[EM] Approval reducing to Plurality

[Juho]

Yes, polls that are arranged before the actual election is an  
interesting approach for Approval since Approval may fail badly if  
there are more than two potential winners in the actual election.  
Particularly this could offer some help in the Burr dilemma set-up  
where e.g. the right wing has two equally strong candidates.   
(Approval may perform better when there are three candidates tied in a  
triangle.)

In the Burr dilemma case one poll might say that R1 is ahead of R2,  
and another poll says that R2 is ahead of R1. Lets assume that right  
wing and left wing have about equal support. In this situation one of  
the right wing candidates can win (=beat the left wing candidate) only  
if close to all supporters of the other right wing candidate approve  
also this candidate. If the right wing candidates remain tied in the  
minds of the voters at the election day, there will be strategic  
problems since both R1 and R2 supporters have an incentive to betray  
the other right wing candidate. It is much better if the fight will be  
fought before the actual election day, since then the right wing  
voters know that the losing group is supposed to approve both right  
wing candidates in order to avoid losing the race to the left wing  
candidate ((in real life there could however still be many enough  
voters who don't understand this, and right wing would lose as a  
result of having two candidates)). With some luck the polls will  
stabilize and systematically point out one of the right wing  
candidates as the dominating candidate. The results of the election  
may also indicate how close the weaker right wing candidate was to the  
stronger one (one could expect about 50% of the voters to approve the  
stronger right wing candidate and maybe 20%-45% to approve the weaker  
one).

The problems are however not quite over yet. One potential problem is  
strategic answers in the polls. It would make strategic sense to R1  
supporters to start the polls by not showing any support to R2. That  
could make R1 look better than R2. And that could lead to a game with  
the polls, both groups trying to present themselves as the stronger  
group.

The good point here is that active polling before the election reduces  
some of the problems of Approval and could make it more usable. It is  
difficult to say how well the problems would be eliminated in real  
life. But certainly this approach makes Approval better.

Juho



On Aug 29, 2010, at 10:58 PM, Raph Frank wrote:

> On Sun, Aug 29, 2010 at 5:31 PM, Kevin Venzke <stepjak at yahoo.fr>  
> wrote:
>> Will Approval just turn into Plurality? Not really, because in  
>> Plurality
>> once you have two frontrunners, this pretty much can't change:  
>> There's
>> no way for a third candidate to break in. In Approval it can: If the
>> third candidate can win, the polls should reveal this prior to the
>> election, changing who the frontrunners are perceived to be.
>
> Exactly.  If people fill in the poll with the strategy of "Approve all
> candidates you prefer to the expected winner", then a condorcet winner
> will be approved by more than half of the voters.
>
> This will push that candidate into the top-2.
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