waughuspolitics on Erroneous Treatment of Un-indi… thomass smith on Against Bernie  waughuspolitics on The World Needs Regime Change… waughuspolitics on The World Needs Regime Change… waughuspolitics on Are Democracy and Capitalism…
- August 2016
- January 2016
- December 2015
- November 2015
- September 2015
- July 2015
- April 2015
- July 2014
- June 2014
- May 2014
- April 2014
- March 2014
- February 2014
- January 2014
- December 2013
- November 2013
- October 2013
- September 2013
- August 2013
- June 2013
- May 2013
- April 2013
- March 2013
- February 2013
- January 2013
- November 2012
- October 2012
- September 2012
- August 2012
- July 2012
- June 2012
- May 2012
- April 2012
- February 2012
- January 2012
- December 2011
1. For every candidate in the race, a voter has a right to give that candidate a “grade” of A, B, F, or G.
So for example, my ballot might look like this:
Nader – A
Gore – B
Bush – G
The ballots should of course be made of paper.
2. Each entry on a ballot, where a voter assigns a grade to a candidate, shall be called a “grading”.
3. The tallying process accumulates an _overall score_ for each candidate. At the start of the tally, the candidate’s accumulated score is zero. The tallying process examines the gradings that the candidate received from the voters. For every grade of “A” found among those, the process adds 50 points to that candidate’s score. For every grade of “B”, it adds 49 points. For every grade of “F”, it deducts 49 points. For every grade of “G”, it deducts 50 points. When all the gradings for that candidate, found on the ballots, have been taken into account, the accumulated score for that candidate is that candidate’s overall score.
The tallying process should of course be carried out by human beings, with witnesses to check to assure accuracy.
4. The candidate with the highest overall score wins the election.
Under this system, my working hypothesis about the best voting strategy for those who favor Nader and strongly oppose Bush, is to vote as in my example above, i. e., Nader A, Gore B, and Bush G. Someone may come along with mathematical reasoning, or made-up example elections, and cause me to reject that hypothesis. Or I could come up with such reasoning or examples myself. But for now, it is my best notion of how they should best vote for their own interests in this scenario.
Approval Voting is a subcategory of Range Voting (Range Voting is also known as Score Voting). The difference between Approval Voting and other variants of Range Voting is the granularity with which the voter may express degree of support for and/or opposition to a given candidate’s winning. In a large election, voters can make up for overly coarse granularity by voting probabilistically.
Probably the simplest way to describe Approval Voting is to say: Start with voting the way it is done in almost all elections in the US. Remove one constraint: that you can only vote for one. That’s Approval Voting.
For greens who want to support their candidates fully in a single-winner election but also want to use some of their political power to affect the lesser-evil portion of the race, I recommend they give something like 99% support to the lesser-evil candidate. The appropriate level of support for the lesser evil depends on ones assessment of the likely behavior of other voters. The more popular you think your acceptable candidates are, the less support you should give to compromise candidates.
I haven’t seen exactly how to prove the following mathematically yet, but I am fairly convinced that voting systems that don’t accord each voter equal political power to each other voter are vulnerable to two-party dominance via the application of political money. Here are some links related to this expectation:
Range Voting and therefore Approval Voting (since it is a subcategory) accord the voters equal power over the outcome of the election. This can be tested for by observing that for any vote that is possible to cast, one can construct an opposing vote that would exactly cancel the effect of the first vote. This is not true of “Instant Runoff Voting (IRV) (a form of “Ranked Choice Voting”) if voters are allowed to leave some candidates unranked. I think I could describe a variant of IRV that would have the property, but I see no advantage of such a variant over rating systems (Range Voting including Approval Voting).
IRV responds pathologically to small changes in the location of the center of public opinion, as demonstrated by http://zesty.ca/voting/sim/ ; see in particular the diagrams under the heading “Shattered”, and the rest of the paper after that heading.
I agree with Gary Swing http://www.newprogs.org/gary_swing_on_election_reform that “IRV will help the two major parties by eliminating the potential threat posed by minor party candidates, but it won’t help the Green Party to win elections” and “If executive office holders are publicly elected rather than appointed by legislators, I consider range voting to be a much better method than IRV for electing single winner office holders.”
Multiwinner elections constitute a separate and more difficult topic from what I am talking about in most of this writing. I suppose proportional representation is a good idea, but I don’t as of yet know how to speak for any particular system for achieving that as adequate.
For the sake of making it possible for Greens to win single-winner elections, and for the sake of defeating the two-party oligarchy, and for the sake of democracy, I call on all Greens to support Range Voting (or specifically Approval Voting if you prefer) for any single-winner elections, and reject IRV along with vote-for-one Plurality Voting and all other systems that don’t accord the voters equal political power.
The same consideration applies to the Libertarians.
[Also posted as a reply in a thread https://secure.gpus.org/secure/GreenPartyForum/showthread.php?tid=719 in a discussion forum that is said to have fallen out of use.]
[Linked from, and discussed at https://www.facebook.com/groups/587432744659202/permalink/975284442540695/ ]
[Linked from https://www.facebook.com/william.waugh.33/posts/808915632550792 ]
[Linked from https://www.facebook.com/groups/greenpartynetworking/permalink/947398498628768/ ]
[ Linked from http://post.mnsun.com/2016/01/12/public-hearing-set-on-ranked-choice-voting-in-brooklyn-park/#comment-2458969123 if they ever approve my comment. ]
[ Linked from https://www.facebook.com/ThomHartmannProgram/?comment_tracking=%7B%22tn%22%3A%22R9%22%7D ]
[Home location https://1787regime.wordpress.com/2016/01/17/greens-and-libertarians-must-promote-equal-weighted-voting/ ]
Bob Wasserchuck may want to comment.
I am taking down from my Facebook stream, a link I posted to an article that I thought made a point I agreed with, bearing on equality, but I have come to understand that the article uses codewords that come from the postmodernist viewpoint, a viewpoint that I reject.
(For reference in case of questions, the link can be reached via http://v.gd/weYJGY).
My purpose in posting this is to add to an interaction about comparing voting systems. The interaction started on Facebook. Only people who have signed up for Facebook and then joined the specific discussion forum thereon can see it, but for the record, here is the link to the start of the debate.
Two aspects of argumentation are (1) trying to carry forward on ones own points and (2) responding to false statements and/or dishonest rhetoric from the other party. Up to this point, I have optimistically tried, much of the time, to concentrate on (1) and I have let some of (2) just sort of slide for the time being. I feel it is time to catch up on (2), in order to do my best against the possibility of some readers being snowed.
Seth Allen Woolley says:
No. Ranking is better than rating. Rating is vulnerable to strategic manipulation and the intermediate values are not well-defined and thus incomparable. It’s equal to approval voting in most features. The corporations funding its advocacy bore me.
What does “vulnerable to strategic manipulation” mean? Perhaps the concept carries no meaning, and the insertion of the words amounts to a word salad intended to distract from the portions of our dialog that do have meaning. Or, perhaps the concept of “vulnerable to strategic manipulation” has something to do with an accusation that the voting system under study accords some parties more power than it does others, to manipulate the result. I suggest that the Greens and other “third” parties and independents need, in order ever to gain in popularity and power, to concern themselves with the question of which voting systems accord one voter equal power to another voter. I could ask Wolley to explain how to test, mathematically, a proposed voting system for “vulnerable to strategic manipulation”, however, I have asked him for clarifications before of some of his expressions and generally he has not provided any. So, based on experience, there is little reason to think that asking him now would bear fruit.
and the intermediate values are not well-defined and thus incomparable.
This is manifestly false. The voting system itself uses the intermediate values, summed, in the very comparison that determines the final (partial) ranking that determines who is elected (unless there is a tie). Given that the system compares the values, they must be comparable. Recall that voting is an exercise in political power. The information it yields has (primarily) the semantics of command, not that of declaration or indication (more nuance on this later — actually there is some declaration or indication, but I argue that the perfection of the accuracy of that part is of secondary importance). The (primary) significance of a vote lies in its effect on the command given by the election, to put so-and-so in office. Whatever is compared for that effect is obviously comparable. If it were not comparable, it would not be possible to compare it, and comparing it is what happens. Therefore, your statement is wrong.
It’s equal to approval voting in most features.
The corporations funding its advocacy
Just because Bush says something does not make it false. You would serve the cause of honest debate better if you focused on the questions related to the comparison of voting systems and did not try to distract attention by referring to peripheral matters such as who is in favor of something. This particular instance of attempted diversion falls under the well-known category of argumentum ad hominem.
Your emotional response is irrelevant to the matter at hand.
Waugh cites http://zesty.ca/voting/sim/ and Wolley responds:
Simulations have premises, and the rating system simulations in particular have serious errors in their premises. Voters act together and lie about their desires. When you take that into full account, IRV and STV and party-list turn into the best systems. I’ve studied these systems for decades and have done my own experiments. Rating systems in real elections are very bad, from personal experience experimenting in local Green elections.
Piece by piece:
Simulations have premises, and the rating system simulations in particular have serious errors in their premises.
The simulation I cited certainly uses a simplified model of how voters vote. However, in general outlines it models that area. It assumes that people are interested in how close in opinion the candidates are to themselves. In reality there may be more or fewer than two dimensions of that opinion, and some of the dimensions might be be discrete rather than anything like continuous. The model uses two continuous dimensions. However, what this simulation reveals is that even using inputs and assumptions that are smooth and continuous, some voting systems produce grotesque fractured results. As the author of the simulations points out, it seems very unlikely that a more-complicated real-life situation will produce less pathological results than the simplified simulation does. Rather, I add, real life is likely to be worse. This particular simulation provides insight into the natures of the mathematical functions at the centers of the voting systems under comparison.
Voters act together and lie about their desires. When you take that into full account, IRV and STV and party-list turn into the best systems.
In our discussion of single-winner systems, the only STV that is relevant is IRV, and party-list isn’t relevant. So let’s look at “lie about their desires” and IRV.
The concept of “lie about their desires” requires a nuanced analysis. If a voting system could serve two purposes perfectly, of on the one hand polling people for an accurate account of their desires, and on the other hand according the people equal political power, then the concept of “lie about their desires” would be simple to understand. In that hypothetical (but unrealistic) world, to “lie about ones desires” would mean to provide input to the system (your ballot) tending to make the system not reflect your real desires in its reporting of aggregate desires of people. However, it is a valid mathematical conclusion that no voting system can do both of those functions perfectly. As progressives, we need the system to elect the person based on equal power, and we need that at the expense of whatever we might have to give up in terms of the indicative information provided in the results.
Nonetheless, we have important progressive reasons to be interested in the secondary information that rating systems provide in addition to the primary signal, which is the command signal to put so-and-so in office. This secondary information gives all readers a measure of how well the losing candidates did and how popular they are. This measure is useful in drawing peoples’ attention to candidates they had ignored as “fringe”, to consider it worth the time to see what those candidates stand for. Such drawing of attention is necessary so that Green positions and candidacies can rise in popularity, and not be stuck on the fringe forever.
I have referred you to arguments by others that demonstrate that given the mathematics of IRV, there are times when a party or faction’s best short-term interests are served by betraying their favorite candidate(s). If that is not “lying about their desires”, I don’t know what is.
The only lying that Range provides an incentive for is shifting the voter’s degree of support or opposition of compromise candidates, without inverting any orders in the (partial) ranking derivable from the ballot. There is no incentive to move down your favorites, nor to move up those you hate the most (love and hate in Range are symmetric). This is a sharp contrast with IRV, where the incentive is to reverse the order of your preferences involving your favorite(s). In exchange for putting up with this degree of partial blindness that Range imposes on analysts of the results in regard to voters’ real opinions about some of the candidates, we get that Range works best in the primary purpose of the system, that is, determining the winner. It would not make sense to confuse an election with an opinion poll and choose a system based on how it reflects opinion at the expense of ending up with a system that elects the wrong candidate. However, Range reveals support for losing candidates much better than vote-for-one Plurality does, to a degree that progressives should see as crucial. The New York poll shows that the voting system matters much in determining outcomes; I can cite that if you ask.
So, IRV comes out much the worse when we look at “lying”. It causes the kind of “lying” that results in electing the wrong candidate in addition to providing wrong information about the levels of popularity of the losing candidates. Range does better in both regards.
I’ve studied these systems for decades and have done my own experiments. Rating systems in real elections are very bad, from personal experience experimenting in local Green elections.
By the parts:
I’ve studied these systems for decades
The amount of time you have spent is not relevant and is a distraction from the argument. No matter how long you have studied, you could have erred. You might just have personality flaws that make you overlook important considerations, even for decades. Let’s please stick to the topic and the logic that bears on it, not something peripheral that looks like an attempt to either build up someone as an authority or tear down someone as an authority. Those are just distractions. Respect for those who take the time to read our conversation requires staying on topic.
I’ve studied these systems for decades and have done my own experiments. Rating systems in real elections are very bad, from personal experience experimenting in local Green elections.
Here you cite work you say you have done, but despite my questions, you keep this work secret. You have not revealed the nature of the experiments you claim to have performed. Accounts of experiments can contribute very validly to discussions, but to do so, they have to give the usual information included in reports of experiments and their outcomes. And of course the most useful experimental results are those that have been repeated. You haven’t exactly earned my trust here as an honest reporter of experiments and their results given the rhetorical devices you have resorted to in this discussion. But if you do describe experimental method, there may be an opportunity for analysis.
Here in Oregon we had range advocates team up with a long list of corporations to try to get range and range-like top two systems in place. The progressives battled them back and won.
Quoting again by pieces:
long list of corporations
get range and range-like top two systems
Here you put “range” and “top two” in the same breath, trying to conflate things that aren’t very related and confuse our readers. A top-two scheme involves more than one election or stage of election in which the voters receive the opportunity to cast ballots. Let us confine our discussion to what happens in one stage or election where that opportunity exists. When we began the discussion, that is what it was about, not proposals involving more than one stage of balloting. If we should find reason to veer during the conversation into such proposals, then what happens at each stage will be at the crux. To mention a two-stage election without saying what happens at each stage just throws a wall in front of what matters.
The progressives battled them back and won.
Maybe some of the people who sided against Measure 90 thought they were serving progressive values, but there is reason to think that if they thought that, they were mistaken. Had the measure passed, there would have been increased opportunity to convince people to support equality of voting power (which progressives should want), because the preamble of the measure stated that as a requirement. Therefore I was convinced that the progressive position to take on it was in favor. Since our debate to start with is about what is in the Greens’ interest, and Greens are presumably progressive, you somewhat beg the question when you insert an offhand assumption about which side of the Oregon question would have served progressive values.
A range vote closer to zero is equal to not voting at all.
This is demonstrably false. No matter what ballot you write for a Range election, I can show an example of the other votes such that adding yours will convert whichever candidate you name between winning and tying or between tying and losing. Please do not make false mathematical statements. I thanked you for correcting me on terminology regarding NP-complete and related concepts (of which I am a very poor student to date), and to behave reciprocally to that would mean you would take this opportunity for correction of your understanding regarding the effect of a Range ballot on the electoral outcome.
I favor a variant of Range that does not allow an explicit statement of abstention or “no opinion” on a candidacy as distinct from an action or inaction that results in a score being used in the tally for that voter-candidate pair. Lack of support amounts to full opposition. However, when I say this, I am not underhandedly switching definition of a Range election to make a statement of yours that was true in the first place look false. Your statement didn’t mention a voter taking the option that is present in some variants of Range that some people describe, to explicitly vote “no opinion” on a candidate, nor to have the default treatment regarding a write-in that others write in but whom you do not write in, to treat that as “no opinion” i. e. average without counting it. What you said is that voting zero amounts to abstention (I’m not sure whether you assume zero at the bottom of the range or in the middle of the range, but you are wrong in either event). I’m just throwing in this information about what version I favor, so that if you choose to take a new look at Range, you look at my favorite version rather than wasting time re-analyzing variants I don’t like.
Otherwise it behaves like first past the post systems.
You have not demonstrated this with any reasoning or data or examples or anything. I can lay out cases where the clear benefit to a voting faction is not to bullet-vote.
Further, a vote for a second choice person must be equal to your first choice in order to actually carry weight to your second choice in as much power as your vote has.
This is true, however, it is part of the price to be paid for according the voters equal power over who gets elected.
Range systems are mainly used in insignificant feedback systems without serious political consequences.
Even innovations that turn out to have merit take time to become properly understood for the value they can bring. The current pattern of usage and non-usage could be an accident of the point in history at which we have this discussion. What we’re discussing is the merits or demerits of advocating change in regard to that pattern. Saying where we are is therefore not very relevant to the discussion of in which direction we should be moving if we want to get elected.
According to at least one source, bees use Range to determine where to move as a colony. This is very “politically” significant for which alleles push out which others in the race for survival.
Comparison/order systems are the gold standard in social choice theory and are resistant to strategy since they must compare against others and create a strict ordering.
Comparison/order systems are the gold standard in social choice theory
“Gold standard” is a pretty loaded expression. What is a reader to take from it? Why should we consider it the gold standard? Are there reasons for such a high valuation? I think you are trying to insinuate here that there is some community of scientific authorities on this question just as there is for say quantum mechanics, that it is some largely settled science and the reader should think there is this huge weight of opinion based on expert knowledge that they should defer to. But it’s not clear to me that this field has that nature. Anyway, if there are reasons for such valuation of ranking systems, you should trot a few out instead of using suggestive wording.
and are resistant to strategy
You have not favored us with a definition of “resistant to strategy”. When you insert words and refuse to define them, you are inserting noise to tire out readers before they can find the energy to sift out the actual arguments.
since they must compare against others and create a strict ordering.
Without that strict ordering, information is lost.
What information? A better statement is, without that strict ordering, noise is not made up out of whole cloth. How is a voter to rank two candidates that the voter rates as equal in value?
The goal of reforms is to maximize [information] available to compare candidates against each other.
A secondary goal of revolution (anything that smacks of “reform” sounds like an effort to keep the current power structure in place) is to increase the expressiveness of the vote. But maximizing information available to compare candidates against each other is not the goal of changing the voting regime. The primary goals should be to implement voting equality, and take away, to the extent feasible, the incentive for lesser-evilism and such features that make people care about electability to the total detriment of the system revealing in the end something about people’s judgements about the merits of the ideas and candidacies. If you see maximizing information available to compare candidates as an intermediate step that is necessary to achieve the political goals, you should argue to show that that is true.
Expressiveness is either related to what you said about information or exactly the same thing. It is a secondary goal. In regard to expressiveness, ranking falls down compared to rating because ranking doesn’t gather any information about the degree to which the voter favors a candidate other than the ranking relative to the other candidates (and as I pointed about above, IRV provides an incentive to lie even about the ranking). So, in regard to quantity and quality of information collected, there are some regards in which it makes sense to see Range as outdoing IRV.
Partial rankings can be derived from ratings, but ratings cannot be derived from partial nor strict rankings. That should tell you something about which form carries more information, and which operations throw away information.
Without that strict ordering, information is lost. The goal of reforms is to maximize information available to compare candidates against each other. That is the actual metric one must use to determine the power of a vote. [spellings corrected]
Questions about the power of the vote can be answered by examining cases where a vote shifts the outcome. You have not brought reasoning to argue about under what circumstances a measure of the quantity of information bears either necessarily or sufficiently on the effect on the outcome. Obviously throwing away all the information would result in failing to convey the political command signal from the voter to the outcome. But reasoning about power should refer to the outcome, directly or indirectly.
If everybody voted first and second choice as max values, as they must, there will be no way to determine the real preference.
It is not always the case that they must. But I agree that in some cases, they must. Even when they really do have a preference. But the equality their power is more important than a complete extraction of their valuations, when these goals conflict.
Responding to all your statements like this is going to take me more than one session. I can’t devote my whole life to it. So I offer the present installment and hope to add later.
This is the version of the argument I direct toward Libertarians.
Defeating the Two-Party System
First, a disclaimer about where I am coming from politically and why I am posting here [not here, on my ‘blog, but there, on a Libertarian group on Facebook].
The pinned post says, “Please understand that there are a lot of right-wing and left wing posters who do not represent the libertarian/Libertarian principles and philosophy, but may try to make you think they do.”
I do not represent the libertarian/Libertarian principles and philosophy.
I am a left-wing poster.
However, I suggest that Libertarians and some others have, or should have, a common interest, to break the stranglehold that the 1% has on US politics, a stranglehold they exert via the two-party system and lesser (not lessor) evilism.
The vote-for-one system increases and strengthens the bandwagon effect, where people tend to think that their vote won’t count unless they are voting for one of the “front runners” in the horse race. We have to advocate for, and spread information about, better voting systems, such as would help unpopular parties and ideas move in from the fringe and garner increased serious attention. We should want people to evaluate ideas on their merits, not on whether the ideas have big-money support. We should want people to feel free to vote for candidates whose ideas impress them, even during stages of history where the candidates are not very popular. With such advanced voting systems, the outcomes of (single winner) elections would include not only the determination of the winner, but also some information about who is gaining in popularity and may be worth some consideration to evaluate their ideas.
For single-winner elections (e. g. governor of a State), I recommend either Approval Voting or finer-grained Range Voting also called Score Voting.
The reason I use that qualification, “finer-grained”, is that in fact Approval Voting is a subcategory of Range Voting.
In Approval Voting, the voters indicate on their ballots, which candidates they “approve”. The candidate receiving the highest count of approvals wins.
In Range Voting also known as Score Voting, the voters are invited to rate or grade so many of the candidates as they choose to, on some range of permissible values. The range is fixed by the election design. For example, it could go from -50 to 50. The election tallying process determines for each candidate, the sum of the scores awarded that candidate by the voters via their ballots. The candidate with the highest total wins.
If write-ins are allowed, the election design has to tell what score they should get from voters who don’t write them in. In my opinion, this should be the bottom of the range.
I think Approval Voting offers a strategy whereby the supporters of unpopular parties or ideas can work their way in. I will discuss that with anyone who asks what that strategy is.
With finer-grained Range Voting, if the grain is fine enough, I think the strategy is easier to explain. When I refer to grain, what I mean is, how close is the second-highest permissible score to the highest one, expressed as a proportion of the length of the whole range. If the range has only two values, the system amounts to Approval Voting.
For those who have heard of “Instant Runoff Voting” (IRV) and heard it touted as better than Approval or Score, I point to a simulation study that shows that IRV behaves pathologically. See under the heading “Shattered” in http://zesty.ca/voting/sim/
If you have heard that “ranked-choice voting” is the answer, that’s probably an attempt to sell you IRV under a different name. Otherwise, I want to know what tallying method is being advocated to use with ranking ballots. Anyway, all ranking systems are subject to Arrow’s Impossibility Theorem.
I favor Score Voting also known as Range Voting. I will now argue as to the fineness or coarseness of the range to use.
One of the concerns I have about voting systems is about whether a system helps a party (or a set of ideas), that is on the fringe in terms of levels of popular support, to move toward being considered seriously by larger proportions of the public. In the earliest stage of such a movement, it’s important for the voters who want to promote the fringe ideas or party, to be able to express support for candidates representing that fringe while also effectively supporting their compromise candidates against their worst candidates, so as to avoid being a victim of political blackmail. In an example election that I lay out in https://docs.google.com/spreadsheets/d/1Kq8Ez4CQGMvUuwNUYLe0VKLlqIpfN57e6J6R50L5C1o/edit#gid=0 , I present I think a fairly realistic idea of how the 2012 POTUS election might have gone with fine-grained score voting. In this fantasy I depict the Greens fully supporting their candidate while giving .99 support to their compromise candidate, Mr. Obama. I don’t remember for sure, but I’m pretty sure that the voter counts in tab “tab01” reflect the actual election, based on the votes for Obama, Romney, Stein, and the other candidates. So I used the vote count for Stein as my estimate of the count of Green voters. Of course this is somewhat of an undercount, since the real election went by plurality (within States to determine the electoral votes) and so many of the Green voters, we can quite justifiably suppose they voted strategically against Stein. However, if we imagine that the first score election happened in 2012 and everything prior went by plurality, the mentality of the people wouldn’t have time to adjust to the possibilities of score voting, and so many of the voters still wouldn’t have taken up Green party membership and advocacy. So for such a state of public mentality, the actual count of Stein voters gives us the order of magnitude of Green adherence. These remarks about Stein and the Greens apply similarly to Johnson and the Libertarians.
To study what can happen with such a fringe when their action could actually affect the corporate portion of the election, let’s make some perturbed versions of this election where we imagine the Elephant and Donkey voter counts as closer together. I probably started this spreadsheet years ago and supposed the Green voters would vote their feelings about Obama, or my feelings, rather than use proper strategy, so I had them giving him .1 although now I think that for strategic reasons, they should give him .99. So in tab “tab02”, I’m adjusting that score to .99 and similarly having the Libertarian voters score Romney .99 for the same strategic reasons from what I suppose their viewpoint to be about who is the worst candidate and who is the compromise candidate. I jack up the count of Elephant voters to equal that of the Donkey voters, and Romney wins because the Libertarian voters, as few as they are, still overwhelm the Green voters.
In tab “tab03”, I cherry-pick the count of Elephant voters so Romney just barely wins.
For tab “tab04”, I suppose that (1) the Score granularity is now .1 instead of .01, that (2) the voters are not intelligent enough to use random variables to simulate finer Score voting, and that (3) no one wants to give anyone but their favorite a perfect score. The result is that the wrong candidate wins, Obama instead of Romney. This is why I promote .01 granularity near the extremes of the range.