I think we're reaching the end of this thread, as I'm not all that interested in continuing further. It's relatively clear that changing your position will take a lot of work, and to put it simply, "I'm not getting paid enough for this" :-) I have recently had other things to focus on, as you may have noticed in my lack of posting to EM of late.

Let me reply to one of your concerns, and then I'll finish with an argument against IRV, based on the point of view of the voters. If you want to reply with your own "closing statement", go ahead and do so; I don't think I will continue.

You say there is something to American exceptionalism, so it isn't unreasonable to put the US on one side and everything else on the other side of the PR line. There might have been a case for American exceptionalism in 1787, but the United States is now hardly unique in having a presidential system, or even a strong presidential system. Other nations have been inspired by the United States' form of government, and so presidentialism has spread (although, to my knowledge, there are still more parliamentary nations than there are presidential ones).

Let's look at the Wikipedia list of republics considered to have a presidential system of government (https://en.wikipedia.org/wiki/Presidentialism). From the beginning, we have "Afghanistan, Argentina, Armenia, Azerbaijan, Belarus, Bolivia, Brazil, Chile, Colombia, Costa Rica, Cyprus, Dominican Republic, Ecuador", and so on.

Intersecting Wikipedia's list with the PR list of my previous posts gives an intersection of Brazil, Colombia, Costa Rica, Cyprus, Dominican Republic, El Salvador, Guatemala, Paraguay, Peru, Sri Lanka, Suriname, and Uruguay. Thus, I don't think you can justify putting the United States on one side of your historical specificity line and all the PR nations on the other.

These are not weak presidential republics either. In Colombia, a favored
approach of past presidents (like Lleras Restropo) was to construct autonomous quasi-governmental organizations, and then give them power. These organizations were designed to be accountable to the executive, but not to the legislature. A similar approach was used in Brazil. Again, quoting Wikipedia: "In Brazil, presidents have accomplished their objectives by creating executive agencies over which Congress had no say". So I do not think you can say they only have figurehead presidents and so don't count, either.

Where they do differ (whether they're Latin American, like Colombia, or not, like Cyprus), is that they don't have two huge parties and a bunch of tiny parties looking for scraps at the table. I think that is a point where the United States is genuinely different, but I also think that the reason they are is because the US has neither PR not a good single-winner method.

To claim that the United States can't use PR or advanced voting methods because it has two+tiny parties while the rest of the world does not is to confuse cause and effect. The reason there are two parties is because so few people want to throw their vote away in such an important contest as a Presidential one is. That is an artifact of the Plurality system. As a consequence, it becomes vitally important for parties and candidates to appear to be electable, and the way they accomplish this is to spend lots of money on very expensive media coverage and on the whole primary and electoral circus. Thus, it takes a lot of money just to overcome the barrier of he-won't-be-elected-anyway. Any method that goes wrong when third parties enter the scene would keep this bug (to the extent that it does go wrong with third parties present), because the candidates still have to spend a lot of money to signal the strategic voters that they are electable -- that the strategists should rank at least him honestly.

In concluding the above: Presidential, even strongly presidential systems with PR do exist. That they don't have extremely expensive primary and presidential races should not be used to claim historical specificity, because that is specificity of the influence of monied interests - part of the what we're trying to change. Instead, it should be used as evidence that strongly presidential systems don't need to waste money on a grand scale; and that multipartyism helps keep the need for such waste down.

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So, my voters' argument. I'll focus on the people in general and the people-as-voters in particular, because it is for the sake of the voters that we're doing this. It is the people that benefit when the system elects representatives that represent them. It is the people that benefit when a single-winner method picks a good winner; and it is the people that ultimately benefit from better governance less encumbered by plutocratic influence, as well.

I'll argue that multiparty democracy is more in line with what the voters actually want. To add strength to my claim that the voters do not prefer two-party situations, I'll go in two directions. First, that non-official results show that people "vote" (express their opinions) in a way significantly less polar when they don't have to compromise to elect the lesser of two evils; and second, that where proportional representation methods have been used, both nationally in other countries and locally in the United States, the result has been a growth of many parties, consistent with multipartyism.

Since IRV does not give multiparty democracy (and you have said as much, and that it isn't what you want anyway), and the voters express their desires in a way as to support multipartyism, that counts against IRV.

Then I'll refer to that the advanced methods don't have the center squeeze problem of IRV. I'll go further and state more general conditions where the advanced methods do well, so as to support that the advanced methods don't act as a patched-up IRV ("IRV 1.1") that just hides the most immediate problem of IRV the way IRV acts as a "Plurality 1.1" that hides the most immediate problem of Plurality.

Finally, I'll conclude that, based on the above, IRV requires that voters twist their votes into an IRV shape merely to get an acceptable result in just the setting where third parties are growing large, whereas the advanced methods do not; or that third parties have to intentionally decide to stay minor to spare the voters of this, whereas that is not the case for the advanced methods. Further, I'll point out that IRV can't justify demanding this of the voters and parties, because it doesn't produce results closer to the multipartyism the voters want than does the advanced methods. Therefore, IRV is worse than the advanced methods twice over, and so I cannot support it even if the other arguments not detailed here were to be invalidated.

Without further ado, the meat:

1.1. According to their preferences, the people prefer multipartyism to two-party rule.

This is where my reference to the Orsay exit poll, the other French and German studies, as well as the two United States exit polls, all shown on Rangevoting, come into play. The Orsay exit poll (but also the other exit polls) show that the people of France and Germany vote in a manner consistent with multiparty preference, while the United States exit polls and studies show that while the United States voters don't vote for third parties to the extent that those parties would win, they nevertheless vote (or express preference) for third parties and candidates to a much greater extent than in the official count.

When I direct your attention to the Approval voting polls (telephone polls, etc.) in the United States, my point is not that Anderson came second. As you say, you don't get a seat for coming in second. My point *is* that the voters vote in such a way as to show that candidates not officially blessed also have some popularity. Stripping away the strategic distortion caused by Plurality, we see that "no-hopers" have some support. What is keeping them down is a catch where they have to be seen as electable to win or gain further support, but can't be seen as electable unless they have a great chance of winning.

In my other posts, I have quantified this tendency in terms of effective number of candidates, at least for the European polls.

1.2. According to the outcomes, the people prefer multipartyism to two-party rule.

Internationally, I need only point to the countries that have proportional representation. If the people wanted a two-party situation in a PR nation, they would only have to vote for the two largest parties to establish that situation. That does happen in some places; most notably, in Malta. Malta uses STV, yet has only two parties. In Malta, the voters only make use of 5-seat STV's capacity for intra-party competition, but not of the capacity for inter-party competition. See more at http://aceproject.org/ace-en/topics/es/esy/esy_mt .

Even in elections for single seats, this pattern appears to be true. When the voters are given a single seat method that can elect candidates from multiple parties, the voters make use of that capacity. To avoid appearing to construct a tautology or to beg the question, I will specify that more clearly: the method is being used in more than ten nations (so you can't claim one-nation micronumerosity), and in more than two thirds of the nations where it is used, that nation has a multiparty democracy. I am, of course, talking about top-two runoff voting. According to http://rangevoting.org/TTRvIRVstats.html, there are 27 runoff-using nations, and 21 of these are multiparty. (If you wish to argue Warren is wrong, go ahead and do so.)

Within the United States, I point to New York under STV. In New York under STV, the voters made use of the capacity of STV to provide for multipartyism and voted (and got results) which let multiple parties get on the assembly. This significantly weakened the party machines, who immediately countered but only got STV repealed after battering down public opinion by the card of red-baiting. This is why the New York STV example matters more than your proverbial hill of beans, and this is why I am surprised you do not look at it when you talk about historical specificity. It shows that American voters also avail themselves of the capacity for multipartyism when they have the instruments by which to do so. Indeed, the leaders of the New York county Republican party had no illusion about this as they worked with Tammany Hall against PR, calling PR "a threat to the two party system" ( http://www.mtholyoke.edu/acad/polit/damy/articles/kolesar.htm ).

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2.1. The advanced methods (most Condorcet methods, as well as MJ, Approval, and Range) do not suffer from center squeeze under honest voting.

This is very easy to check. One may simply go to Ka-Ping Yee's one-dimensional Gaussian vothing method visualization and push the wings closer to the center. In Plurality, the center vanishes quickly. In IRV, the center lasts a little longer, but first it splinters nonmonotonically, and eventually it fails altogether when the center does not have enough first place votes to outlast the wings. That happens even in a completely symmetrical situation where the major parties are equally far from the center, "clustered around it".

In contrast, both the rated/approval methods and Condorcet methods elect the candidate closest to the middle-most voter (in ratings, possibly as weighted by strength of preference). This is a reasonably fair standard, because one can imagine left-wing voters "canceling out" right-wing voters until the centermost remains.

In fact, Condorcet methods will always be impervious to center squeeze in a left-right situations like the above. I'll get to that later. Some Condorcet methods may behave strangely in higher dimensions (such as a contrived "CW if there is one, otherwise the Plurality winner" method), but most will degrade gracefully.

The theoretical result can also be empirically verified in two cases. First, the Burlington election of 2009: all the Condorcet methods picked Montroll, as would Range under certain assumptions (of monotonically decreasing ratings). Second, by ranked votes from a French exit poll in Faches-Thumesnil and Nord in 2007, Condorcet methods elect Bayrou (as does Range and MJ using the Orsay data from another exit poll in the same election), whereas IRV sides with Plurality and elects Sarkozy. See http://rangevoting.org/French2007studies.html for more.

I will point out that I am not talking about dynamics. This part of the argument is about the voters not needing to learn to vote for the stronger wing, or the minor parties not needing to stay out of the way if the voters don't learn.

2.2. The advanced methods are significantly less impacted by adding or removing candidates than is IRV and Plurality.

For the rated methods of Range and MJ in particular, as well as for Approval, this is also simple to see. When the voters are honest and rate according to an objective standard, these methods pass a rated-version variant of IIA. This means that if you add or remove a candidate X, that doesn't alter the winner unless the winner used to be X (in case of removal) or X is now the new winner (in case of adding candidates). Thus, no amount of extra candidates can make the method misuse honest voters' votes to squeeze out the center. I think that this particular variant of IIA is stronger for MJ than Range, since MJ suggests voters compare the candidates to a common graded standard and gives less incentive for voters to deviate from that standard, whereas in Range, normalization may be considered honest (and so the IIA variant would fail).

For the monotonicity-fixed SODA, as it is based on Approval, it passes an analogous version of IIA. If a new candidate appears, either the old winner will keep winning, that new candidate will win, or a candidate preferred to the old winner on the new candidate's delegation order will win.

For Condorcet, the details are more complex. In a left-right scenario, as one might expect when third parties are just getting off the ground, Black's single-peakedness theorem shows that the Condorcet winner will always be the candidate closest to the median as defined above, no matter the amount of other candidates and their positions. Since maximum likelihood estimation over relatively simple error models imply Condorcet while IRV can only be considered an MLE if you make the error model very complex indeed, I think voter uncertainty will drag IRV further from this in reality than it will drag Condorcet.

But perhaps that is not enough. In that case, I refer to James Green Armytage's paper on voting strategy, http://www.econ.vt.edu/seminars/seminarpapers/2011/jamesgreenarmytage10142011.pdf In it, James proves that when there is a Condorcet winner, Condorcet methods are vulnerable to neither exit nor entry (candidates being removed or added). Furthermore, his computer simulation results indicate that minimax (which is not even cloneproof, but is Condorcet) provides nearly no incentive for strategic entry or exit, but IRV's incentive to strategic exit increases with the number of candidates, and eventually reaches Plurality's in the case of single-candidate exit.


Thus, I reason that the advanced methods are not simply patches to IRV; their improvements with regards to candidate exit and entry, and resistance to center squeeze, are general (not specific), and don't lose power as the number of candidates is increased further.

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3.1. IRV requires that either votes twist their votes into an IRV shape to get an acceptable result, or that parties intentionally stay small to avoid the conditions where the voters have to do so, or both.

This follows from the center-squeeze vulnerability shown in 2. In order to avoid center squeeze, either the third parties can stay far enough away that their votes can't make the wrong winner win, or the votes can vote as if the third parties were that minor.

Burlington provides an example of what happens when the voters don't and the parties don't, either. You've said that it did, but you claim that dynamics will fix it. Those dynamics don't counter this point, since the dynamics take the shape of voters or parties altering their behavior to accomodate IRV in a similar, though somewhat reduced manner, to how voters or parties alter their behavior to accomodate Plurality.

3.2. IRV doesn't give multipartyism.

This is not contended by you, and it is a simple consequence of the nature of IRV. If IRV breaks to center-squeeze when third parties become too large, and the countermeasure is for either the parties to be small enough that IRV doesn't fail, or for the voters to act as if the parties were, then the parties can never by themselves grow large enough to lead to multi-party rule within the area of the IRV election in question.

Further evidence can be seen, though scarce as it is, by that all the nations that use IRV have two-party rule where IRV is used. Australia has two-party (or two-and-a-half party, since the NatLib coalition is pretty much a party) rule in its IRV body. You have not disputed this, but you have argued that this would be countered in the non-IRV bodies that would use PR but would not give multipartyism in general. Also, in Fiji before the military coup, the system was coalescing to two-party rule despite being in the context of a diverse nation, and despite ethnic quotas. See http://rangevoting.org/FijiPol.html for that data.

3.3. Therefore, IRV fails twice.

By 3.1., IRV imposes demands on voters and/or on parties that the advanced methods do not. That counts once against IRV, but it wouldn't by itself be so bad IRV could justify that demand by providing better outcomes in return. However, it does not. By 3.2., IRV fails to give the multiparty outcomes that voters appear to want (as established in 1.). Therefore, at the very best, IRV is no better than the advanced methods in bringing about multipartyism, and realistically (supported by the presence of single-office voting rules that actually do give multipartyism), IRV is worse than the advanced methods.

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