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:
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.
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
And the following are not:
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."
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:
| 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)% |
| 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].
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) 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.