(Possible sidebar Graphic to add extra content & interest)

Note to ed.: you can if you want attribute this example to S.J.Brams: The AMS Nomination Procedure Is Vulnerable to 'Truncation of Preferences,' Notices of the Amer. Math'l. Soc. 29 (Feb. 1982) 136-138 ; or (since I have modified Brams' discussion considerably) you could leave it un-sourced, whichever you prefer. Also, you could include a "(see fig.)" at an appropriate point in the editorial.

Strange phenomena in Instant Runoff Voting

#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 would be better off "not showing up" to cast their honest vote, since that way they would get a better election winner!
  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 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.