MN supreme court rules Instant Runoff Voting (IRV) Constitutional

The State of Minnesota Supreme Court (case A09-182, filed 11 June 2009) ruled that Instant Runoff Voting was constitutional, contrary to the assertions of the plaintiff, the "Hennepin County Minnesota Voters Alliance."

At the present time, based on this case and the earlier 1915 MN supreme court case Brown v. Smallwood which they continued to affirm, the following voting systems are constitutional in Minnesota:

And the following are not:

Why is that? And what about (say) Condorcet systems? Would they be constitutional? The answer is, we have no idea and the classification above makes no sense to us. I believe there is no reasonable way to affirm both the 1915 and 2009 rulings. First, the 2009 court should have overruled its 1915 ruling. Second, while the 2009 court may have been correct in its 2009 decision "yes, IRV is constitutional," it definitely it made factually incorrect statements inside its ruling in its reasoning leading to that conclusion.

False statements made in the supreme court ruling

"Respondents contend that monotonicity is merely a mathematical concept, and not a constitutional requirement. They explain that monotonicity is one of several characteristics identified by economist Kenneth Arrow as desirable in a democratic election system. See generally Kenneth Arrow, Social Choice and Individual Values (1951). Arrow proved mathematically, in what is known as Arrow's Theorem, that no voting system can satisfy all of the desired conditions that he identified. Respondents contend that because no election system can comply with all the characteristics, it is inappropriate to use any of them as a constitutional requirement...
Although it is disconcerting to acknowledge that a voter cannot be sure that his or her vote for a candidate will help, rather than hurt, that candidate, any system that involves a process for narrowing a field of three or more candidates has that potential."

This is false. First of all, Arrow's theorem does not involve monotonicity. Second, this is not anybody else's theorem either, because four well known examples of "processes which narrow a field of three or more candidates down" to 1, and do so in a wholy-monotonic manner, are

  1. range voting,
  2. plurality voting
  3. Borda count
  4. Schulze beatpath Condorcet voting
Indeed, the first three of these can also be used to narrow N down to M for any M,N with 1≤M<N, and they will do so in a wholy-monotonic manner. That is, increasing your vote for X will, in any of these systems, never decrease X's winning chances; and decreasing your vote for X will, in any of these systems, never increase X's winning chances.

In contrast, IRV is not monotonic. That is, by voting X top, you can stop X from winning whereas if you had instead voted X bottom that would have caused X to win. (E.g. see this example, noting point #5 there.)

"In particular, respondents point out that, as the district court found, even the Minneapolis primary/general election system was non-monotonic, and therefore the fact that IRV is non-monotonic cannot be fatal."

This seems likely to be false too, though I admit I am not completely sure(?). The usual primary+general system used in most parts of the USA is monotonic – voting for X can increase but never decrease X's winning chances for the seat. (It also is monotonic in each round individually – voting for X can increase but never decrease X's winning chances for that round.)

The above two false statements by the court were basically just repetitions of false statements by the defendants which were inadequately (if at all) refuted by the plaintiffs.

What the court perhaps meant to say, but failed to say, was that ordinary 2-round "top two" runoffs (which are used in, e.g. the Louisiana governor election and Los Angeles mayor election) are non-monotonic. That would be true (although, viewed in any given single round, they are monotonic). That is, voting for Y in the first round, can increase X's chances of winning the final round, while voting X in the first round, can prevent X winning the final round. But voting for X cannot decrease X's winning chances in that round.

"Even if non-monotonicity were viewed as an indication that the right to vote may be burdened, a further problem with appellant's monotonicity argument is that they have provided no evidence, even on a hypothetical basis, of the frequency with which the non-monotonic effect is likely to occur in a real-world... In the context of a facial challenge, this is significant, in two respects. First, the risk of this adverse characteristic of IRV is at this stage purely hypothetical, not because IRV has not yet been implemented, but because the non-monotonic effect of IRV may or may not occur in the real world. As we have already noted, in a facial challenge to constitutionality, the challenger bears the heavy burden of proving that the legislation is unconstitutional in all applications. E.g., Wash. State Grange, 128 S. Ct. at 1190. Where the harm alleged is hypothetical and may or may not occur, the challenger has not met that burden."

Real-world examples of IRV and STV non-monotonicity include

"Second, a key issue in a challenge to voting regulations is whether the regulations impose a severe burden on the right to vote. Wash. State Grange, 128 S. Ct. at 1191. The fact that there may be some burden is not enough to invoke strict scrutiny. Burdick, 504 U.S. at 433-34. See our discussion infra Section III. The Supreme Court has recently reiterated that where the regulation and the burden imposed affect a limited number of voters, the burden cannot be characterized as severe. See Crawford, 128 S. Ct. at 1622-23. Although it is apparently undisputed that the IRV methodology has potential for a non-monotonic effect, there is no indication, much less proof, of the extent to which it might occur, and so there is no way to know whether the alleged burden will affect any significant number of voters. Accordingly, appellants have not established that non-monotonicity imposes a severe burden on the right to vote."

Here is mathematical analysis in three different probabilistic models of the frequency of non-monotonicity in IRV elections. We repeat the "summary tables" from there:

3-candidate IRV elections:
Probabilistic model type-I failure prob type-II failure prob monotonicity failure prob
Random-elections = Impartial culture (12.157±0.001)% (2.3119±0.0005)% (14.469±0.002)%
Dirichlet [uniform in 5-simplex] 13/288=4.513888...% (0.90935±0.0001)% (5.4232±0.0001)%
1D "Political spectrum" 5/72=6.9444...% (2.7778±0.0003)% (9.7222±0.0003)%

N-candidate IRV elections in N→∞ limit:
Probabilistic model type-I failure prob monotonicity failure prob
Random-elections = Impartial culture →100% →100%
Dirichlet [uniform in (N!-1)-simplex] →100% →100%
1D "Political spectrum" →100% (conjectured) →100% (conjectured)

The proofs for the N→∞ cases seem also to indicate that asymptotically 100% of the voters and candidates are affected [but this is not the case when N=3].

Did the yes/no ruling make sense?

Maybe. The plaintiffs and/or their lawyers were apparently exceptionally stupid. (I.e, they ignored my advice. Which turns out to have predicted all of the below correctly.) In the court's view their case consisted of two elements:

  1. IRV is non-monotonic,
  2. IRV "unequally weights votes."

(1) was a stupid argument to make because we know that some non-monotonic systems (top-two two-round runoff) clearly are constitutional. (I suppose the plaintiffs could have argued that they are monotonic in each round, so their monotonicity violation is less serious than IRV's, but they did not try. And if they did try, they'd be resting on thin ice.)

Then re (2) the court either did not understand, and/or the plaintiffs failed to adequately explain, how IRV can "unequally weight votes." I would contend that IRV can, in a manner which seems arbitrary and capricious, decide to count some A>B votes but meanwhile not count some B>A votes, when deciding to eliminate A and not B. As a result, IRV can elect X even though Y is preferred, over both X and everybody else, by an arbitrarily large majority. That's because the vast majority of Y>X voters were ignored, i.e. their votes deweighted to zero, when it mattered. Non-monotonicity can also be viewed as a side effect of such "unequal weighting." If Z wins, but then after more votes for Z, Z stops winning – why did that happen? Well, it is because the capricious IRV decisions to count some votes and not others, got redone in a different capricious manner, this time less beneficial for Z.

The court then pointed out that the plaintiffs in trying to get the pro-IRV voter-referendum result ruled unconstitutional on its face (without any actual problem having arisen, since no IRV election under this has happened yet) faced an extremely severe burden of proof. The court said the plaintiffs had failed to meet that burden. Case closed.

In my opinion: there might be a good case IRV is unconstitutional (though I repeat, that's not at all clear to me) but if so, this good case was not made by the plaintiffs and not considered by the court. Then on top of that, unfortunately the court (encouraged by the defendants and inadequately discouraged by the plaintiffs) made various false statements, documented above.

I also think: if IRV opponents really want to get IRV ruled unconstitutional by high courts, then they are tactically stupid to challenge a law which was passed by referendum and has never been used – in order to make themselves face a huge burden of proof and be unpopular. Dumb. That way, they'll lose and they will also set up precedents which will make it harder for anybody to win an actually-good case. They, in short, will hurt their own cause. If you want to do this, do it right. For example, the Burlington 2009 election would have (I would think) have made a much better basis for a lawsuit, if some Burlington IRV-victim wished to pursue it (which they might not, in which case the smart move would be to do nothing and wait until a better case came along).

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