Why Range Voting is Better than IRV (Instant Runoff Voting)

(Executive summary)    (Skip to end)    (Common Errors, Myths, Mis-statements, & Lies about IRV)
(How we know IRV just leads to 2-party domination)    (Quick summary why third parties should not want IRV)
(oversimplified argument why third parties should not want IRV)     (Peru 2006 election=apparent IRV failure)
(Flawed "two and a half" candidate thinking) (Quick example of "Nader spoiler" phenomenon under IRV) (Another) (Another)
(Argument for IRV-proponents that AV & RV is better)

1. What they are. Range voting: In an N-candidate election, each vote is an N-tuple of numbers each in the range 0 to 99. The Kth number in the tuple is a "score" for candidate K. You take the average of all the Kth entries to find the average score for candidate K. The candidate with the highest average score wins. (Voters are allowed to leave an entry blank to denote "don't know anything about that candidate." Blank entries not incorporated into average.)

IRV: Each vote is an ordering of the N candidates from best to worst. (Voters are not allowed to omit a candidate they know nothing about, and are not allowed to regard two candidates as equal.) We proceed in "rounds". Each round, the candidate top-ranked by the fewest voters is eliminated. (Ties must be broken by some means, such as a coin flip.) After N-1 rounds, only one remains – the winner.

2. Examples: Say the N=3 candidates are named Amy, Bob, and Cal, and the 9 range votes for them are:

Candidates➧ Amy Bob Cal
1st voter: 99 77 0
2nd voter: 98 98 X
3rd voter: 87 0 71
4th voter: 99 1 98
5th voter: 52 99 X
6th voter: 26 98 5
7th voter: 10 96 X
8th voter: 0 70 99
9th voter: 0 1 99
sum: 441 540 372
average: 49 60 62
(The X's denote "intentionally left blank" by that voter to denote the fact he wishes to express ignorance about Cal and wants to leave the decision about his score to other, more knowledgeable voters.)

Because Cal has the highest average, he wins with range voting.

The corresponding 9 IRV votes (assuming all the voters ignorant about C "play it safe" by ranking him last – which anyway is effectively necessary since IRV does not permit "no opinion" votes and regards all unranked candidates as ranked last – and that voter #2, since forced to choose between Amy and Bob, gives a slight preference to Amy) are

Voter His Vote:
1st voter: A>B>C
2nd voter: A>B>C
3rd voter: A>C>B
4th voter: A>C>B
5th voter: B>A>C
6th voter: B>A>C
7th voter: B>A>C
8th voter: C>B>A
9th voter: C>B>A

Then C is eliminated in the first round, at which point the second and final round is won by B by 5-to-4 over A.

3. Monotonicity and Honesty: In range voting, if any set of voters increase a candidate's score, it obviously can help him, but cannot hurt him. That is called monotonicity.

Two of IRV's flaws are that it is not monotonic and dishonesty can pay. In the example, suppose the 1st voter, instead of honestly stating her top-preference was A, were to dishonestly vote C>A>B, i.e. pretending great love for her truly hugely-hated candidate C, and pretending a lack of affection for her true favorite A. In that case the first round would eliminate either C or B (suppose a coin flip says B) at which point A would win the second round 5-to-4 over C! (Meanwhile if C still were eliminated by the coin flip then B would still win over A in the final round as before.) In other words: in 3-candidate IRV elections, lying can help. Indeed, lying in bizarre ways can help.

In this IRV example, voter1's vote for her true favorite (here A) actually caused him to lose!! Analysis by W.D.Smith shows that about 15% of 3-candidate IRV elections are non-monotonic. (See also puzzle #4.) (Whenever this happens we would expect tremendous rage from the "robbed winner" and calls for reform of the idiotic IRV voting system, and for the heads of the idiotic activists who originally advocated IRV and got us into this mess. That has been prevented in practice by simply keeping the votes secret to try to prevent anybody from proving this occurred.)

In contrast, in 3-candidate range elections, it is never a smart strategic move for any voter to be dishonest about her relative ordering of A, B, and C; if an intelligent range voter feels that A>B, she will never provide a vote in which B>A.

4. Wise to vote for your favorite? In range voting, scoring your favorite candidate top can never hurt you. In IRV, it can – indeed as we just saw it can even hurt that favorite candidate directly, although more commonly it prevents, say, both your first and second favorite from winning.

As Mike Ossipoff has often emphasized, it is very important to make democracy work well that it always be a good idea – not a bad idea – to vote for your favorite candidate.

5. Simplicity: Range voting is simpler than IRV. If you don't believe me, try writing a computer program to do both. The range voting program will be shorter. Range voting also is simpler in the sense that it requires fewer operations to perform an election. In a V-voter, N-candidate election, range voting takes roughly 2VN operations. However, IRV voting takes roughly that many operations every 2 rounds. In a 135-candidate election like California Gubernatorial 2003, IRV would require about 67 times as many operations. (In fact, range voting is simple enough that it could be done with hand calculators, if necessary.)

Another aspect of that: every possible way to give the candidates scores is a legal range vote. Not every possible way to give the candidates rankings is a legal IRV vote – if you accidentally rank two candidates equal, for example, IRV would consider that an illegal vote and your ballot would be discarded. In, say, the 135-candidate CA governor-recall election of 2003, the chances you would screw up when trying to provide a full rank ordering of the 135 candidates, would be immense. But it would be easy to produce a valid range ballot. In other words, range voting is a lot less susceptible to ballot spoilage than IRV.

Think I'm confused? Check the data on actual observed rates of ballot spoilage errors.

6. Strategy and 2-party Domination: A lot of voters will, in an election like Bush v Gore v Nader 2000, exaggerate their good and bad opinions of Bush and Gore by artificially ranking them first and last, even if they truly feel the third-party candidate Nader is best or worst. They will do this in order to give their vote the "maximum possible impact" so it is not "wasted". Once they make this decision, in IRV, Nader automatically has to go in the middle slot, they have no choice about him. If all voters behave this way, then automatically the winner will be either Bush or Gore. Nader can never win an IRV election with this kind of strategic voters. (Unless it is an exact 3-way tie and the tie-break goes Nader's way, which'll never happen in reality.)

In view of this, third parties are silly to push IRV. They should advocate range. (Fact: The countries that used IRV as of 2002, namely Ireland, Australia, Fiji, and Malta, all are 2-party dominated in their IRV seats [and Malta throughout]. Here is a deeper look at how we know IRV causes 2-party domination.)

Analogously, in range voting, if the voters exaggerate and give Gore=99 and Bush=0 (or the reverse) in order to get maximum impact and not waste their vote, then they are still free to give Nader 99 or 0 or anything in between. Consequently, it would still be entirely possible for Nader to clearly win with range, and without need of any kind of tie, and even if every single voter is acting in this exaggerating way.

Think this kind of strategic thinking won't matter much? Wrong:

  1. The "National Election Study" showed that in 2000, among US voters who honestly liked Nader better than every other candidate, fewer than 1 in 10 actually voted for Nader. That was because of precisely this sort of strategic ploy – these voters did not wish to "waste their vote" and wanted "maximum impact" so they pretended either Bush or Gore was their favorite. (Same thing happened with voters whose true favorite was Buchanan.) In short, strategy has an enormous impact in the real world, and over 90% of voters act strategically and not honestly, given the chance. That is exactly why third parties always die out and we are stuck with 2-party domination.
  2. Here is a proof that this kind of insincere-exaggerating voter-strategy is strategically-optimal asymptotically 100% of the time in a mathematical model of a "large random electorate" with IRV voting.

7. Potential for nightmare ties and near-ties: Remember how Bush v Gore, Florida 2000, was officially decided by only 537 votes, and this caused a huge lawsuit and chad-examining crisis? Ties and near-ties are bad. In IRV there is potential for a tie or near-tie every single round. That makes the crisis-potential inherent in IRV much larger than it has to be. That also means that in IRV, every time there is a near-tie among two no-hope candidates, we have to wait, and wait, and wait, until we have the exact vote totals for the Flat-Earth candidate and for the Alien-Kidnapping candidate since every last absentee ballot has finally arrived... before we can finally decide which one to eliminate in the first round. Only then can we proceed to the second round. We may not find out the winner for a long time. The precise order in which the no-hopers are eliminated matters because it can affect the results of future rounds in a repeatedly amplifying manner.

Don't think this will happen? In the CA gubernatorial recall election of 2003,

    D. (Logan Darrow) Clements got 274 votes, beating Robert A. Dole's 273.
Then later on in the same election,
    Scott W. Davis got 382 votes, beating Daniel W. Richards's 381.
Then later on in the same election,
    Paul W. Vann got 452 and Michael Cheli 451 votes.
Then later on in the same election,
    Kelly P. Kimball got 582 and Mike McNeilly 581 votes.
Then later on in the same election,
    Christopher Ranken got 822 and Sharon Rushford 821 votes.
Have you had enough yet? Eventually Schwarzenegger won. Oh, was that what you wanted to know?

(Incidentally, imagine the horror if each voter were required to provide a preference ranking of all 135 candidates in this race. Meanwhile with range voting they just rank the ones they know about and leave the rest blank, or they could opt to "fill in all the rest with Z" where Z is a number they specify. Much less labor for the voter – and no worries about accidentally giving two candidates the same rank, thus invalidating your IRV vote. Also it is much more honest to rate most of them "unknown" i.e. "blank" – which honesty will lead to a far less distorted result – but that honesty is forbidden with IRV.)

Think the CA 2003 recall was a monster not likely to recur? Actually in New South Wales (Australia) in 1974 they had an IRV election with 73 candidates, and voters were required by law to (1) vote and (2) rank all 73 of them (none missed) – but they also were given the option of voting a pre-prepared straight-party ticket instead. Might that have produced some biases?

Think this all isn't really a problem because those elections were specifically chosen by me as nightmares? (And yes, they were.) OK, check our remarks below about typical elections.

Meanwhile, in range voting, the only thing that matters is the top scorer. Ties for 5th place, do not matter in the sense they do not lead to crises. Furthermore, because all votes are real numbers 0-99 rather than discrete and from a small set, exact ties are even less likely still. (And if the range were, say, 0-999 then they would be even less likely still.) Exact ties in range elections can thus be rendered extremely unlikely, while exact ties (or within 1) in IRV elections can be extremely likely. Which situation do you prefer?

8. Communication Needs & Nightmare Potential: Suppose a 1,000,000-voter N-candidate election is carried out at 1000 different polling locations, each with 1000 voters. In range voting, each location can then compute its own subtotal N-tuple and send it to the central agency, which then adds up the subtotals and announces the winner. That is very simple. That is a very small amount of communication (1000·N numbers), and all of it is one-way. Furthermore, if some location finds it made a mistake or forgot some votes, it can send a corrected subtotal, and the central agency can then easily correct the full total by doing far less work than everybody completely redoing everything.

But in IRV voting, we cannot do these things because IRV is not additive. There is no such thing as a "subtotal" in IRV. In IRV every single vote may have to be sent individually to the central agency (1,000,000·N numbers, i.e. 1000 times more communication). [Actually there are clever ways to reduce this, but it is still bad.] If the central agency then computes the winner, and then some location sends a correction, that may require redoing almost the whole computation over again. There could easily be 100 such corrections and so you'd have to redo everything 100 times. Combine this scenario with a near-tie and legal and extra-legal battle like in Bush-Gore Florida 2000 over the validity of every vote, and this adds up to a complete nightmare for the election administrators.

Don't think IRV nightmares really can happen? Here's what really happened when San Francisco adopted IRV:

9. Voter Expressivity: In range voting, voters can express the idea that they think 2 candidates are equal. In IRV, they cannot. (There are modifications of IRV which permit equalities, but they are much more complicated. They involve considering "every possible compatible ordering." In fact they are so complicated I doubt most voters will ever be able to fully describe how they work. Later note: Tom Ruen suggested a new simple IRV variant which permits ranking-equalities in votes: you just view K equally-top-ranked candidates as each having 1/K of a vote!)

A lot of voters want to just vote for one candidate, plurality-style. In range voting they can do that by voting (99,0,0,0,0,0). In IRV, they can't do it. (Actually in some variants of IRV – with "truncation" – they can. In many Australian elections, full orderings of all candidates are required or your vote is invalid. But in Ireland and Malta, just naming your first few choices and not the others is allowed.)

Range voters can express the idea they are ignorant about a candidate and want to leave the task of rating him to other, hopefully more knowledgeable voters. In IRV, they can't choose to do that. (Even in IRV with ballot "truncation," a voter simply cannot express the idea that Gandhi is best, Hitler is worst, and he is ignorant about Perot and Anderson.)

IRV voters who decide, in a 3-candidate election, to rank A top and B bottom, then have no choice about C – they have to middle-rank him and can in no way express their opinion of C. In range voting, they can.

If you think A>B>C>D>E, undoubtably some of your preferences are more intense than others. Range voters can express that. IRV voters cannot.

10. Bayesian Regret (For Statistics Nerds): Extensive computer simulations of millions of artificial "elections" by W.D.Smith show that range voting is the best single-winner voting system, among a large number compared by him (including IRV, Borda, Plurality, Condorcet, Eigenvector, etc.) in terms of a statistical yardstick called "Bayesian regret". This is true regardless of whether the voters act honestly or strategically, whether the number of candidates is 3,4, or 5, whether the number of voters is 5 or 200, whether various levels of "voter ignorance" are introduced, and finally regardless of which of several randomized "utility generators" are used to generate election scenarios.

Smith's papers on voting systems are available here as #56, 59, 76, 77, 78, 79, 80, 81, 82, 89, 90, 95, 96, 97,...

11.USA History Lesson: About 2 dozen US cities have over the years adopted IRV or related single-transferable-vote systems, the largest being New York City in 1936. However, almost all of those cities later decided to get rid of it. (As of 2000 apparently the only exception was Cambridge MA, which still uses PR-STV, which is a multwinner system which in the single-winner case reduces to IRV.) I guess IRV advocates should be asking themselves – why did these cities backslide? But oddly enough, they never seem to ask themselves that. In fact, they usually don't even know it.

12. Occasional Extremely Nasty and Illogical Results.
#voters their vote simplified
50 A>B>C>D>E A>B
51 B>A>C>D>E B
100 C>D>B>E>A C>D
53 D>E>C>B>A D
49 E>D>C>B>A E>D

In this 303-voter example by Mike Ossipoff, the centrist candidate C is the favorite of far more voters than anybody else, and not only would win a head-to-head contest with any single opponent (based on these votes) but in fact would do so by approximately a 2:1 margin. (Details: C beats A by 202 to 101; beats B by 202 to 101; D by 201 to 102; and E by 201 to 102.) So the "right" winner here clearly seems to be C, and almost every ranked-ballot voting system would indeed elect C. But not IRV. IRV elects D! That's because IRV only examines the preference relations in the "simplified" votes, and ignores the others.

(Incidentally, this example is highly realistic of the sort that arises in "one-dimensional politics" – it only requires that the favoriteness support taper off somewhat gradually with distance from the center – not a controversial assumption.)

You can make this example even sicker: [the reader may enjoy this easy exercise] construct a scenario in which the Condorcet Winner beats each other candidate pairwise by at least a 99:1 margin (!), and every voter ranks him top or second-top, but nevertheless he is eliminated in the very first round of IRV voting!

Here is another example illustrating several crazy IRV phenomena in a single election. (Source: S.J.Brams: The AMS Nomination Procedure Is Vulnerable to 'Truncation of Preferences,' Notices of the Amer. Math'l. Soc. 29,2 (Feb. 1982) 136-138 .)
#voters their vote
7 B>G>N>F
6 G>B>N>F
5 N>G>B>F
3 F>N>G>B

B wins this IRV election. (F, G, and N are eliminated, in that order.)

Illogical but true facts:

  1. This is despite the fact that G would win direct pairwise elections versus every opponent, e.g. G would beat B by 14 to 7.
  2. If the 3 voters in the last row had ranked F first but refused to say more, i.e. refused to provide their 2nd, 3rd, & 4th choices – then G would have won (which those voters prefer over B). This shows how IRV voters can be motivated to truncate, i.e. refuse to rank-order some of the candidates, thus defeating IRV's goal of gathering ordering information from the voters.
  3. This same election but with no F thus also illustrates a "no show paradox": the 3 voters in the last line then would be better off "not showing up" to cast their honest vote, since that way they would get a better election winner! (See that again in slo-mo)
  4. That no-F scenario also shows how the voters in the last line would be motivated to "betray" their true-favorite N (Nader) by dishonestly voting G>N>B to rank G (Gore) top; then G would win, whereas their honest vote causes both G and N to lose. This refutes the myth that IRV "cures" that "spoiler" problem with plurality voting.
  5. And: if these 3 voters instead had dishonestly voted B>F>N>G, then G would have won (which they'd prefer to the old winner B) despite the fact this just raised their opinion of B from last to first place! That is a severe example of "non-monotonicity" and "raise-to-top failure."

Meanwhile: range voting is monotonic, showing up to cast a range vote can never hurt you, "raise-to-top failure" never happens, "betraying" your favorite by voting him sub-top is never strategically useful, and range never seems to do anything especially illogical and hard to justify.

And here is a simple winner=loser IRV paradox also illustrating several other pathologies; another nasty example; and here is an explanation of why the whole underlying philosophy of IRV is self-contradictory.

13. IRV ignores many of the votes: One of the reasons for the bad behavior in the table two-above was that IRV only examines the "simplified" parts of the votes, and ignores the rest.

What would you say about a project-manager who made irrevocable decisions, having looked at only a tiny fraction of the available information? That's what IRV does when it eliminates candidates based only on first-place votes. In fact we can prove a theorem that IRV ignores asymptotically 100% of the information available in the ballots, see puzzle 34.

In contrast, Approval, RV, Condorcet, and Borda all take into account all information in all votes, ignoring none.

14. IRV can't be counted with a lot of existing voting equipment. Nor can Condorcet. However, Range Voting and Approval Voting can be counted with all existing voting equipment. That could make a big difference in success rate and monetary savings for voting-reformers trying to change the system.

15. Q. Do you really expect me to believe that non-monotonic IRV elections, "no-show paradox" nightmares, and near-tie IRV nightmares really are going to happen in real elections? Because I've never heard of an example. I bet examples are unbelievably rare and will never really occur.

A. "Yes," we really expect you to believe this, and "no," such examples are not unbelieveably rare.

In most IRV elections that have been held throughout history, the votes were simply never made public, preventing anybody from knowing about whatever non-monotonicity occurred. However, Debian has employed ranked-ballot elections for their leader each year since 1999 and published the votes in the most recent 5 of these 7 cases, i.e. 2001-2005. See this discussion of the Debian elections, including why they may be the only real and consequential moderately large ranked ballot elections with publicly available full vote sets in the entire world. (If you know of any others, please tell me about them!) Of these 5 elections, one exhibited an exact tie in an IRV round, and another exhibited a 1-off near-tie. The 2003 Debian election, with 4 candidates and over 450 voters, was a complete nightmare for IRV since it involved at least two different IRV near-ties, severe-nonmonotonicity examples, and no-show-paradox examples each!

We also recently ran a range-voting exit poll in the 2006 Texas governor election (5 candidates), and voila – our poll's IRV winner was Perry, but Strayhorn was preferred pairwise over every other candidate by our pollees. (Strayhorn was heavily victimized by IRV because a tremendous number of voter's "Strayhorn>Others" preference relations were ignored by IRV, which eliminated her in the second round.) Range Voting actually agreed with IRV in this case that Perry was the winner, but Range correctly gave it to Perry by only a very small margin over Strayhorn. (More voters said Strayhorn>Perry than said Perry>Strayhorn, but the Perry voters gave Perry higher scores, which was enough to make range voting elect Perry.) This exit poll was also interesting in this sense – a tremendous number of voters wanted to express no opinion about certain candidates. Those voters were not trying to rank those candidates last. They could have done so, but chose not to, and chose to explicitly circle "no opinion" on that ballot slot. IRV tells those voters: "Tough. No matter if you are totally ignorant and fully admit it – we demand that you express an opinion even though you do not want to." Is that likely to lead to good results?

Then, to really put the nail in IRV's (and plurality-with-delayed-runoff's) coffin, in the Peru election of 2006 Garcia won despite the fact that, pre-election polls indicated Lourdes Flores was pairwise-preferred over both him and Humala! (More examples, e.g. Chile 1970.) And Ireland 1990 was the only case, in all of Irish history, where a federal IRV election gave a different winner than plain-plurality voting – and it exhibited numerous pathologies including no-show and (in a modified scenario) non-monotonicity (if Lenihan voters had voted for his arch-rival Currie, then Lenihan would have won)! And the famous Lizard vs. Wizard Louisiana 1991 election was another example of non-monotonicity (if Duke voters had instead decide to vote for Edwards, that would have stopped Edwards from winning)! Indeed if you look at all the Louisiana governor elections one finds lots of pathologies. I also examined the most recent 2007 Australian IRV elections cycle (involving 150 IRV elections to the federal house). At least 9 exhibited pathologies.

Next question?

16. Q. OK, OK, I concede IRV is a worse voting system than Range Voting, but it has the Reform-Momentum right now. So you by promoting range voting are doing us all a disservice, and being strategically unwise by splitting voting-reform forces.

A. While that assertion may initially sound plausible, in fact a deeper understanding shows that it is exactly wrong: range is actually unifying reform forces that would otherwise remain divided.


17. Summary: Isn't the purpose of voting to provide information about your opinions? Why would you want to have a system (IRV) that forces you to express less information, when you can have one (Range) that permits you to express more?

Why would you want a more complicated system, with more nightmare potential, more tie-potential, longer delays, more chance of extremely goofy illogicality, and vastly larger communication needs (IRV) when you can avoid all that with Range?

Why would you want a system where voting for your favorite can actually hurt both him and you (IRV) when you could just have a monotonic system (Range) in which voting for your favorite never hurts him? Bottom line: A voter who feels Nader>Gore>Bush, by thus-voting Nader top, can cause both Nader and Gore to lose to Bush, under either plurality or IRV voting (whereas voting Gore top would have caused him to win). With range voting, voting Nader top cannot cause Gore to lose to Bush. Ever. Under any circumstances. Period. (Gore could still lose to Bush, but not as a result of a range-vote for Nader.)

Why would you want a system (IRV) that goes to a lot of trouble to collect votes, then ignores them?

Why would you want a system that can't be handled by many of today's voting machines (IRV) when you can have one that runs on every voting machine in the USA, right now (range)?

If you think 2-party domination is a bad thing and would like to see a greater diversity of parties and more voter choice, then why would you want IRV (in which, with strategically-exaggerating voters, 3rd parties have no chance, and which in Australia, Malta, and Ireland still led to 2-party domination) when you could have Range?

And why wouldn't you want the best system (among all commonly-proposed rivals), as measured by "Bayesian regret" (Range)??

(Duh!) You want range voting. Forget IRV voting.

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