Re: Range Voting - the simpler better alternative to Condorcet voting

["Barak A. Pearlmutter" <barak@cs.nuim.ie>]

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 <barak@cs.nuim.ie>
 Hamilton Institute & Dept Comp Sci, NUI Maynooth, Co. Kildare, Ireland
 http://www.bcl.hamilton.ie/~barak/