Refutation of False Statements about Instant Runoff Voting (IRV)

(Extra: Click link for corrections of errors in the Vermont "easy as 1-2-3" pro-IRV report.)

Unfortunately, a large number of false statements have been made and continue to be made in newspapers, magazines, and on the internet, about Instant Runoff Voting (IRV). And unfortunately, the CVD (Center for Voting and Democracy, a pro-IRV group later calling themselves "FairVote") often says false things.

For example, the CVD, discussing mathematical imperfections in IRV in a page "last updated on 12/11/2009," misleadingly claims:

Choice voting has been used in public elections for over 100 years in the US and around the world, and we have not uncovered even a single example where any of the theoretical defects have occurred.
This includes tens of thousands of elections with tens of millions of voters. If the theoretical problems with choice voting occurred even as frequently as 0.1% of the time, there would be many such examples, but there are none.

Ludicrous. Actually, when I examined the five Debian elections 2001-2005 I immediately found that two of them had such problems. In our list of national presidential elections, there are several clear presidential-level examples (Peru 2006, Chile 1970, France 2007) where IRV gave the "wrong winner" plus several more unclear examples where that may have or would have happened (France 2002, Slovakia 2004, Cyprus 1988, Mexico 2006, Iran 2005), plus when we examine the 150 federal IRV elections in Australia 2007 we find at least 9 and probably more like 20 pathologies. This all is far more than "0.1%." Plus if we were to extend the list to also cover, e.g, Senate races, then there would be many more examples, such as the New York State 1970 Senate race. And you can check the 2009 Burlington VT mayor election for a large number of IRV pathologies all in one election – despite the fact fairvote called this election a "great success" for IRV and had pushed for Burlington to adopt IRV (after this election, it repealed it). Or the Ireland 1990 presidential IRV election, again often cited by Fairvote as a "great success" example, but actually demonstrating some serious pathologies. (Fairvote apparently always ignores the pathologies in the very elections they highlight as "great successes" then says things like these pathologies have never ever occurred. All lies.) And the CVD forgot to say that usually, the votes in IRV elections have been kept secret which has prevented anybody from noticing a problem. Continuing on to the next false CVD statement in this same document:

"Single Transferable Vote Resists Strategic Voting," Social Choice and Welfare 8 (1991) 341-354.
This article shows mathematically that choice voting is virtually impossible to manipulate, which explains why no real world example has ever been found. The only examples people raise are highly unrealistic, artificial ones.

A complete lie. Many simple and realistic counterexamples are provided on CRV pages e.g. this and this one. In fact, the examples of hard-to-manipulate elections used in the article they cited are (as its authors would readily admit) what are "unrealistic and artificial." IRV ("choice voting," as the CVD here calls it) often is easy to manipulate in realistic scenarios, i.e. with a bounded number (such as 3 to 7) of candidates; only in their paper's hard examples with half as many candidates as voters is manipulation proved computationally difficult. Is that "realistic"? I don't think so! (Next time you find a realistic election with 5000 candidates and 10000 voters, let us know.) Indeed, this entire line of research was refuted by this paper by Conitzer & Sandholm showing that every "reasonable" rank-order voting system is usually easy to manipulate.

Crispin Allard, "Lack of Monotonicity – Revisited," Representation 33 (1995) 49.
As Professor Amy writes in Behind the Ballot Box, referring to the Allard paper, "One statistical study founded that if STV elections were to be held through the United Kingdom, a nonmonotonic result would occur less than once a century."
Another complete falsehood: Allard's work was based on an incorrect calculation. You can find more details of the incorrect calculation in
Crispin Allard: "Estimating the Probability of Monotonicity Failure in a UK General Election," Voting matters 5 (January 1996).
But if you redo Allard's calculation correctly then you find out that in Allard's probabilistic model of 3-candidate IRV elections, a nonmonotonic one happens once every 95 elections, i.e. for the 659-member UK House of Commons, 7 members would be elected nonmonotonically each time! And that's only counting one kind of nonmonotonicity – count the other and we are up to 5.4% of elections in Allard's model. Furthermore, in different, arguably more realistic probabilistic models than Allard's, a nonmonotonic election happens much more often, namely 5-15% of the time in 3-candidate IRV elections and 100% of the time in N-candidate elections when N is made large.

"The rate of spoiled ballots did not increase in any of the U.S. cities when they switched to IRV." – Fairvote.org web post, June 2008.

False. San Francisco, Fairvote's "biggest success," immediately after switching to IRV experienced an increase in spoiled ballots versus the plurality-voting races held on the same day (same voting booths, some voters) by a factor of seven.

Here are a selection of IRV errors from newspapers:

  1. Mickey Marshall: Runoff voting is better, The Columbian (WA) 9 December 2004: "The [plurality voting] winner will not have a majority of the votes. In other words, it is possible that a majority of the voters would prefer the losing candidate. Instant Runoff Voting is better than our plurality voting system because it ensures majority winners."

    False! In this counterexample election the losing candidate C is preferred by a nearly 2-to-1 majority (201 to 102, to be precise) over the IRV winner D!
  2. Runoff vote system makes good sense, Southwest Florida News Press, 3 January 2005 (editorial advocating IRV): "What if we were able to streamline our city and town elections, make them less expensive, and at the same time, ensure that the winner garnered a majority of more than 50 percent of the vote?"

    False! Election expense will certainly increase by using IRV rather than voting systems which can use present-day plurality-type voting machines not connected together via a computer network. For example, see this news article about Minneapolis MN's experience. See this press article about the University of Vermont IRV cost study. It may be that the cost "decrease" they had in mind was versus plurality with a second runoff election. It is true that a single IRV election is cheaper than two elections (original plus runoff), if all other things are equal – which is the point of the word "instant." However, because most places that require runoff elections only need them rarely, the expense ratio on average is not anywhere near 2-to-1, and hence the expense of switching to IRV would usually exceed the savings for a long time (and considering the need to continually replace machines, perhaps forever). [Oakland finances discussed here.] Also, once again, this "majority" nonsense is thrust upon us. IRV only produces a "majority" winner after all the others have been eliminated – not exactly an accomplishment!
    About IRV "majority winners": Some IRV advocates love that IRV always ends by pitting one candidate against another and declaring one the "majority winner." All this means is that the winner has majority support versus one other candidate. So what? If I were to just pick two candidates at random, then pick whichever was majority-preferred, that'd also have that property. In the nasty election example, IRV declared D a "winner" because of its final victory over B, while ignoring the fact C had approximately 2:1 supermajority support not just against one candidate, but against everybody including D.
    What makes this lie particularly appalling was that the official wording of the ballot question that enacted IRV in San Francisco was:
    &nsbp;  Shall the City use Instant run-off voting to elect City officers with a majority of votes without separate run-off elections? (YES / NO).
    In other words, they lied to the voters of San Francisco right on the ballot question itself, not just in advertising (although the same lie also was told in propaganda brochures urging enactment).
  3. Wilmington Star News: A better way to settle primaries, 8 September 2004 (editorial): "Runoff winners can be chosen by a pitiful handful of voters – about 3 percent in the recent Democratic runoff for superintendent of public instruction. If North Carolina used `instant primaries'; instead, winners would have substantial, if not necessarily enthusiastic, support. We'd vote for two candidates instead of one, and rank them in order of preference. For example: First choice, Meg Scott Phipps; second choice, Osama bin Laden.
    If no candidate got more than 40 percent, the second choices would be piled on. Thus, `instant runoff.' "

    False! This is just a wrong definition of the IRV system. The system they are actually describing here is the "two round Bucklin system" albeit with a 40% cutoff not 50%.
  4. Opednews.com: Competitive Elections: A Challenge for Spitzer, by Kimberly Wilder and Ian Wilder 31 Jan 2007: "Institute Instant Runoff Voting (IRV). IRV is the method used to determine the Heisman Trophy, the Baseball MVP, and some municipal elections on California. You do not have play a game of voting for the single candidate you least hate to block the one you most hate. Instead you rank your choices. You can always vote for the candidate you love first. The winner has to get over fifty percent of the vote. If no one gets fifty percent on the first round, then the bottom votegetter drops off as voters' first choice and their second choice moves up. This removes the worry of spoilers and prevents negative campaigning since every candidate wants to be your second or third choice."
    Unfortunately the above paragraph is packed with untruths:
    1. IRV is not used to select the Heisman trophy winner. Proof:
      http://www.heisman.com/history/balloting.html.
    2. IRV is not used to select the baseball MVP. Proof:
      http://www.findarticles.com/p/articles/mi_m0FCI/is_11_63/ai_n6332589,
      http://en.wikipedia.org/wiki/MLB_Most_Valuable_Player_Award.
    3. IRV does not "remove the worry of spoilers." Spoilers can and do still occur under IRV – in fact an even worse kind of spoiler occurs where voting for the spoiler top not only can prevent your "lesser evil" from winning, it actually can even prevent the spoiler himself from winning! Proofs:
      http://rangevoting.org/IRVpartic.html
      http://rangevoting.org/IRVcs.html
      http://rangevoting.org/IRV1519.html
      http://rangevoting.org/rangeVirv.html#BramsEx
      http://rangevoting.org/IrvRevFail.html
    4. You cannot "always vote for the candidate you love first" because that act can actually cause that candidate to lose. (Examples cited above.) This is worse that the voting system we have now in the sense that at least now, by voting for X, you cannot cause X to lose.
    5. The claim IRV "prevents negative campaigning" cannot be called "false" since it is subjective and vague and undefined – but it similarly cannot be called "true." There is, in fact, some evidence to the contrary. E.g. see this actual campaign ad from the San Francisco 2011 mayoral election using IRV. Also, it is clear from computer simulation evidence (see the IRV pictures) that IRV with honest voters tends to favor "extremists" and prevent "centrists" from winning, in contrast to approval voting which favors centrists.
    Summary: The Wilders in their op-ed unfortunately exhibited massive ignorance about the properties of instant runoff voting, and even worse, spread those myths to a wider audience. However, they were on the right track in feeling that our present voting system has some major deficiencies, and that two of them are "spoilers" and the inability to vote for your favorite without being strategically stupid. IRV does not fix either of these two deficiencies. But a simpler and better voting system called "range voting" fixes them both. I repeat: with range voting, voting your favorite top never hurts either him or you; and "spoilers" no longer exist in the sense that voting for a "spoiler" never in any way affects your vote on the question of who is better, A or B, where A and B are two other candidates. And to make the obligatory sports reference (this time a correct one) Range voting has been used in the Olympics to select gold medal gymnasts.
    Range voting also has the advantage versus IRV of reducing (not increasing) the risk of ties and near-ties, and of working on every voting machine in the USA, right now (computerized or not) with no modification and no reprogramming needed.
    To learn more about range voting and its properties, please check http://RangeVoting.org. Thank you. I hope you will endorse range voting. You can do that on the rangevoting.org web site by clicking "endorse" and following subsequent directions.

    The League of Women Voters of Minnesota put out a study (2.5MB) on alternative voting systems which unfortunately made IRV look considerably better than it should have. Their quick summary of IRV is highly misleading:

    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)
    1. Ensures majority rule
    2. Allows voters to express preferences among candidates
    3. Eliminates problems of spoiler candidates knocking off major candidates
    4. Eliminates need for run-off elections
    5. Does not meet mathematical requirement for monotonicity
    Of these 5 items, numbers 1 (counterexample) and 3 (counterexample election and another and another and another!) are simply false. The League also misleadingly characterizes Condorcet methods by saying "May result in a tie that requires pre-election decision on how to break tie." While I suppose that is technically true, the same thing is true for every election method: and ties seem far more likely to happen in IRV than in Condorcet methods since a crucial tie can happen every IRV round.

    The League report criticizes Plurality, Approval Voting, Borda, and Condorcet for being "vulnerable to manipulation." But they don't criticize IRV for being vulnerable to manipulation. A naive reader would reach the false conclusion that IRV was immune to manipulation! (In fact, Approval is probably superior in this respect to IRV, and in at least some ways, Condorcet is also.)

    The League also always stress that Approval Voting, Borda, and Condorcet were good methods only according to "mathematical" considerations. They always stress that IRV's violation of monotonicity was only a "mathematical" problem. They always stress that only mathematicians consider e.g. the Condorcet criterion and the monotonicity criterion important. This is annoying and misleading.

    The League also quotes Ramsey County Election Manager Joe Mansky as saying that counting IRV elections is no problem: "with the right computer software, we can count any ballot you want." That's completely false because IRV elections simply cannot be counted in individual precincts. It doesn't matter what software you have or how much work you are willing to do. It simply cannot be done. IRV elections can only be counted statewide – as opposed to range and plurality voting where precincts can count their own totals and send only them to a statewide center. This whole point is totally ignored by the League report and would require a massive change in all or almost all US states' procedures.

    The League also screws up in their appendix 3 where they discuss the constitutionality of various voting systems. They claim IRV is constitutional and Approval, Borda, and Condorcet are not because IRV passes both these tests:

    1. There is no more than one vote per voter per office.
    2. Second preferences do not hurt first preferences.
    It seems to me, however, that all four methods pass their first test, and indeed IRV is unfair in the sense that much of a voter's vote is often ignored, whereas with, e.g, Approval Voting, that is not the case. Approval voting votes are "more equal" in power than IRV votes because, if the election comes down to an A versus B tie, then you with your Approval Vote, even after you have chosen your Approval Votes for all the candidates other than A and B, can then break that AB tie your way. With IRV, if there is a crucial A versus B tie, then it is often the case that even if your ballot states that you prefer (say) B over A, that that statement by you will be ignored and will not break the tie. However other IRV voters who expressed an IRV preference of A over B will break the tie and be counted. This seems unequal and "unfair." The League's second test seems to me to be rather ridiculous. I do not understand where in the Minnesota or US constitutions this requirement is stated. I do not believe the 1912 court decision they cited can be taken seriously for contemporary purposes. We have books and we have experts on voting methods now. The Bucklin system which was used for many years in many US states to elect governors would be "unconstitutional" according to both the League's alleged tests.

    Here are 4 sentences by Steven Hill, "senior analyst for the Center for Voting and Democracy (CVD)" and author of the book Fixing Elections: The Failure of America's Winner Take All Politics:

    1. "The instant runoff ensures the election of the candidate preferred by most voters."
      False: counterexample election.
    2. "It eliminates the problem of spoiler candidates knocking off major candidates."
    3. "It frees communities of voters from splitting their vote among their own candidates."
      Sorry, the preceding two statements are false or misleading. The "spoiler" problem in plurality voting is where voting for your honestly-favorite third-party candidate is strategically stupid because it causes both him, and the least-worst major-party candidate, to both lose. Therefore you are best off under plurality voting by "betraying" your favorite and voting for the least-worst major party candidate, thus perpetuating two-party domination. The exact same phenomenon can happen under IRV as is shown by e.g. this example election, and IRV also leads to 2-party domination as is described there.
    4. "It promotes coalition-building and more positive campaigning."
      This statement perhaps is too vague to justify. Anyhow Hill and the CVD give no historical evidence for it. And there is some evidence against it. Another incredibly vague and undefined claim made by the CVD in their "talking points for IRV (September 2005)" web page is "Creates a clearer mandate for a winning candidate's agenda, better direction for policy-making." Well, let us just say, subjective garbage claims like that can be made about any voting system whatever and there is no way to refute them... real and valuable claims are those that cannot be made about every system, which actually are clearly defined so one can hope to decide if they are true, and which are demonstrably true.

    Indeed, the CVD is a font of falsities about IRV:

    1. In the article by CVD founder Rob Richie, with Terrill Bouricius & Philip J. Macklin in Science Magazine 294,5541 (May 2001) 303-306: "Used for decades in Australia and Ireland and considered in 13 state legislatures this year, IRV lets voters rank candidates in preference order. A voter's best strategy is to sincerely rank the candidates."

      False! Counterexample election and another and another! This is one of the most basic and well known facts about IRV, and Richie et al are simply telling a flat-out lie. Not only in IRV, but in fact in every ranked-ballot voting system in which unanimously top-ranked candidates win and in which there is not always a "dictator" voter who can singlehandedly decide everything , in at least some elections, it is not a voter's best strategy to sincerely rank the candidates. This is called the Gibbard-Satterthwaite theorem and is one of the most famous and well known (if not the most famous and well known) theorems in all of voting theory. (So the CVD's ignorance of this theorem is rather instructive about their level of expertise.) To learn more about such "impossibility theorems," see #79 and #97 here.
    2. Incidentally, this same Science piece also intentionally misleads in other ways. For example in its note #1 it lauds the Ireland 1990 presidential election as an example of a successful IRV election, simply ignoring its pathologies. In its note #2 it explains how approval voting strategic calculations could seem complicated and could depend on how the other voters vote, neglecting to mention that in IRV, strategic computations are more complicated and also depend on how the other voters vote. In its note #3 they talk about how approval voting could allow somebody with "strong majority support" to lose, omitting to note that a similar phenomenon occurs with IRV.
    3. From the CVD web site: "No voting system is perfect, but IRV is generally considered the best method for measuring both the breadth and intensity of the voter's support for a candidate."

      Well, since "measuring the breadth and intensity" is undefined meaningless hogwash, we can't actually brand this as false. However, among academic experts IRV is "generally considered" to be a comparatively silly system with many flaws. More about the state of expert consensus (or lack thereof) as of 2005.
    4. And here is another bogus CVD "talking point":
      "[IRV] Minimizes `wasted' votes, votes that don't help elect a winner. To the fullest extent possible, your vote will contribute to electing a candidate that you like."

      This is false. In fact, large parts of your vote can be completely ignored by the IRV system. (In contrast: with many other systems, such as range voting, all of your vote is used with none ignored.) If you prefer A over B, and say so in your IRV vote, then IRV can elect B and not elect A, and never even look at the fact that your vote said that you thought A was better than B. This counterexample election involves plenty of such ignoring (only the "simplified" parts of the votes in that election are looked at by IRV, resulting in a completely crazy IRV "winner" D disliked more – by approximately a 2:1 margin – than C). The whole "spoiler" phenomenon can be considered to be about wasting votes – i.e. if you vote for the third-party candidate you are "wasting" a vote which could have been used to benefit the least-worst major-party candidate – and as we have seen that still happens under IRV, still leading to 2-party domination.
    5. And here, right on the front page of the CVD's "instant runoff bulletin board" (20 August 2006) is the false statement that
      Instant runoff voting eliminates concerns about "wasted votes" and the "lesser evil" dilemma.
      Both those statements are false. In our counterexample (or this) we repeat for the umpteenth time, if you honestly vote Nader>Gore>Bush, then your vote is "wasted" and causes both Nader and Gore to lose, whereas a dishonest vote for the lesser evil Gore would have caused Gore to win (which you prefer).

    Dan Cooper correctly remarks: Approving of Kerry and Nader will never help create a Bush victory [under "approval voting"], whereas ranking Nader above Kerry could help Bush win under IRV voting. Once IRV voters understand that, strategic voting is guaranteed.

    I would like to thank Markus Schulze and Abd ul-Rahman Lomax for bringing some of the above falsities to my notice.

    From the 2004 Green Party USA platform:

    8. We demand choices in our political system. This can be accomplished by proportional representation voting systems such as
    Choice Voting (candidate-based),     Mixed Member Voting (combines with district representation), and     Party List (party based);     and semi-proportional voting systems such as Limited Voting, and     Cumulative Voting.
    All are used throughout the free world and by U.S. businesses, and community and non-profit groups to increase democratic representation. We call on local governments to lead the way toward more electoral choice and broader representation.
    9. We believe in majority rule and reject the present method of election without a majority. Accordingly, we call for the use of Instant Runoff Voting in chief executive races, (mayor, governor, president, etc.) where voters can rank their favorite candidates (1,2,3, etc.) to guarantee that the winner has majority support and that voters are not relegated to choosing between the lesser of two evils.
    10. We believe in multi-party democracy for partisan elections as the best way to guarantee majority rule, since more people will have representation at the table where policy is enacted. We assert that introduction of a multi-party democracy is essential because
    • The change in the structure of electoral politics will moderate the influence of extremist views and domination by the larger parties, and offer more fair representation to a greater number of citizens; and
    • A third party can validate and raise other points of view that need to be heard.

    Unfortunately this platform is in error in several respects:
    (a) "Choice Voting" (at least as that word often is used by fairvote.org) is a simplified form of Instant Runoff (IRV) voting, which is a single-winner, hence not a proportional representation, system. See this discussion. (Also, the fact the Greens "believe in majority rule" completely contradicts their call for "proportional representation," which they would recognize if they understood these ideas.)
    (b) Instant runoff voting does not cause the winner to have "majority support" as we keep saying again and again, and keep referring you to this counterexample election.
    (c) Instant runoff voting does not prevent the "lesser of two evils" effect, as we also keep saying again and again, referring you to, e.g, this counterexample, or this one, or this or this.
    (d) Sure, it'd be great to have "multi-party democracy" but the Green Party – suicidally stupidly – here is endorsing a system known to lead to self-reinforcing 2-party domination! Death wish? See this list of reasons US third parties should not want IRV.

    From the Libertarian Party platform (amendment enacted 5 July 2002):

    Electoral systems matter. The predominant use of "winner-take-all" elections in gerrymandered, single-member districts fosters political monopolies and creates a substantial government-imposed barrier to election of non-incumbent political parties and candidates. We propose electoral systems that are more representative of the electorate at the federal, state, and local levels, such as proportional voting systems with multi-member districts for legislative elections and instant runoff voting (IRV) for single winner elections.

    The Libertarians here are considerably more accurate in their wording than the Greens, but the bottom line is they still, suicidally stupidly, endorse IRV even though that is known to lead to self-reinforcing 2-party domination. Again, see this list of reasons US third parties should not want IRV, stop having a death wish, and start endorsing a system that will actually lead to third parties being able to stably exist. Try range voting.

    Is there any truth hidden in the above false statements?

    There's a little in some of them. Similarly to what the LoWV says, it is true that IRV is usually thought to be comparatively immune to manipulation in practice. But Approval voting was designed with that goal in mind, a fact the LoWV report fails to mention.

    The Vancouver Columbian in its 22 March 2003 editorial "In Our View: A Better Ballot?" said:

    "WA State Rep. Jim Moeller, a Vancouver Democrat and sponsor of HB 1390 [bill calling for IRV elections], also hopes the method will make campaigns more civil. `You don't want to sling mud and call people names if you have a chance of being the second choice,' Moeller told The Columbian's Don Jenkins last week."

    This may make logical sense. We are not sure. If one candidate is leading, it certainly seems in the interests of the remaining ones to attack him or her. There may be a case that IRV (or other voting methods – just which are unclear) reduces "negative campaigning" (whatever that is), but we are unaware of any clear and irrefutable argument for it (or even a clear definition of it). It seems largely an unsubstantiated hope rather than a reality – but it might have some truth. One thing we can say for sure is that IRV favors extremists, which seems on its face to contradict the notion compromise and centrism is a desirable strategy for candidates in IRV races.

    Also, IRV is "immune to vote splitting" in the following (fairly weak) sense. Suppose the electorate (and the candidates) consists of various disjoint "camps," where every voter in camp j ranks all type-j candidates ahead of all non-j candidates. Then,

    Theorem: regardless of how the camps "split their votes" among their-type candidates, if there exists a camp containing over 50% of the voters, then some candidate from that camp is guaranteed to win the IRV election.

    Proof sketch: at some point a top-camp candidate will have >50% of the top-rank votes (after transfers) and hence can never be eliminated. Q.E.D.

    But if no camp contains >50% of the voters, then it is not the case that a candidate from the most numerous camp must win an IRV election. (E.g, camp A could have 35% and camps B and C 32 and 33% of the voters, but a type-C candidate could still win if many of the B-voters transfer their allegiance to him after all B-candidates and appropriate other candidates are eliminated, and whether this happens does depend on how the B-voters [and A- and C- voters] split their votes among the As and Cs.)

    The property of the theorem is not a terribly strong property and it is not unique to IRV. (Still, it is a good IRV benefit. Most ``weighted positional'' systems like Borda disobey this property, so in this sense IRV is superior to them.) For example, the property of the theorem is also obeyed by every voting system obeying the "winner in Smith set" property, such as Schulze beatpath voting, Heitzig River voting, Tideman ranked pairs, many Condorcet methods, Copeland, Nanson, and Woodall-DAC. So IRV in no way specially enjoys some kind of anti-splitting property.

    For another example, approval voting (AV) also obeys this property provided camp members approve all candidates from their camp and disapprove of all others, and indeed AV then obeys the much stronger property that a candidate from the most-numerous camp then must win.


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