[Election-Methods] Fwd: RE : Corrected "strategy in Condorcet" section, Chris

[Chris Benham]

Kevin Venzke wrote:

>I think a better method that would achieve everything you are  
>trying to do with your method (technically
>if not "psychologically") would be this:
>
>"1) Voters indicate one Favourite and also Approve as many  
>candidates as they like.
>
>2) Any candidate voted as favourite on 50% or more of the ballots  
>wins.
>
>3) Eliminate any candidate whose max. approval opposition score is  
>greater than 50%, unless that is all
>the candidates.  
>
>>>4) Of the remaining candidates, the two voted as favourite on the  
>>>most ballots go to the second round."
>>>
>>>This uses a more expressive ballot and mainly confines the split- 
>>>vote problem to the "top" of the ballot.
>>>So the normal recommended strategy in the 3 viable candidates  
>>>scenario would be vote the most preferred
>>>of the 3 as favourite, and approve all the candidates you prefer to  
>>>the least preferred of  the 3.
>>>
>>>What do you think of that?
>>>      
>>>
>
>I've had this exact thought... I agree that on paper this should be 
>similar in effect and better.
>
>I'm a little concerned about approving candidates strategically. If you
>have three factions, A B C, with A and B being the frontrunners and C
>being an oddball, if both the A and B supporters approve C in attempt
>to disqualify their opponent, and C supporters don't approve anyone else,
>then C automatically wins.
>
>40 A>C
>40 B>C
>20 C
>  
>

Kevin,

There are a lot of good methods that can't help the voters if they are 
so reckless as to vote an "oddball"
the 60-40, 60-40 CW!  But I see that your version (VFA) is "safer" 
because only one candidate can be
disqualified.

>>Maybe three years ago I suggested a rank-ballot, single-round, ranking-
>>    
>>
>implies-approval method in which the pairwise winner of FPW (first-
>preference winner) vs. AW (approval winner) contest was elected, except
>that the AW would be elected despite losing to the FPW if the FPW had
>a loss to a third candidate that was stronger than the FPW's win over
>the AW (measured according to WV). I called this method "NWL" for "...and
>has No Worse Losses."
>
>  
>
>>The point of the NWL rule was to avoid inappropriate FPW wins in a
>>    
>>
>scenario like this:
>
>  
>
>>7 A>B
>>5 B
>>6 C
>>2 D>C
>>    
>>
>
>  
>
>>The FPW is A and the AW is B; A defeats B pairwise, but an A win is
>>    
>>
>deemed inappropriate due to A's loss to C (strength 8 vs. strength 7).
>So NWL elects B.
>
>  
>
>>Anyway, it occurs to me that instead of the NWL rule you could have a
>>    
>>
>second round between these two candidates. The ballots say that A will
>beat B, but there was plenty of reason for other voters not to vote
>for B, even if they had a small preference. If they hold a second round
>between A and B, and the C and D>C voters truly do not care to express 
>a preference between them, then I'm fine with allowing A to be elected.
>

For a two-round method that is certainly something simple and  
"intuitive" that improves on standard
plurality TTR.  I assume the details are "in first round vote for one as 
favourite and approve as many
as you like. FPW wins with FP score of 50% or more. Otherwise qualifiers 
are FPW and most approved
alternative candidate. (Of course "favourite" also counts as "approved").

Of course in this method voters who are confidant that their favourite 
will be the FPW have a big incentive
to approve all the turkeys and conversely voters who are confidant that 
their favourite will be the AW might
have incentive to vote a turkey as their favourite.But I doubt that the 
risk of both qualifiers being turkeys is as
great in approval top-2, and all this attempted "turkey raising" might 
help minor parties survive. :)

For method that uses ranked ballots either in one round or in the first 
of two rounds, I prefer "elect the winner
of the pairwise comparison between the IRV (Strict) winner and the 
Approval winner".   That wouldn't have a
clone problem, supporters of weak candidates would have no "favourite 
betrayal" incentive, and it would meet
Majority for Solid Coalitions and Dominant Mutual Third.

(An alternative ballot-style would be to allow voters to give an 
approval cutoff, so they can rank among
unapproved candidates.)

>... a potentially useful set:
>"the set of candidates whose approval score is higher than  their  
>maximum approval opposition score".
>  
>
>I think it's pretty interesting... I'm having trouble thinking through
>these particular methods, but as a criterion it seems pretty good. I
>note that in the 7 5 8 plurality failure example, again B is required.
>
>It reminds me of "pairwise plurality" (at least, my conception of it),
>where a candidate can't win if their worst loss is stronger than their
>best win.
>  
>

Notice that in your NWL example

>7 A>B
>5 B
>6 C
>2 D>C
>
the set is {B}, the winner by many of our preferred methods.  I invite 
you to suggest a name for this set.



Chris Benham




-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20070820/1eedc67d/attachment-0003.htm>