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

[Benjamin Grant]

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?

 

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.

 

-Benn Grant

eFix Computer Consulting

 <mailto:benn at 4efix.com> benn at 4efix.com

603.283.6601

 

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