The example you give is a perfect instance of the DH3 problem. You have a population of voters whose true preferences are
31x A>C>B>X>D 32x B>C>A>X>D 37x C>B>A>X>D 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 B>C>A>X>D but instead cast the ballot B>A>C>X>D 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 C>B>A>X>D but instead casting C>A>B>X>D 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 PROTECTED]> Hamilton Institute & Dept Comp Sci, NUI Maynooth, Co. Kildare, Ireland http://www.bcl.hamilton.ie/~barak/ -- To UNSUBSCRIBE, email to [EMAIL PROTECTED] with a subject of "unsubscribe". Trouble? Contact [EMAIL PROTECTED]
