Alternate Voting Systems Study by the Michigan League of Women Voters

On Saturday January 15, 2011, the League of Women Voters of Northwest Wayne County sent out a newsletter, in which they mentioned a study of Alternative Voting Systems, commisioned by the LWV of Michigan in 2009.

At the 2009 Biennial League of Women Voters of Michigan Convention, the delegates approved a study of Alternate Voting Systems. Over the past 14 months, the Study Committee has compiled a report that addresses three Voting Systems. It is now the job of members from local Leagues to review and discuss the material, and then indicate whether we support or oppose the three voting systems. Once the responses from local Leagues across Michigan are compiled, the study conclusions will be formed into a position that will be voted on by the delegates at the 2011 state convention.

The newsletter goes on to list the three voting methods addressed by the study, along with a short list of "pros and cons" extracted from the study. While the description of Plurality Voting is accurate, the statements on Approval Voting and Instant Runoff Voting unfortunately contain several seriously misleading and even erroneous statements, as well as important omissions.

 Approval Voting System
(Voters select as many candidates as they wish;
candidate with most votes wins)		 Instant Runoff Voting System
(Voters rank candidates; votes for candidate with fewest first-choice votes are redistributed according to their second choices until one candidate achieves a majority)
  • Is easy for voters to understand.
  • Expands voters‟ choices because they can vote for more than one candidate.
  • Might eliminate “wasted” votes, and “spoiler” 
    candidates in some cases.
  • Measures only whether or not a candidate is 
    acceptable; does not distinguish between 
    intense and weak approval.
  • Could lead to defeat of a candidate whom a 
    majority support as their first choice.
  • Is vulnerable to manipulation.
  • Ensures majority rule.
  • Allows voters to express preferences among candidates.
  • Eliminates problems of spoiler candidates knocking off major candidates.
  • Eliminates need for run-off elections.
  • Does not meet mathematical requirement for monotonicity.

IRV "ensures majority rule"
Simply false. In the 2009 mayoral election in Burlington, Vermont, the Progressive candidate won, even though voters preferred the Democrat to the Progressive by 54% to 46%. In the 2010 San Francisco district 10 election, Malia Cohen won with 21% of the vote (4321 votes from 20550 total). This "win with less than 50%" phenomenon happens frequently with IRV, due to ballot exhaustion. In fact, it is even possible with IRV for candidate X to win even though candidate Y was preferred to X by a majority of voters and got more first place votes than X.

Approval "could lead to the defeat of a candidate whom a majority support as their first choice"
While this is theoretically possible, it is unlikely and misleading. Especially because the author omitted the fact that, in an election with millions of voters, IRV can elect a candidate who was the first choice of only two voters, and to whom a majority of voters preferred every other candidate but one.

IRV "eliminates" spoiler candidates, while Approval Voting "might" do so in "some cases"
This is actually backwards. Score Voting, whose simplest form is Approval Voting, completely eliminates the "spoiler effect". While IRV can indeed suffer from this problem, as demonstrated in this simple example.

IRV "eliminates the need for runoff elections"
Simply put, IRV is a different system than Top-Two Runoff (TTR). Despite common misconceptions, one is not an equivalent substitute for the other. Therefore, it would have been just as accurate (or just as inaccurate) to claim that Approval Voting (or any other alternative voting method) eliminates the need for runoffs.

Approval Voting is "vulnerable to manipulation"
This argument is again backwards. Approval Voting performs better than IRV with any ratio of tactical voters, as objectively quantified via extensive Bayesian regret calculations. In fact, the advantage of Approval versus IRV actually increases, the more strategic voters there are. Perhaps the most damning observation in that link is that IRV actually incentivizes a type of tactical exaggeration which causes it to degenerate into an approximation of Plurality Voting. Quite ironically, the study repeated the thoroughly debunked myth that Approval Voting would degenerate into Plurality Voting.

Approval Voting "measures only whether or not a candidate is acceptable", while IRV "allows voters to express preferences among candidates"
This gives the impression that IRV allows voters more expressiveness and leads to more representative outcomes than Approval Voting, because it uses a more expressive ballot. However, that turns out to be false, because IRV incentivizes insincere rankings, and discards more information than Approval Voting, thus nullifying the benefit of a more expressive ballot.

Mototonicity is a "mathematical requirement"
The report's discussion of monotonicity actually begins with a refreshingly accurate definition of this term, which refutes FairVote's common false claim that e.g. the 2009 Burlington mayoral election did not actually exhibit a failure of monotonicity.

Monotonicity: The mathematical criterion which states that with the relative order or rating of the other candidates unchanged, voting a candidate higher should never cause the candidate to lose, nor should voting a candidate lower ever cause the candidate to win. The idea is that voting for one’s choice will help one’s candidate.

Unfortunately the authors then proceed to let FairVote confuse the issue in a myriad of ways.

First, the authors mention a FairVote article titled "No System Is Perfect", which they say "reminds readers that Arrow’s Impossibility Theorem proves that every system has problems". What they don't mention is that Arrow's Theorem does not even apply to Score Voting and Approval Voting.

Next the report claims that "the problem of non-monotonicity exists only in theory, not in the real world", and then quotes the FairVote piece:

“If the theoretical problems with choice voting occurred even as frequently as 0.1 percent of the time, there would be many such examples, but there are none.”

This is completely false. Here are a handful of readily verifiable examples.
Unfortunately, full ballot sets are not readily available for all IRV elections. If they were, we would presumably find many more examples.

Warren D. Smith, a Princeton math Ph.D. and voting method researcher, has extensively studied the issue of monotonicity, and calculated that the probability of non-monotonic IRV elections is somewhere in the neighborhood of 10% to 20%. However, when we consider only elections in which IRV yields a different result than ordinary Plurality Voting (i.e. the cases FairVote especially touts as "successes"), then the rate jumps to 25%-36%.

Finally, the report demonstrates a misunderstanding of why non-monotonicity is a problem, citing Samuel Merrill's view that "it would be relatively impossible in an election with large numbers of voters to use nonmonotonicity to a candidate’s advantage."

Tactical exploitation is not the problem with non-monotonicity. The problem is that a non-monotonic election pair gives us 100% mathematical certainty that IRV elects the wrong candidate in at least one of the two "mirror image" election scenarios. It is impossible to know for sure whether it is in the actual election, or its hypothetical opposite, so in any non-monotonic IRV election, there is effectively a 50/50 chance that the wrong winner was elected. We have pointed this out to FairVote and others on numerous occasions to no avail.

Summary

This report by the League of Women Voters contains numerous fatal errors. This is the unfortunate consequence of relying on inaccurate information from FairVote.