Corrections to Vermont report's "section 16"

Misleading quote: "Another related confusion has to do with the notion that if low-ranking candidates were dropped in some different order, their ballot transfers could produce a different winner. This is not true."

Correction: That was a lie. Well, there is the problem that it is impossible under the rules of IRV to "drop candidates in a different order" since the IRV rules themselves specify the order except if there is a tie. So even talking about this is, technically, ludicrous. However, since the Vermont report insists on talking about it, let us consider the case where at some round there is an exact tie between two candidates being considered for elimination (both of whom have no hope of winning), and then consider the consequences of eliminating one rather than the other. Does it matter? Or will the other just be eliminated next round so it will not matter and either way we get the same winner at the end of the day?

The answer is, if does matter and the order in which you choose to eliminate the "no hopers" can affect the winner. Here is an example:

#voters their vote
120 A>?
150 B>A>?
100 C>B>?
100 D>C>?

In this 470-voter election, there is an exact tie between C and D for last place in the top-rank vote count. (It does not matter what preference happen inside the parts of the votes marked "?", since IRV ignores whatever those parts of the votes say.)

  1. Suppose we decide to eliminate D. Then 100 votes transfer to C, causing B to lose the next round, whereupon A wins the election 270 to 200 over C.
  2. But suppose we instead had decided to eliminate C. Then 100 votes transfer to B. Then D is eliminated, then B wins the election 250 to 120 over A (actually the 250 and 120 will have whatever amounts of D-votes transferred to them added on, but whatever those amounts are does not matter – B wins regardless.)

Not only that, but you can set up "amplifying cascade" scenarios where tiny changes in the votes for the wacko no-hope fringe candidates, end up having enormous effects on the vote counts for the final winners. Dummett in his book Voting Procedures (Oxford Univ. Press) calls this "chaos."

And ties can be quite common among the low-vote-getters so this is not at all an unrealistic scenario. For example 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?

Misleading quote: "Every voter has exactly the same clout with IRV."

Correction: Since "clout" is not formally defined, this sentence could be defended as not, strictly speaking, "false" but rather "meaningless." However this example election shows a scenario in which 102 voters say "D>C" while 201 voters say "C>D" but D wins the election!?! Why? Well, evidently some IRV voters are more equal than others... the 102 voters here get noticed but the 201 do not. More precisely, as is explained in the commentary to that election-example, IRV chooses to ignore parts of the votes but not other parts, causing D to beat C in the non-ignored parts of the votes.

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