Re: Range Voting - the simpler better alternative to Condorcet voting
The example you give is a perfect instance of the DH3 problem.
You have a population of voters whose true preferences are
Assuming the B supporters know that C is the front runner, some of
them might notice that if a handful of the B supporters do not cast
the "honest" ballot
but instead cast the ballot
then B could win. Especially if some of the A supporters do the
analogous thing. Woo hoo!
If a few of the C supporters are smart, they'll notice that, since C
is the front runner but B is the runner-up, they'd be wise to increase
C's slim margin of victory --- or perhaps preserve C's deserved
victory and prevent the unjust election of B by a few clever B
supporters --- by not casting the "honest" ballot
but instead casting
As you have doubtless noticed, if enough of the C and B supporters
exhibit this cleverness, then A will win.
The existence of an X option does not eliminate this problem. As you
note, if everyone ranks X second, the winner is again not any of the
top three "honest" options, but is instead X, even though every single
voter believes X a worse option than any of the three options A, B, C.
So having an X on the ballot doesn't help.
Barak A. Pearlmutter <email@example.com>
Hamilton Institute & Dept Comp Sci, NUI Maynooth, Co. Kildare, Ireland