Several recent editions of RISKS discuss some evidence of the dangers of IRV (Instant Runoff Voting) systems. Which is a shame since I hoped that they would offer a better approach that could help break the stranglehold of the two-party system. When they discuss paradoxical results, one is the situation such as if three people vote and the votes are:
A preferred over B B preferred over C C preferred over A
What is the solution to this that will result in the “right” person being elected? There are other paradoxes as well that can occur when people leave the race before it is decided too.
Well, I at least wanted to be able to have a “negative vote” where I could specify a lack of desire for a candidate. There may still be hope.
Runoff elections are expensive, which has led to various approaches to avoiding them by having voters express priorities among the various candidates. However, an important paper by Kenneth Arrow (RAND Corp, 1948) provides mathematical evidence that no voting system that ranks preferences among more than two candidates can guarantee logically fair nonparadoxical results.
A nice example of a “winner-turns-loser” paradox with Instant Runoff Voting (IRV) is given by William Poundstone, Why Elections Aren’t Fair (And What We Can Do About It), Hill & Wang, 2008, by considering hypothetically what might have happened in the 1991 Louisiana governor’s race if IRV had been used. I oversimplify slightly (and ignore the political positions that might have made this logical!):
34% of the voters were for Edwin Edwards, 32% for David Duke, 27% for Buddy Roemer. Under IRV, Roemer would have been eliminated, and his votes reallocated – which could have resulted in Edwards winning.
Suppose Edwards managed to have swung 6% of Duke’s voters to have switched to Edwards. Then Duke would have been eliminated, and the reallocation could have resulted in Roemer being the winner.
There’s a nice review article on Poundstone’s Gaming the Vote, and Spencer Overton’s Stealing Democracy: The New Politics of Voter Suppression, Norton, 2008, in *The Nation*, 2 Jun 2008, written by Peter C. Baker. https://www.thenation.com/doc/20080602/baker
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“In many real-world elections, there is a “Condorcet” winner, ie someone who is preferred by a majority of the electorate to every other candidate (it may be a different majority in each case). If there is such a winner, then electing them fulfills Arrow’s theorem. The problem is that in some elections, preferences are circular (ie A>B, B>C and C>A, where > represents ‘is preferred to’ rather than the usual ‘is greater than’). Where this occurs, no system can fulfill Arrow’s criteria - either the system will elect someone who would lose in a simple majority two candidate election (which fails Arrow’s dictatorship criterion) or IIA will be breached, as any proposed winner can be defeated by the withdrawal of one of his opponents.”