[EM] Approval reducing to Plurality

[Juho]

Yes, at its best Approval could be "like condorcet with a slight  
utility bias". But there are some problem scenarios.

The simplest problem scenario is maybe one where the polls say  
something like
26: R1>R2>L
26: R2>R1>L
48: L>R1>R2 or L>R2>R1

R1 or R2 will probably be the Condorcet winner.

How should the R1 and R2 supporters vote? In order to make one of the  
right wing candidates win they should all approve both R1 and R2.

- if some R1 supporters are "smart" and don't approve R2, then their  
own favourite will win (but the R2 supporters could do the same, maybe  
to retaliate, maybe because they don't trust the R1 supporters)
- if all R1 and R2 supporters approve both candidates, then one of  
them will win, but the winner could not be the CW (=> random right  
wing candidate will win, depending on the few weird voters that  
approved only one of the right wing candidates)
- if more than few R1 and R2 supporters will not approve the other R  
candidate then L will win

This set-up is highly unstable. It could become stable enough if polls  
would point out one of the right wing candidates as clearly more  
popular than the other. But still the voters should be very  
disciplined and all the supporters of the weaker right wing candidate  
should systematically approve the other right wing candidate to make  
the Approval method work as expected (= right wing wins, CW wins).  
Some supporters of the stronger R candidate should not approve R2 to  
make the method work as expected.

It is quite probable that some R1 and R2 voters will bullet vote (and  
not to approve the other R candidate) just because that option is  
available to them. (The interest of L supporters to approve one of the  
Rs is not as high.) This means that the method is not clone proof in  
practice. Nomination of numerous candidates (by one party or one wing)  
means lower probability of winning the election. This means that some  
of the spoiler effect is still left.

Actually this spoiler effect may well change the result also when one  
of the R candidates is much more popular than the other (since all  
weaker R candidate supporters will not follow the "approve both"  
recommendation anyway).

I agree that some real life Approval elections would tell us better  
what will happen.

Juho




On Aug 31, 2010, at 11:03 PM, Raph Frank wrote:

> On Tue, Aug 31, 2010 at 11:08 AM, Juho <juho4880 at yahoo.co.uk> wrote:
>> The serious problems of Approval come into play only when there are  
>> more
>> than two potential winners. As long as T1 and T2 are called "T" (i.e.
>> "minor") things are fine.
>
> I disagree.  However, we don't really know the how the mechanics of
> approval will work out in practice.
>
> I think that it would allow a little utility weighting to come into
> it.  Voters who see two candidates as being almost identical would
> probably just approve both.
>
> It is like condorcet with a slight utility bias.