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

[Jameson Quinn]

2013/6/17 Benjamin Grant <benn at 4efix.com>

> *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.
>

I think you're close to right here, but not quite. In Bucklin, an
additional top-rank vote does not hurt X; it always helps their individual
median score and/or tiebreaker. It's just that that same ballot might pull
the median for some Y upwards even further, so that Y leapfrogs ahead of X.

In what circumstances would this happen? First, the ballot's rating for Y
must be above Y's median. And second, Y must have dramatically fewer
ratings at or just above its median than X does. Considering the
psychology/politics of such a situation, we have reason to believe that it
would be rare, and also it is arguable that Bucklin (not Buckley) is
actually doing the right thing here.

Why would it be rare? For some reason, Y is a polarizing candidate, with a
bimodal grade distribution. Voters seem to either love them or hate them,
with few falling in between. Such candidates certainly do exist in reality.
For instance, a candidate with a compelling ethnic- or class-based
narrative of whom to blame for the country's problems usually excites such
reactions, with little middle ground. But voters who support such
candidates tend to do so exclusively. For instance, in Balinski and
Laraki's study of the 2007 French election, right-wing candidate Le Pen
showed that kind of appeal; Le Pen got few middle rankings, and Le Pen
voters gave relatively few high rankings to other candidates. Thus, a
ballot which fails participation, giving a high-but-not-top rating to a Y
like Le Pen, but also giving an even higher rating to some other X, would
be the rarest kind of ballot.

And in the rare cases where this happened, it is actually arguably the
right thing to do. The extra ballot only shifts the result because it puts
Y over the 50% threshold of "high" versus "low" ratings (where "high/low"
means "above/below X's median"). That's not an arbitrary threshold. If Y
has >50% of the electorate who think they deserve a high rating, chances
are that they could win the election if all such voters were strategic.

> ****
>
> ** **
>
> 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.
>

This is, indeed, another way that Bucklin could fail participation: through
a ballot which gave below-median ratings to both X and Y, and thus caused X
to fail to meet a threshold. But it's the opposite of what you were
discussing above, which is a way that Bucklin fails mono-add-top.

>
>
****
>
> ** **
>
> 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.
>

Yes, your intuition is getting stronger, my young padawan. But there's
still something you're missing. As I argued above, there is sometimes a
good reason to leap or lurch when a 50% threshold is crossed. If the voting
system doesn't so lurch, the voters may take it upon themselves to do the
lurching strategically; and they, with imperfect knowledge, are almost
always likely to do a worse job at it than the voting system.

> ****
>
> ** **
>
> 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?
>

Not wrong; but as you can see, I find IRV's overreactions to be unjustified
and common, while I see Bucklin's as being justifiable and likely rare.
This is a contentious issue, though, and there are certainly those here who
disagree with me.

****
>
> ** **
>
> 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.
>

Well, it's true that no system can elect half-A-half-B. So discontinuity in
general is a feature of voting. But you're right that there is a real sense
in which a system like Score is "less discontinuous" than one like Bucklin.

Jameson
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