From: Daniel Bishop <[EMAIL PROTECTED]>
Subject: [EM] Condorcet failure of Approval Voting (was Re: Dave
reply)
MIKE OSSIPOFF wrote:
...
[Dave] continued:
BUT the voter's actions, such as strategy, have to be based on what is practical for voters to learn and use (it is too easy for EM members to design strategies that sound nice in EM debates, while not practical for public election voters to either get the data or process it).
I reply:
Of course we're very aware of that. That's why our favorite Approval strategy to tell people is:
Vote for whom you would in Plurality, and for everyone whom you like better.
That's not complicated, but it's perfectly good for maximizing expectation in Approval, and for quicklyl homing in on the CW.
It's better than Plurality in this regard, but not perfect.
For example:
2: Bush>Perot>Clinton (approval vote = Bush) 1: Perot>Bush>Clinton (approval vote = Bush + Perot) 2: Clinton>Perot>Bush (approval vote = Clinton)
The approval vote totals are:
Bush: 3 Clinton: 2 Perot: 1
and so Bush wins. But Perot is the Condorcet winner!
Let's see how the homing in works in this example:
After this first election (above) with Bush winning, rational voters will put their approval cutoffs next to Bush on the side of Clinton (unless extreme individual utilities dictate otherwise, as in Bart's examples):
2 Bush 1 PerotBush 2 ClintonPerot,
so Bush and Perot tie for first the second time around.
Next time the cutoff is between Bush and Perot:
2 Bush 1 Perot 2 ClintonPerot
So Perot wins and Bush comes in second. From here on the cutoff stays between Bush and Perot, so the same approvals repeat until the set of candidates change or until the voter opinions of them change.
If these changes are gradual, approval will remain locked on to the current CW as long as there is one. If not, it will quickly (one or two cycles) lock on to the new CW.
Forest
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