[EM] reply to Dan Bishop's "Condorcet Failure ..."

[Forest Simmons]

> From: Daniel Bishop <dbishop at neo.tamu.edu>
> 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