[EM] Single-winner method with strong winners (was: Poll for favorite single winner voting system with OpaVote)

[Juho Laatu]

On 19.10.2011, at 5.37, Kevin Venzke wrote:

> Hi Juho,
>  
> Firing off quick responses, sorry:
> 
> --- En date de : Lun 17.10.11, Juho Laatu <juho4880 at yahoo.co.uk> a écrit :
>>  
>>  
>> I think that your method is similar to my single contest method. I believe you determine
>> the critical pair of candidates in exactly the same way. However, while my method just
>> has an instant runoff between those two candidates, you are possibly letting in some
>> other candidates.
> 
> That is essential. Those "additional" candidates and extra round with some Condorcet method (= a good single winner method) are needed to make it work in the intended way (= according to the requirements in the requirements section).
> 
> 
>> I don't think there is a big problem on paper... It's quite likely that I tested in my sim
>> some methods very similar to your proposal, and didn't report on them just because I
>> found them to be .
> 
> 
> What would you expect to be the problems in this category of methods? Why are they less than the best?
>  
> I considered them (i.e. your type, bringing in more candidates) less than the best for
> my purposes at the time because there is more strategy in the rank component of
> the ballot.

Yes, two candidates means no strategy, three opens the possibility of strategy.

>  
> It may be, and I hope I once noted, that transferring all the strategy to the approval
> component, so that said strategy can't be given clear pejorative names, may just be
> a magic trick. But I'm fond of tricks if they're good.

The Condorcet tricks are well known. And yes, the approval part may introduce and hide problems (maybe even some that are linked to the Condorcet part).

>  
>  
> 
> Note also that the target of the method is somewhat different that the regular requirements for single winner methods (i.e. elect the strongest, not the compromise candidate). It is planned for a "few-party system" that should be an improved version of a plurality based "two-party system". But I guess strategic vulnerabilities should be treated pretty much the same way as with other methods.
> 
> 
>> What I found to be of interest, of course, is that very little strategy remained on the
>> ranking side of the method, since its main purpose was to resolve a two-way race.
>> Your method will compromise on that a bit...
> 
> 
> What do you mean with a two-way race? And what is the compromise?
>  
> Since my method only allows two finalists, there is only a two-way race to be
> decided using the rankings.
>  
> The compromise your method makes is that more strategy will be possible on the
> rank component.


True. But I couldn't avoid it because I wanted to allow all candidates that can be considered to be "strong" to take part and maybe become elected. My method is thus "Condorcet for strong candidates".

Maybe a good name for these methods could actually be "strong candidate Condorcet". That makes the "strong candidate" part a modular component of the name (Condorcet being the other modular component), and allows that expression to be used also elsewhere as needed. (It hides the use of approval, but that's just one way to measure what "strong" means.)

>  
>  
> 
> The idea is to pick the winner among those candidates that can be considered to be at least equal in strength with "what single candidates of traditional two leading parties would be". Those candidates were picked by comparing their strength (= their level of approval) to the strength of the members of the most liked "proportional" pair.
>  
>  
> Yes, I get that.
> 
>  
>> Do you have majority favorite covered...?
> 
> 
> What do you mean with this?
>  
> I'm simply asking whether your method satisfies majority favorite. My method has
> a rule tacked on to make sure it satisfies it. It's ugly and contrary to my stated
> goals for the method, but seems to be better than the alternative.

Majority favorite criterion: "If a majority (more than 50%) of voters consider candidate A to be the best choice, then A should win"

51: A > B > C >>
47: B > C >>
1: B >>
1: C >>

98: A > B > C >>
1: B >>
1: C >>

With these two vote sets A is a majority favorite, but pair < B, C > is most approved (100%) and A has less approvals than B or C. The method will elect B (A will not make it to the Condorcet round) and thus does not meet this criterion. This method thus emphasizes the meaning of approvals and picks a widely approved candidate rather than the one that is less approved but who is the favorite of majority.

The majority behind A could force A to be elected by not approving B and C. This would introduce a strategic interest in some cases. In the first set of votes almost all A supporters should however do so to change the result.

One could change the way how strength is measured. Since the original idea was to seek a method that would implement a few-party system that would improve the current plurality based two-party approach, allowing a candidate that has 51% or more approvals or first preferences could well be included in the Condorcet round (= sounds natural). I'll make some variants of the rules:

This is the original version (with ties of pairs covered explicitly):
Use a Condorcet method to elect the winner among the most approved candidate pair(s) (P) and those who have at least as many approvals as the least approved candidate in P.
- a pair of candidates is approved by a voter if she approves at least one of those candidates

Then a variant where also candidates that have 50% of the approvals of the most approved pair are strong:
Use a Condorcet method to elect the winner among the most approved candidate pair(s) (P) and those who have at least half of the approvals of one of the pairs in P or at least as many approvals as the least approved candidate in P.
- a pair of candidates is approved by a voter if she approves at least one of those candidates

And one more variant with a different approach to counting the approvals of the candidates:
Use a Condorcet method to elect the winner among the most approved candidate pair(s) (P) and those who have at least as many approvals as the least approved candidate in P when only votes that do not approve this candidate are considered.
- a pair of candidates is approved by a voter if she approves at least one of those candidates

These new variants should consider also A strong, and then elect A. The last version requires more information to be collected to be summable (approvals when compared to x).

Juho



>  
> Kevin
> ----
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