[EM] More re: to Kristofer Munsterhjelm wrt Fuzzy Options.

[David L Wetzell]

>
> I wrote: it could also mean that political spaces are at best somewhat
>> useful constructs and that the "true" distribution is something that's
>> constantly being manipulated, not taken as given.   This understanding
>> makes me tend to be more middle-brow than most people on this list.
>>
>
> KM wrote:Well, yes, but people seem to vote at least in a somewhat spatial
> manner. Consider, for instance, Tideman's voter models and SVD/PCA fits
> like http://politics.beasts.org/ . While the results might have been
> colored by the polarizing effects of Plurality, I think it shows we can use
> political space as a way of visualizing voting behavior. If nothing else,
> it at least gets the point across in an intuitive manner - one can
> generalize later.
>
[endquote]

dlw: I agree it's a helpful way to simplify a lot of info and make things
more transparent.  This is why it's a useful construct.  But my bigger
point is that most rational choice models of elections take political
preferences as exogenous, or given.  This is not true in real life.
 Moreover, there are limits to the benefits from giving voters more and
more options.

This is part of why democracy is always an ongoing experiment and why
rational analysis of election rules cannot settle the matter of which
election rules ought to be used.

>
> KM wrote: SVD/PCA has also been applied to legislature records, where one
> would think the Plurality polarizing effect to be diminished. See, for
> instance, http://www.govtrack.us/**congress/spectrum.xpd<http://www.govtrack.us/congress/spectrum.xpd>.


[endquote]

Interesting, so the gap in the center is likely due to plurality voting???

>
>>
>>    KM wrote:However, fuzzy opinions can cause greater problems with IRV.
>>    Because IRV is sensitive to the order of eliminations, it doesn't
>>    just have the clean cell transitions of Condorcet; it can also have
>>    disconnected regions near the edges or in the middle of one of the
>>    regions. In essence, these are the same as the "island of other
>>    candidates" artifacts, but in two dimensions rather than one.
>>
>>
>> dlw wrote: I'm afraid you lost me there.
>>
>
> KM wrote: Okay, I'm going to go a bit more thoroughly through it. For the
> sake of the model, I'm going to assume a 2D opinion space with a normal
> distribution around a central point that depends on the society in
> question. These assumptions can be altered, but the difference between
> methods like most Condorcet methods and methods like IRV will persist, to
> my knowledge. I'll eplain what the difference is, but first, to get some
> things out of the way:
>
> If you have a spatial model with an attendant distribution for each point,
> then you have win regions. Inside each win region, the candidate assigned
> with that win region will win. For instance, if the center of opinion is
> solidly within the left-mainstream region, then the Democrat candidate will
> win. Similarly, if the center of opinion is solidly within the
> right-mainstream region, then the Republican candidate will win.
>
> Look at the "Equilateral" diagram on http://zesty.ca/voting/sim/ . There
> you can see that if the center of opinion is closer to, say, the red
> candidate than to the other two, then the red candidate wins, and it is the
> same with the green and blue candidates.
>
> Now, what effect does vote fuzziness have? The effect is that the election
> outcome is as if the voters were centered on a particular pixel, when in
> fact they were centered on a pixel some distance away. The distance between
> the two arise from noise.
>
> This is not a problem if the voters are solidly inside a given win region,
> because both points (the voters' true center as well as the center you'd
> infer from the votes alone) lie within the same win region. So vote
> fuzziness degrades the outcome only when the voters' true center is close
> to the border between two (or more) win regions, because then the noise can
> push the inferred center to the other side of the border, which could lead
> to another candidate being elected.
>
> So how often could this happen? Well, that depends on how many points of
> the voting space have another region close to it. If the regions are
> compact or the borders between straight, most of the outcomes will be
> solidly within a region and therefore will give the right result even if
> vote fuzziness adds noise. However, if the borders are long, zigzags all
> over the place, or have disconnected regions inside some other candidate's
> win region, these all increase the probability that the true center will be
> in one candidate's region, but the inferred center (from the votes, which
> is the only thing the method knows about) will be in another candidate's
> region.
>
> Finally, looking at Yee diagrams such as "Nonmonotonicity", "Square",
> "Shattered", and "Disjoint" on Ka-Ping Yee's page (whose link I've given
> above), or the IRV pictures on http://rangevoting.org/IEVS/**Pictures.html<http://rangevoting.org/IEVS/Pictures.html>shows that elimination methods in general and IRV in particular can have
> such zigzags and disjoint regions whereas Condorcet methods usually don't.
> Hence, IRV is more affected by vote fuzziness than are Condorcet methods,
> which was what I wanted to show.
>
> The difference then, as I said I would explain, is that IRV has longer
> borders and less compact win regions, which makes wrong-winner outcomes
> more likely if there is vote fuzziness. If vote fuzziness impacts Condorcet
> methods, it impacts IRV more.
>

[endquote]
dlw: What if the fuzziness comes from the candidates more so, as opposed to
from the voters? A candidate could take an FDR-style approach(as Obama did
in 2008) of avoiding specifics while campaigning so as to garner more
contributions from major intere$t$ and less pointed opposition from any of
them.    If the candidates positions are shifting at the same time as the
voters, it's easy to conjure up examples of static models with weird
results that aren't likely in real life.

I'm going to have to reflect on this some more.  For me, I don't trust
clear-cut contrasts based on models that treat what is oft quite muddled
and changing or in play as given.

>
> KM:If you take a step back, it's not that hard to understand. In IRV, a
> change in one of the elimination rounds can lead a different candidate to
> be eliminated, which in turn can lead a different candidate to be
> eliminated in the next turn, and a different candidate to be eliminated as
> a consequence of this, and so on. A single vote can change the outcome
> radically. IRV can be sensitive to initial conditions. On the other hand,
> if you look at something like Borda (not a good method, but it shows the
> concept clearly enough), a single vote will only alter the point sum of
> each candidate by a bounded amount. This might be enough to hand the
> victory to another candidate, but it is more well-behaved: the initial
> difference doesn't amplify into greater differences that amplify into
> greater differences in turn.

[endquote]

dlw: What I'm getting from you is that IRV or IRV3 makes the outcome more
unpredictable, where as a Condorcet method would reliably give a centrist
outcome.

But I think the import of the contrast depends on the number of
candidates... there tends to be 3 or 4 serious candidates in a
single-winner election, in large part due to the cost of running a campaign
and the relatively low chance of winning, especially with an already
somewhat crowded field.
As such, models that assume 7 "serious" candidates would tend to over-state
the diff between the two methods.  And there are ways to reduce the
difference by hybridization.  Wouldn't it make a diff if IRV3/AV3 were used
so that the number of candidates is reduced to three in a first stage that
treats any ranking of a candidate(with up to 3 rankings permitted) as an
approval vote?  Then, there'd only be one candidate eliminated by IRV.

So the race would be uncertain mainly when there are three competitive
candidates, which can be a good thing in getting voters to get interested
and vote more often...

>
>> dlw: Well, 1. IRV3 doesn't let folks rank all of the options and so it
>> hopefully has more quality control on which options are ranked.
>>
>
> KM: IRV with a few candidates will do better than IRV with many
> candidates, but with the number of candidates held the same, other methods
> will still be more well behaved.


[endquote]

dlw: But with fewer candidates, the diff between IRV or IRV3 and other
methods will be reduced further.  And so the fact there tends to be
relatively few serious candidates makes much ado about getting the right
single-winner election rule to be counter-productive for progress???


> KM:Also, you could consider the 3-rank limit (if only the number of
> rankings rather than candidates are limited) another form of noise. The
> noise is, in essence, the same as if every voter didn't know their later
> preferences and so truncated after three. (I'll note, though, that it's not
> unambiguously noisy: IRV restricted to one rank would simply be Plurality,
> and Plurality doesn't have the zigzag and disjointness of IRV).

[endquote]

dlw:If the noise is endogenous, since our bounded interest/rationality
leads us to give less attention to our less favorite candidates, then the
truncation of rankings could lower the over all amount of noise...

>
> dlw wrote: 2. by not always giving us the "center", it does permit
>> learning about the different viewpoints.  Remember, since I'm middle-brow,
>> I don't put as much significance on optimizing within the distribution of
>> political opinion space.
>>
>
> KM:You can get that with other methods, too. I think a good comparison
> would be to PR. In most countries that make use of proportional
> representation, the method also includes a threshold whose purpose is to
> keep sliver parties from gaining kingmaker power - e.g. a far right party
> only joining a coalition if the coalition agrees to kick out all the
> immigrants.
>

dlw: Aye, but I'm limiting us to single-winner elections right now(My zen
of electoral reform position is that what matters most is to balance
single-winner and multi-winner/PR elections in a system as a whole, with
the latter needed more so in "more local" elections that tend to rarely be
competitive with single-winner elections, regardless of which election rule
is used.), so as to ensure that there's an effective hierarchy.

>
> KM:In a similar manner, if the "always center" or "weak CW with no core
> support" objections are important and could break Condorcet, well, just
> institute a threshold. Say that a candidate who gets less than n% of the
> votes (or who is ranked on less than n% of the ballots) will not be counted.
>
[endquote]

dlw: Isn't that a little complicated and unfair?  If we eliminated all but
three candidates in a first stage then we could simplify things for public
consumption a lot more quickly.

>
> KM:If you want to be really sophisticated, you could probably use a
> cloneproof method for the threshold to avoid perverse incentives, but
> that's getting a bit too complex - all I'm saying is that if a weak center
> is a problem, there are ways around it.

[endquote]

>
> dlw: I think there are other ways to dispose of the clone problem that
> affects some election rules, which thereby doesn't have to be wired into
> the election rule used for the sake of simplicity.
>


>
>
>> dlw: 3. It introduces some uncertainty in the circulation of the elites,
>> which can give alternative viewpoints a chance to get a better hearing.
>>  When a new third party gains ground, it'll get a serious hearing and
>> hopefully the de facto center will be moved.
>>
> KM:All the good methods do that, and they do that by providing
> competition. On a level playing field, minor parties can pull major parties
> in their direction (but not unduly so) because the method is responsive -
> and in a predictable way - to shifts in votes and sentiment.
>
[endquote]
dlw:  Aye, and that's why I'm reluctant to try and pronounce any one
election rule as the best.  I support IRV, because it works and has been
successfully marketed in the US and will remain so, unless we get
perfectionistic about electoral reform.

>
> KM:Plurality does very badly here because strategic Plurality isn't
> responsive. IRV is better, but it can be unpredictable, as the simulations
> show. Yes, it's possible to weaken the effects of the unpredictable nature
> by making alliances (as you've suggested could be done in Burlington), but
> that imposes a further burden on the parties. Instead of requiring the
> parties to know when to cooperate and when to go at it alone, just have the
> voting method deal with it by shifting the center smoothly in the direction
> given by the people's preferences.
> [endquote]

dlw:Or we should take as a given that there's going to be such a give and
take among parties and not get carried away pushing for the (single-winner)
electoral rule that would adjudicate justly among them all.  In which case,
there'd be more opportunities to push for experimentation in mixing single
and multi-winner election rules so as to balance the need for hierarchy and
equality, change and continuity in how we work out our differences.

If we put more of our hopes for change in extra-political cultural
movements then nailing the right outcome with the best election rule
becomes less important.  This then makes it so we don't get caught up in
our own rivalry over election rule alternatives, which inevitably tends to
make it harder to change and keep changed the status quo use of
first-past-the-post.
dlw
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