(Possible sidebar Graphic to add extra content & interest)
Note to ed.:
you can if you want attribute this example to
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
B wins this IRV election. (F, G, and N are eliminated, in that order.)
Illogical but true facts:
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.
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.
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!
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.
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
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.