[EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?

[Juho Laatu]

On 18.6.2013, at 4.24, Benjamin Grant wrote:

> From: Jameson Quinn [mailto:jameson.quinn at gmail.com] 
> Sent: Monday, June 17, 2013 3:14 PM
> Subject: Re: Participation Criteria and Bucklin - perhaps they *can* work together after all?
>  
> Unfortunately, Bucklin systems fail that one too.
>  
> Hold on a sec. Let me think this through.  If we are using a Bucklin system, perhaps a strictly ranked one, and X is currently winning.  Adding a single ballot that has X ranked as the highest does two things: it changes the threshold, and it awards one more vote to X.  The only way it can hurt X – ie, cause X not to win, is if the harm in changing the threshold is greater than the benefit of getting another first place vote.
>  
> That’s the key to why Buckley keep failing Participation!!  I think I finally grasped the essential Participation flaw with Buckley!!
>  
> Each added ballot changes the threshold. Changing the threshold will either have NO effect, or it will change how “deep” we have to go to find a winner.
>  
> In this case, even if we know ALL the ballot we are adding have X at the top, adding even a single on if it changes the threshold enough will suddenly bring into your totals all the next place rankings for the existing ballots.  In other words, Buckley fails Participation because it is not a “smooth” curve, it is a fragile one that can leap and lurch, if you see what I am saying.
>  
> In its own way, Buckley is as unpredictable as IRV.  Both have fractal moments where a very small change can completely swamp the system and produce a very different result.  Any system as – what’s the right word, jagged? sensitive? fragile? is going to have one or more issues with appealing to our common sense, because each has a point in which a tiny change can cause a system wide shift.
>  
> Am I right?

Yes. This is a good approach to describing the problem.

I tend to categorize different methods also as heuristic and "more mathmatically exact" methods that try to describe the outcome or wanted features of the winner more directly. IRV is a good example of a method that is based on an algorithms that makes pretty much sense to us, but that is anyway just an approximation of what we want. Also Bucklin is based on a similar kind of algorithm that does pretty good job, but still is just a serial stepwise approximation based on guesses on what direction we want to take (and which candidates might be bad enough so that we can eliminate them already at this step).

>  
> I don’t know what this kind of trait is called, this oversensitivity, this ability to suddenly shift from condition One to Condition Two with no smooth transition points in between – but I think these kinds of systems will suffer from problems like these.
>  
> Now, for all I know ALL voting systems have this kind of issue – we’ll see.

I think out of the discussed methods at least Range does not really have this kind of randomness / fractal behaviour / oversensitivity / stepwise guesses based problems. It simply measures the quality of the candidates (=sum of utilities) and picks the best candidate as the winner. Range has other strategic problems in competitive environments, but that is due to strategic voting, not due to an oversensitive algorithm. Also FPTP is quite ok, if one assumes that all voters vote sincerely and we are supposed to elect the candidate that has highest first preference support.

According to my experience the most typical way to get an oversensitive method is to use some serial elimination based algorithm that makes serial (heuristic) guesses on which candidates are potential winners and which ones are not. Those methods can be good methods though, if the randomness caused by the algorithm causes less harm than the other properties of the method give us benefits.

If we want to avoid this kind of oversensitivity / randomness, one good approach is to simply define a (candidate quality) criterion that points out which one of the candiates is the best for our needs.

Juho


>  
> -Benn Grant
> eFix Computer Consulting
> benn at 4efix.com
> 603.283.6601
>  
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info

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