Rob Richie's "proof" of the flawed nature of range voting and superiority of IRV

Rob Richie of the Center for Voting and Democracy, a pro-IRV advocacy group (IRV="instant runoff voting") published a well-written essay which claimed to demonstrate in clear terms the superiority of IRV over all other common voting method proposals, including range voting. We critique it below. You also can read a local verbatim copy of Richie's original essay and another (perhaps more readable) critique by Lomax.

Richie centers everything around 3 criteria:

Criterion 1. "Does the system meet the common sense principle of majority rule? In an election with two candidates, the candidate preferred by a majority should always win."

Richie argues that range and approval fail criterion #1, which is technically true, but in practice false. (Richie "explains" how in a 2-candidate approval election, approval voting could fail to elect the majority winner because 99 voters might approve both candidates [although they all prefer the first candidate to the second], while one last voter votes for the second candidate only. Right.) In fact for practical purposes, every voting method ever seriously put forward passes criterion #1 and we would probably be very hard pressed to find any voters as stupid as Rob Richie postulates.

It is extremely rare for voters in approval voting elections to approve all candidates. For example of the 2587 voters in the French study, only 5 of them approved more than 67% of the candidates, and only 2 of them cast all-approval votes (we are amazed to find even those two). That indicates that this voter behavior is rarer than one in a thousand. In some rules-variants of approval voting, such as the method used by the United Nations to choose its Secretary General, all-approval votes are not permitted and would be rejected even if anybody tried to cast them. And actually, if you insist on such quibbling, then we point out that under IRV, voters can either rank zero candidates or cast a vote that top-ranks two or more candidates. Either way, under the very IRV rules advocated by Richie's own organization, your vote will have the same effect as an all-approval vote, i.e. none. Hence according to the strict letter of the law, IRV does not obey Richie's criterion 1 either. In the San Francisco IRV elections of 2004 these voter behaviors occurred 0.6% and 8.3% of the time, respectively, which in total is a rate approximately 100 times the all-approval voting rate for approval voting in the French study. Thus, Richie's argument, if taken seriously, would be a far greater indictment of IRV than approval voting!

In voting system design, it is an error to focus on a minor semantic non-problem and elevate it to the status of a "common sense principle" that must be passed come hell or high water. This is surely one of the most pathetic arguments "against" approval voting (and "proving" the "superiority" of IRV) that has ever been proffered. (And incidentally, range voting does obey a variant form of the majority criterion.) Thankfully we now move on now to Richie's

Criterion 2. "Does the system meet the common sense principle of requiring a minimum level of core support? A winner should be at least one voter's first choice."

Criterion #2 is a little more interesting. All Condorcet methods, as well as range and approval, fail it. However,

  1. I don't actually see why criterion #2 is desirable at all. With an electorate consisting of two mutually hostile factions, the best winner could be a neutral, "compromise" candidate who is no one's first choice but is everyone's second choice. E.g. in a hypothetical 1930s election between Adolf Hitler (supported by raging German patriots) versus Josef Stalin (supported by raging communist Russians), and perhaps throw in Mussolini (supported by raging Italian fascists) – all versus a comparatively uninspiring and unpopular figure such as, say, Herbert Hoover, who would you prefer to win? Are you sure you want to insist on principle that Hoover not be permitted to win, because of his lack of a dedicated "core" of die-hard, maniacal supporters? Or would you argue that Hoover might be preferred over Stalin by the Hitlerites (and vice versa) and all in all would be a better choice? I do not see why "common sense" demands Richie's criterion 2 at all. In fact, I think the opposite – common sense requires us to insist that Richie's criterion 2 should not be demanded.
  2. To say the same thing again:
    #voters Their Vote
    35 A > B > D > C
    33 C > B > A > D
    32 D > B > C > A
    In this situation, B seems clearly the "best winner" since changing the winner from B to anybody else will make at least a 65% supermajority (larger than the greatest "landslide" in US presidential election history) less happy. But Richie insists, as a matter of principle, that B must not win! (Instead, IRV awards the victory to C. Make sense to you?)
  3. Also, in practice I think violations of this criterion in large elections will be extremely rare. E.g. in every election where candidates get to vote for themselves, I think we can count on everybody being at least one voter's first choice! If so, then Richie's criterion #2 would be satisfied in practice by every voting method.
  4. IRV, in a 100,000-voter 18-candidate election, can unambiguously elect a candidate who has only two top-rank votes. So Richie in using one vote as the threshold in his criterion to "distinguish" between IRV and Condorcet methods, really is caring about two versus one or zero, i.e. the precise value of this number is utterly crucial for him.
  5. Here's a simple example of an election where C beats every rival pairwise by 8-to-5 ratio, and M has the second-least amount of core support (in particular M has less core support than C), but IRV says M is the winner. (Another.)

Again, Richie takes a minor semantic non-problem, which essentially every voting system obeys in practice (and which probably is not even abstractly desirable) and elevates it to the status of a "common sense principle" that must be passed to the strict letter of the law come hell or high water.

Criterion 3. "Does the system meet the common sense principle of rewards for sincere voting? A voter should not likely be punished for voting sincerely under the system's rules."

Criterion #3 is vaguely phrased ("not likely") in order to allow IRV allegedly to "pass" it. (It sadly seems obvious Richie began with IRV and engineered his criteria to make IRV look best, rather than beginning with criteria and then choosing methods to meet those criteria.) It can be argued IRV fails it – depends on what is meant by "not likely" – but actually every deterministic non-dictatorial rank-order-based voting method fails it if the subjective term "not likely" is replaced by the objective word "never." (That's a famous theorem of Gibbard and Satterthwaite.) Richie certainly seems to have an amazing talent for picking criteria satisfied by every or by no voting method as a means of "discriminating" among them.

Richie then cites Tideman to the effect that IRV is not very vulnerable to strategy, but Tideman's "vulnerability to strategy" measure is unfortunately extremely misleading and misguided. (E.g. it ignores the strengths of effects caused by strategic voting, erroneously regarding all effects as equal in severity; it ignores the fact that many different voter factions all would simultaneously strategize, instead pretending that just one does so; and it ignores the fact that strategic voters will be working with incomplete information about the other voters. All that adds up to a severely distorted measure of "strategic vulnerability." And indeed, Tideman's measure claims approval voting is actually "substantially worse" than plurality voting, whereas as far as I can tell every other worker in the field has unanimously concluded otherwise and indeed approval voting was designed to exhibit low vulnerability to strategy. If one runs computer simulations now taking those ignored factors into account, range voting comes out with far superior Bayesian regret than both IRV and Condorcet methods whether the voters are honest or strategic or any mixture. Unfortunately Tideman was unaware of our computer simulations at the time he wrote his book.)

Also, while citing Tideman so admiringly, Richie conveniently forgets to mention that the very Tideman book he cited (summary table page 238), concludes as its bottom line that IRV is an "unsupportable" voting method (provided it is "feasible" to compute a table of pairwise preference margins, which it is). Tideman also concluded Approval and Range are "unsupportable"...

And this quote from Nagel that Richie also cites so admiringly to demonstrate how he is "grounded" in scholarship (Richie actually gave the wrong page numbers when citing Nagel's paper, for the correct cite see this)

[Exploitation of non-monotonicity] is indeed possible under [IRV], but the conditions it requires are extraordinarily restrictive. Note that the kind of strategic voting required to exploit non-monotonicity under [IRV] demands far more of voters (and organizers) than its counterpart under approval voting. The approval voter who truncates nevertheless votes quite sincerely for his first choice, whereas the [IRV] manipulator must put her last choice first.
is also somewhere between very misleading and flat-out false. First of all, Richie misleadingly acts as though the only problem with IRV is non-monotonicity and voters seeking to strategically exploit it. Actually the most major problem with IRV strategic voters is "favorite betrayal" where it is strategically better to vote to for your non-favorite rather than your favorite. A simple computer examination of all possible 3-candidate N-voter elections (N large) – which note is not at all "restrictive"! – shows that a "favorite betrayal scenario" happens under IRV in 19.6% of them.

IRV's admission of favorite-betrayal scenarios, and commonly, is a clear way that IRV actually does not "satisfy" Richie's criterion 3. (Meanwhile: By theorem, Range voting never suffers from either favorite-betrayal or non-monotonicity.)

Second, such strategic voting under IRV does not require any "organization" whatsoever. You simply vote for your preferred major-party candidate top, and your unpreferred one bottom, thus dishonestly not voting any third-party candidate top, even if they are your true favorite. This is a very simple strategy, it works, and it explains why every IRV country has been massively 2-party dominated in all IRV seats. Because 19.6% is a lot larger than the historical chances of third-party candidates winning IRV seats (well below 1%), this strategy is well justified. Finally, it is completely false (as we just showed) to say that the IRV manipulator "must put her last choice first" either when it comes to favorite betrayal (see this example or this) or when it comes to non-monotonicity, e.g. consider this 17-voter example:

#voters Their Vote
8 B>A>C
5 C>B>A
4 A>C>B

If two of the B>A>C voters change their vote to A>B>C, that causes their true-favorite B to win under IRV. (If they vote honestly ranking B top as is, then their most-hated candidate, C, wins.) That's an example of "non-monotonicity." Note that this disproves Richie's false and out of context Nagel quote since nobody puts their "last choice first"; all put their last choice last. Another example of that.

Richie's counter to this criticism (and our counter-counter)

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