - and I agree that these should be two separate topics.

[Paul Cohen]

I disagree, though the formulation of the system as range voting with all positive values does give the impression of 50% support.  Abstaining from voting for a candidate (0) means not taking a position on that candidate; opposition means opposition (-1) and support (+1) means support and the tally as an average interprets meaning correctly.

[William Waugh]

Paul Cohen, I'm pretty sure that your writeup of "balanced approval voting" (a poor name, since approval voting is also balanced) does not make clear that the tally is to divide by the count of approvals + disapprovals for a given candidate and leave out abstentions. If you modify it to specify that kind of tallying, then it will allow true abstentions, distinguishable from a middle level of support on the grounds of the effect on the determination of who wins.

Again, I would have a concern with the system if it did not allow a voter to disapprove the write-in candidates that that voter does not write in.  I don't feel I would be meeting my civic responsibility if I were to abstain on fascist candidates, and there could be any number of them I don't know the names of.

I suggest this name for such a system: Approval Voting with Abstention.

[William Waugh]

I guess there has to be a special rule to the effect that if a candidate receives no votes for or against, they should not be elected. Otherwise, you would have to divide by zero.

[Paul Cohen]

First of all, approval voting does not provide a way to vote against a candidate - not in the sense that it will cancel out a vote for that candidate.  It provides no way for a voter to distinguish between ambivalence and opposition. Approval voting only allows a voter to vote for a candidate or not to vote for that candidate. 

It is true that taking an average rather than simply counting abstention as the center vote does slightly penalize a candidate with a large number of abstentions.  If this is objectionable for some reason then yes, abstentions could be simply eliminated from the count.  This might make counting ballots by hand a bit more confusing but it probably would not often affect the outcome. 

As for changing the name, I would defer to Shakespeare.  Would a rose by any other name not smell as sweet? 

[Paul Cohen]

Perhaps I need another cup of coffee.  No one should be talking about averages here - only vote count.  With balanced approval voting there is no difference whatever between omitting abstentions and counting them as zero in tallying a vote-count. 

[Bruce Gilson]

On Thu, Oct 29, 2015 at 10:49 AM, Paul Cohen <pec...@fairpoint.net> wrote:

Perhaps I need another cup of coffee.  No one should be talking about averages here - only vote count.  With balanced approval voting there is no difference whatever between omitting abstentions and counting them as zero in tallying a vote-count.

​Paul's ideas are close to my own. I am writing this simply to express my agreement.​

[William Waugh]

"First of all, approval voting does not provide a way to vote against a candidate - not in the sense that it will cancel out a vote for that candidate."

Wrong.

Let's see if we have the same understanding of "cancel". To test for cancellation, we look at all the possible cases where there is some "bulk" of votes B already collected and we're contemplating adding a vote x and a vote y, and we ask whether, for all possible values of x, there is a possible vote y such that adding x and y to B will make the election rank the candidates the same way as it would with just B and not x nor y. I will now construct the y for any x. Vote y is just the complement of x under the list of candidates. So for example, if the candidates are Reagan, Bush, Sanders and La Riva, and you vote Reagan and Bush and I vote Sanders and La Riva, my vote cancels yours. The addition of x and y adds an equal score to each candidate, and this does not change the final ranking. If t1 > t2, then t1 + 1 > t2 + 1 QED.

There is more discussion of balanced voting in this forum at https://groups.google.com/d/msg/electionscience/wU2tiqtHbfI/-NKgAM73HYcJ

"No one should be talking about averages here - only vote count.  With balanced approval voting there is no difference whatever between omitting abstentions and counting them as zero in tallying a vote-count."

There used to be commercials on television for something called "ginsu knives". I have read that "ginsu" was just made up; there was no such category known in Japanese or any other culture. Would you say the advertising was deceptive? Do you want to connect deceptive advertising to voting reform? Is it your purpose to try to throw in a monkey wrench and reduce the chance that we can get voting reform accepted? Just advertising that a certain act in the voting booth is an "abstention" does not make the term meaningful, useful, or correct in that context. Belief that just by using words and not tailoring actions to them, that that produces a better result, amounts to tokenism and religion, prayer, and faith. Since you are using the totals to determine the winner, this particular act that you are mislabeling as "abstention" has the effect on the electoral outcome of mid-level support for the candidate. You are putting out deceptive propaganda when you call it an abstention. In effect you are trying to connect voting reform to deceptive propaganda in the minds of those who might evaluate it. When they figure the deception out, they will be put off to voting reform generally. Your "abstention" is just a ginsu mid-level of support. In fact, it's worse than ginsu, because "abstention" means something to people, and ginsu doesn't. It's not just deceptively meaningless, it's deceptively meaningful and a lie.

[Bruce Gilson]

On Thu, Oct 29, 2015 at 6:51 PM, William Waugh <2knuw...@snkmail.com> wrote:

There used to be commercials on television for something called "ginsu knives". I have read that "ginsu" was just made up; there was no such category known in Japanese or any other culture. Would you say the advertising was deceptive? Do you want to connect deceptive advertising to voting reform? Is it your purpose to try to throw in a monkey wrench and reduce the chance that we can get voting reform accepted? Just advertising that a certain act in the voting booth is an "abstention" does not make the term meaningful, useful, or correct in that context. Belief that just by using words and not tailoring actions to them, that that produces a better result, amounts to tokenism and religion, prayer, and faith. Since you are using the totals to determine the winner, this particular act that you are mislabeling as "abstention" has the effect on the electoral outcome of mid-level support for the candidate. You are putting out deceptive propaganda when you call it an abstention. In effect you are trying to connect voting reform to deceptive propaganda in the minds of those who might evaluate it. When they figure the deception out, they will be put off to voting reform generally.

​​

Your "abstention" is just a ginsu mid-level of support. In fact, it's worse than ginsu, because "abstention" means something to people, and ginsu doesn't. It's not just deceptively meaningless, it's deceptively meaningful and a lie.

​You seem to assume (in fact, you've said as much) ​that voting is simply expressing a degree of support for a candidate. In

 

​fact, when​ I vote, sometimes I want to support someone, and other times I want to express my opposition to a candidate. The state

ment that "

​

Your

​'​

abstention

​'​

is just a

​...

 mid-level of support"

​ is just not true. Giving someone the lowest possible rating (whether in Approval or Score) does not mean simply zero support; it means I actively oppose the candidate and do not want to see him elected. Giving someone a rating exactly halfway between the lowest possible and the highest possible (if the voting system permits it) is truly an abstention, meaning I neither support nor oppose him.​ Where you go wrong is that you fail to see that voting can indicate degree of opposition and not merely degree of support.

[Paul Cohen]

So let me clear up what I mean when I say abstention.  In any voting system like approval, or range voting (of which balanced approval voting is an example) I am assuming that a voter need not mark anything at all on some lines of the ballot.  Possibly the voter fails to mark any lines at all in which case I would say he (or she) is abstaining from voting at all; but if the voter fails to mark just some of the lines for particular candidates then I would say the voter is abstaining from voting for those particular candidates. 

Now what I called "balanced approval voting" is, as you have pointed out, isomorphic to range voting with a range of three and in particular to the system {-1, 0, 1}.  So consider a vote, f, in this system.  It is a function with domain a subset of the candidates into the set of values {-1, 0, 1}.  Another voter might cast the vote, g, with the same domain but with the values g(x) = -f(x) for all x in the domain.  These two votes cancel one another out exactly, without forcing the voter to take stands on every single, including candidates that the voter is unfamiliar with.

It appears that you are emotionally committed to approval voting and you don't like the idea of anyone suggesting it might have flaws.  I've encountered the same kind of attitude among people who think that IRV is the greatest system in the world and nothing could improve on it.  These IRV advocates take exactly the same stance that offering up some alternative system is really a way to throw a monkey wrench into the possibility of voting reform.

I will almost certainly vote for IRV when it comes up in an election in Maine - even though I know - and I tell people that there are better alternatives.  Approval voting would, in my view be better and of course I think balanced approval voting would be better yet.  But then I'd like there to be more than just two parties in contention in our elections and it is apparent balanced voting would lead to more parties.  Someone who wants to preserve our two party system would of course prefer to avoid adopting a balanced system. 

[William Waugh]

On Thursday, October 29, 2015 at 9:21:40 PM UTC-4, Paul Cohen wrote:

So let me clear up what I mean when I say abstention.  In any voting system like approval, or range voting (of which balanced approval voting is an example) I am assuming that a voter need not mark anything at all on some lines of the ballot.  Possibly the voter fails to mark any lines at all in which case I would say he (or she) is abstaining from voting at all; but if the voter fails to mark just some of the lines for particular candidates then I would say the voter is abstaining from voting for those particular candidates.

If the only meaning you give to "abstention" is that the voter can leave a line unmarked, every voting system has abstention.
 

Now what I called "balanced approval voting" is, as you have pointed out, isomorphic to range voting with a range of three and in particular to the system {-1, 0, 1}.  So consider a vote, f, in this system.  It is a function with domain a subset of the candidates into the set of values {-1, 0, 1}.  Another voter might cast the vote, g, with the same domain but with the values g(x) = -f(x) for all x in the domain.  These two votes cancel one another out exactly, without forcing the voter to take stands on every single, including candidates that the voter is unfamiliar with.

Your analysis above shows, correctly, that {-1, 0, 1} score, and therefore your equivalent system as well, are balanced.

Why don't you acknowledge that {0, 1} is also balanced, as I argued?

 

It appears that you are emotionally committed to approval voting and you don't like the idea of anyone suggesting it might have flaws.

I love the idea of someone suggesting it has flaws, if those suggestions accord with facts and logic.

I did not express a preference for approval over finer-grained score. My preference is for a range including {1.00, 0.99, 0.01, 0.00} and maybe some more steps toward the middle. The range  {1, 0, -1} is semantically closer to what I prefer than {0, 1} is, on the grounds that it has shorter intervals in it (normalized 1/2), which is semantically closer to the even shorter interval that I prefer for near the extremes. So I have some reason to actually prefer {1, 0, -1} to {0, 1}, provided that unknown candidates do not automatically get a score above the bottom of the range, -1.

[William Waugh]

The purpose of an election is to arrive at the outcome. The proper semantics of the terms used to describe voter actions come solely from their effect on the outcome. You object to the terms I use and you emphasize that your terms are somehow better, but you do not explain the distinction in terms of the electoral outcome. Therefore, based on what you have explained to date, your distinctions remain provisionally meaningless.

On Thursday, October 29, 2015 at 7:26:31 PM UTC-4, Bruce R. Gilson wrote https://groups.google.com/d/msg/electionscience/KbddzUQz56Y/C4O79JriCAAJ

[Bruce Gilson]

On Thu, Oct 29, 2015 at 11:56 PM, William Waugh <2knuw...@snkmail.com> wrote:

The purpose of an election is to arrive at the outcome. The proper semantics of the terms used to describe voter actions come solely from their effect on the outcome. You object to the terms I use and you emphasize that your terms are somehow better, but you do not explain the distinction in terms of

​​

the electoral outcome. Therefore, based on what you have explained to date, your distinctions remain provisionally meaningless.

​All right. I will talk, in the following post, of "

​

the electoral outcome." Let us take the specific case of an election using what Paul Cohen calls "balanced approval voting" and which I prefer to call "approval/disapproval voting." (Also known as "yes/no voting"; see, for example, http://upcommons.upc.edu/bitstream/handle/2117/7476/Freixas+Anonymous+yes+no+voting.pdf?sequence=7) Let us use

​​

(-1, 0, +1) as the values because it makes terminology easier, as the words "negative," "zero," and "positive" can be used; I need more complex language if any other numerical values are assigned to the possible votes.

​

​

When I give a

​​

positive score to a candidate, it really means I would be 

​​

happy with an 

​​

outcome in which that candidate wins the election.

​ ​

​

When I give a negative score to a candidate, it really means I would be 

​​un

happy with an 

​​

outcome in which that candidate wins the election.

​ ​

​Thus, a positive rating means support, while a negative rating means more than just lack of support: it

 

​means active opposition. The in-between (zero on a ​[

​

-1, 0, +1

] scale) rating is not really an indication of 50% support: it really, truly, means that I have no idea whether the candidate's election would make me happy or not.​ This analysis explains both my feeling that Paul Cohen's characterization of a zero rating as an abstention is accurate and my preference that failure to rate a candidate should not be construed as a minimum rating, but rather as a middle rating 

(zero on a ​[

​

-1, 0, +1

] scale).

 

To repeat, in slightly different terms, when I give a blank rating to a candidate, it means I truly want to have no effect on the candidate's winning or losing. If I do not know anything about a candidate, I do not want my vote to cause him to lose, which treating such votes as minimum-rating votes (as you favor) might do. I want to express the opinion that I am not qualified to rate that candidate, and therefore my vote should not count for or against him.

Have I sufficiently explained myself, or is there any further information I need to provide to explain my position?

[William Waugh]

"...[W]hen I give a blank rating to a candidate, it means I ... want to have no effect on the candidate's winning or losing." [your emphasis]

The tallying method most recently endorsed by Paul Cohen (and approved by me as well) won't achieve that for you. This method says to total the scores and see who has the most.

Here I notate the scores based on a range from -1 to +1 inclusive.

Assume three candidates, C1, C2, and C3.

The totals from the voters other than you are C1 has zero, C2 has zero, and C3 has -2.

If you do not make it to the poll because your car breaks down, the election total is the above. C1 and C2 are tied for the lead.

You get your car started in time to make it to the poll before it closes. You vote C1 1, C2 0, and C3 -1.

The new totals including your vote are C1 1, C2 zero, and C3 -3.

In this example your vote has converted C2 from being tied for the lead, to being a loser, even though your desire was that your vote would not have an effect on C2's winning. Therefore, this tallying method does not meet your stated constraint, that it must produce no effect on a candidate's winning or losing as a result of your casting a vote that gives a blank rating to that candidate.

On Friday, October 30, 2015 at 7:44:40 PM UTC-4, Bruce R. Gilson wrote https://groups.google.com/d/msg/electionscience/KbddzUQz56Y/ChG-abHTBAAJ

[Bruce Gilson]

On Sat, Oct 31, 2015 at 7:02 AM, William Waugh <2knuw...@snkmail.com> wrote:

​​

"...

​​

[W]hen I give a blank rating to a candidate, it means I ... want to have no effect on the candidate's winning or losing." [your emphasis]

The tallying method most recently endorsed by Paul Cohen (and approved by me as well) won't achieve that for you. This method says to total the scores and see who has the most.

Here I notate the scores based on a range from -1 to +1 inclusive.

Assume three candidates, C1, C2, and C3.

The totals from the voters other than you are C1 has zero, C2 has zero, and C3 has -2.

If you do not make it to the poll because your car breaks down, the election total is the above. C1 and C2 are tied for the lead.

You get your car started in time to make it to the poll before it closes. You vote C1 1, C2 0, and C3 -1.

The new totals including your vote are C1 1, C2 zero, and C3 -3.

In this example your vote has converted C2 from being tied for the lead, to being a loser, even though your desire was that your vote would not have an effect on C2's winning. Therefore, this tallying method does not meet your stated constraint, that it must produce no effect on a candidate's winning or losing as a result of your casting a vote that gives a blank rating to that candidate.

​That is an interesting point, and it means I need to rephrase what I said, because obviously, C1 and C2 are tied, and I vote to improve C1's chance of winning, by that very act I​ harm C2. However, the problem is not with Paul Cohen's system but with the way I phrased my statement. I'll have to think of a better way of stating what I meant to say.

Tentatively, my point is that 

​

"...

​​

[W]hen I give a blank rating to a candidate, it means I ... want" that particular vote "to have no effect on the candidate's winning or losing." But the ratings I give to other candidates (positive or negative) can raise or lower the first candidate's chance of winning, in examples like the one you gave. But this may yet require some revision of the wording, so do not hold me to this as final, though you may comment on this to help me come to a better phrasing.

[Paul Cohen]

In view of the confusion that seems to surround the idea of balanced voting, I have prepared a short paper that presents and discusses the idea in a more mathematical manner.   You can find it HERE if you are interested. 

On Thursday, October 22, 2015 at 11:36:25 PM UTC-4, William Waugh wrote:

As an addendum to your definition of balanced voting, you add that "In a balanced voting system, the votes of two voters who feel exactly the opposite about the candidates will simply cancel one another." You don't assert the converse, that any system in which the votes of two voters who feel the opposite about the candidates will cancel one another is a balanced system. If you did, and if you made the addendum statement and its converse the definition of the term "balanced voting", then you would be defining the term the same way Mark Frohnmayer does.

So let's go back to how you do define it.

"I defined a balanced voting system as any voting system that gives voters an equal opportunity to vote for or against any particular candidate; balance does not come simply from allowing a negative vote but by allowing equal (balanced) opportunity to express a negative or positive attitude towards a candidate.", you write.

A voting system consists of two mathematical objects. The first object is a constraint that says what freedom the voter has in filling out a ballot. The second object is a function that takes as input, the ballots, and as output, identifies the winner(s) and may give some additional information about how well the losers did.

(I assume the discussion you present in your articles concerns only single-winner systems, and I am commenting in that context.)

It's not clear to me that your definition implies a procedure that just anybody could execute mechanically, without inserting any judgment of their own, to determine whether a given voting system meets your definition.

What does it mean to say that a voter has an opportunity to vote for or against any particular candidate?

If your vote could swing the election from electing candidate A to rejecting A and electing someone else, does that mean you have an opportunity to vote against A?

In [1], you state that Approval Voting is not balanced. However, a voter in that system gets to approve or disapprove each candidate. If I approve every candidate except A and disapprove A, I can cost A the election. In fact I could cost A the election by approving one other candidate besides A and disapproving A and the others. Have I not then voted against A? Did I not therefore have the opportunity to do so? This seems to prove that Approval meets your definition of "balanced". But you go on to deny that, so I must be failing to understand the meaning of the definition you give. Please specify out your definition so anyone who knows math[2] could apply it.

[1] http://www.opednews.com/articles/What-Might-be-the-Best-Vot-by-Paul-Cohen-Polarization_Voting-Laws-State_Voting-Reform-140529-132.html

[2] "maths" if you are not from the US.

On Thursday, October 22, 2015 at 7:56:25 AM UTC-4, Paul Cohen wrote:

I just published an article on Op Ed News related to this discussion. If the link does not work for some reason, here is the URL:

http://www.opednews.com/articles/Neither-Positive-nor-Negat-by-Paul-Cohen-Alternative-Voting-Systems_Systems_Voting_Voting-Laws-State-151021-661.html

[Paul Cohen]

Bruce,

Thank you for your comments.  I have written up what seems to me a precise definition of balanced voting as I have been thinking of it.  You can download a copy of it HERE. 

On Saturday, October 24, 2015 at 10:14:01 AM UTC-4, Bruce R. Gilson wrote:

On Sat, Oct 24, 2015 at 8:52 AM, Paul Cohen <pec...@fairpoint.net> wrote:

​[

.

​.​

.

​]​

 

But first, at the risk of seeming too much of an engineer, let me make clear where I find a problem with approval voting.  Let us suppose a (female) voter goes to the polls to vote in an election with ten candidates running for office.  Probably that voter has a few candidates she likes and a few that she dislikes - for the sake of the example, lets say there are three of each.  Now there are four remaining candidates she is ambivalent about; perhaps she has never before even heard the names of a couple of them and the other two she is simply undecided about.  With approval voting, how would she vote?   Probably she would vote for the three candidates she likes - leaving the voting system uninformed about the three she dislikes because, with her vote she cannot distinguish between them and the four she feels ambivalent about.   Or perhaps she might find some creative way to vote strategically in an attempt to make the distinction - perhaps voting for all seven of the candidates she does not actively dislike. 

On the other hand, with what I called "balanced approval voting" she would vote for the three candidates she likes and against the three candidates she dislikes.  The voting system is clearly informed about the three different categories. 

​You are here expressing a point which I have been trying to get across many times. There are people on this mailing list who refuse to accept my criticism of approval voting as valid, so I applaud your making this point.

​

 

Returning to the problem of modeling this mathematically, through careful definitions, I'm not really sure how to proceed.  Probably it would require some time and effort trying to formulate and prove some theorems to see what definitions are actually needed for logical arguments.  My immediate impression is that it would be best to add some additional concept - like expressiveness to be used along with balance.  

​Please continue in this direction. You seem to be one of the few on this list who shares my point of view.​

[William Waugh]

Your newest definition of balanced is met by a different set of systems than the set of those under which for any vote that can be included, another could be included such that the final ranking of candidates would remain the same as though the two votes had not been included.

On Tuesday, November 3, 2015 at 7:18:20 PM UTC-5, Paul Cohen wrote:

In view of the confusion that seems to surround the idea of balanced voting, I have prepared a short paper that presents and discusses the idea in a more mathematical manner.   You can find it HERE if you are interested.

Let's lay aside for a moment the problems of write-ins and "abstentions" and ask what is the best social and political interpretation of the result of a score election. Let's try to understand that in a way that will give the same interpreted result no matter what range of numbers has been used to offer the voters the levers of influence. Say for example, the range is {999, 1000, 1001}. If two voters have exact opposite opinions on the candidates, the sum of their votes will then increase each candidate's score by 2000. An obvious part of the answer is the determination of who wins the election. But do the results say something about how well the losing candidates did? Can we use the results to show if a candidate who ran more than once gained in popularity? Clearly we can at least go so far as to look at a ranking of the candidates by their final total scores. That's the ranking of how well they did in the election. But suppose we find a candidate's name in the ranking bracketed by the name of the candidate who did the next better and the candidate who did the next worse. Is that all the information available, or can we go yet further and understand something about how well the candidate did even within that bracketing? Did the candidate do almost as well as the one who did the next better, or only just barely any better than the one who did the next worse, or maybe midway? Yes, in fact we can normalize the result based on the highest and lowest totals any candidates could have gotten if the electorate had expressed total favor for one and total opposition to another. For our standard of normalization, we could assign the number zero to the worst any candidate could do, and one to the best any candidate could do. Or we could use -1 and 1. Or maybe even -pi/2 and pi/2, then the number would look like an angle, and you could draw a picture of an analog meter, with the angle of the needle indicating how well the candidate did. The standard to use is a matter of taste. But once we pick a standard, I contend that we will have found what it should mean for one election to be considered as isomorphic to another, or one score voting system to be isomorphic to another. The systems are isomorphic, if for any sequence of votes that would map to the same sequence if normalized, the tallies would map to the same as each other if also normalized.

The type of isomorphism I describe just above might not be the type you had in mind when you mentioned isomorphism in your latest writing.

Cohen balance is not the same as Frohnmayer balance (anymore).

You define balance by giving a seed case, R = {-1, 0, 1}, and saying that's balanced, and then you say that any system isomorphic to a balanced system is balanced. I'm not sure what you consider isomorphic for the purpose of the definition. But in any event, I don't know that the concept you are defining is particularly applicable for describing any properties that would have political or social import.

You go on to discuss abstention regarding a candidate. Not in this particular writing, but in this discussion thread, you say you want to forbid write-ins. So that class of abstention, where some voters write in a candidate but others don't and maybe never heard of the candidate, seems to be off the table for the systems you favor, so you duck that part of the problem. So that leaves the kind of abstention where the candidate's name is written clearly on the ballot before the voter touches the ballot, and the voter fails to indicate a score for that candidate. I think there is a problem if you tell or hint or insinuate in a way that the voters can see or hear you do so, or let it be assumed, that the meaning of an abstention is that the voter doesn't care whether that candidate gets elected. I think there is a problem with printing ballots that fail to tell the voter exactly what the effect of an abstention will be on the tally.

When you recommend treating abstention as a score in the middle of the range, the zero if zero is the middle, I fear you may be under the impression that scoring a candidate this way cannot elect that candidate, or that it cannot keep the candidate from being elected, and I fear that your readers may also not understand the truth about this. I have shown an example in this discussion thread, that proves that scoring a candidate in the middle of the range can convert that candidate from tying for the lead, to being in the loser field. It's just as easy to show that one vote that scores the candidate in the middle of the range can convert the candidate between being the sole lead to tying with someone else for the lead.

I think it is misleading to tell voters that they can abstain on a candidate in the sense of casting a vote that doesn't influence that candidate's final position. The best thing is to treat abstention as total opposition and tell the voters that that is the effect it would have. They should be told that if they don't want to express total opposition to a candidate, they should rate that candidate using their writing instrument.

Waugh

[Bruce Gilson]

On Tue, Nov 3, 2015 at 7:21 PM, Paul Cohen <pec...@fairpoint.net> wrote:

Bruce,

Thank you for your comments.  I have written up what seems to me a precise definition of balanced voting as I have been thinking of it.  You can download a copy of it HERE. 

​I like what you wrote. I think the two of us are in total agreement on this point.​

 

[William Waugh]

Consider the following voting strategy for an antiplurality election or a plurality/antiplurality choose-one election. First, what do I mean by those terms. A "plurality/antiplurality choose-one election" means an election in which the voters have the freedom to choose to support or oppose one candidate of their choice, and the winner is determined by giving each candidate a point for each vote for them and taking away a point for each vote against, and the candidate with the highest total wins. We have discussed in this forum a very similar system under the name "Negative Vote". When we discussed it, I argued against it as unnecessarily inexpressive compared to straight Score, and having no advantages over such.

However, consider the following voting strategy: First, the voting strategist for a party determines what vote she would recommend to that party's members under arbitrarily-fine-grained Score Voting, using whatever strategic considerations she would apply if that were the voting system in place. These scores are normalized so that zero is the highest score and -1 is the sum of the scores. Negate these numbers. You now have a vector of numbers that add up to 1. They can be interpreted as probabilities. For each voter that is declaring an interest in following advice from the party strategist, pick a random number from some source of random numbers, and use it to advise that person to vote against one of the candidates. Pick which candidate, in such a way, that the probability of a given candidate being picked equals the number associated to that candidate from the vector of probabilities.

I am not saying necessarily that I am taking the time now to code up the simulation to estimate numerically the Bayesian Regret (BR) of this strategy, but I invite you to speculate about how well or poorly such a combination of strategy and voting system would work at defeating the two-party syndrome, as compared with say the best strategy you can think of for Score Voting or for whatever voting system you think allows the most effective strategy to do that.

As I think about how to design simulations to try to evaluate voting systems for some measure of a degree of resistance to bipartisanship that they allow, I imagine simulating a fight between two factions, where one faction is very determined to keep the two-party system going and the other faction is very determined to defeat it. Each of these factions could comprise more than one party. Parties could have differing opinions about the candidates, but I would assume they find common ground with the other parties in the same faction on the matter of whether there should be two parties or not. A system that is not two-party could have multiple parties, or it could be a system in which parties make no difference and what counts is the voters' positions on the candidates. Testing a voting system would require trying to think of the best strategy for _each_ of these two factions, and letting those strategies fight each other in the simulation, and see who wins.

William Waugh