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

[Kristofer Munsterhjelm]

David L Wetzell wrote:
>>>       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.

> 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.  

It's true that the center changes and political preferences aren't 
given. Yet artifacts regarding fuzziness of votes or voters have an 
impact on the actual outcome at the time of the election in contrast to 
the ideal outcome, had the voters been precise enough about their votes, 
and known their minds well enough.

Hence, any change that affects that analysis must happen while the 
election is going on. If the centers (and win regions for that matter) 
change between elections, then the image is still frozen at the time of 
the election, for that particular election.

To clarify a little, that's not precisely true. There might be 
interaction where the voters notice weird behavior and shy away from 
voting in such a way that could lead to the weird behavior in a sort of 
"better get the lesser evil than what amounts to a coin toss between who 
I really like and someone I despise". Parties, too, can react in that 
manner.

>>     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> .

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

Indirectly so, perhaps. For the Senate picture, the Senators appear to 
be clustered around their party's center. These party centers are some 
distance away from each other, which might in turn be due to Plurality 
voting, with the Democrat party sitting somewhat left of center and the 
Republican party somewhat right of center, each covering voters that are 
closer to themselves than to the other party.

I'm not sure why you don't get the convergence to center that would be 
predicted by the median voter theorem. Perhaps this is a result of 
internal party dynamics where, to attract membership, the parties have 
to look somewhat different from each other, while on the other hand, to 
attract voters, they should move closer to the center? I have no proof.

>>    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.

> 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.  

If the voters' votes are exact but the candidates are fuzzy, then you 
get a clear Yee diagram. The winner will thus be the "right" one 
according to the voters' beliefs about what the candidates are actually 
promising, and so methods with long and short borders should do about 
the same, all other things equal.

But if the votes are exact, then Condorcet compliance is exact, too. One 
could object that Condorcet compliance with regards to the candidates' 
claims rather than their actions aren't important. However, the same 
thing goes for every method, in that case: no method can do better than 
optimize the outcome according to the votes. At least Condorcet 
compliance will improve upon the case where the voters know how to 
separate vacuous speeches from real action, or knows how the candidates 
have fared in the past.

> 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.

Okay.

>>     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.

> 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.  

I'm saying that even by its own standards, the risks of IRV getting the 
wrong outcome due to a butterfly effect that originates in a single 
change of preference is greater than would be the case for a more well 
behaved method.

That is to say: if you had IRV in this corner, and you had another 
method that was similar to IRV but had compact win regions, then the 
latter would handle fuzzy votes better than the former.

As an extreme example of this, consider a method where candidate A 
always wins. This method never has a problem with fuzziness because it 
never crosses any borders (though it's otherwise quite awful). On the 
other hand, if you had a method where all the ballots were hashed 
together under a secure cryptographic hash, and then the candidate whose 
name's hash is closest to the result wins, then that method would be 
extremely sensitive to fuzziness because of the avalanche effect. That 
method would also be pretty awful (though amusingly enough, hard to 
manipulate).

Condorcet methods then happen (in my opinion) to give both good outcomes 
and reliable outcomes: the former because they pick the runoff winner if 
  a single candidate would win runoffs against every other candidate, 
and the latter because they have compact and straight win regions.

Some Condorcet methods might be less well behaved than others. BTR-IRV 
would inherit some of IRV's chaos whereas Schulze would not, for 
instance. The exact extent to which the former would be chaotic depends 
on how often there's a Condorcet winner in real elections.

> 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.

I haven't tested that particular combination of methods, so I couldn't 
say for sure. I imagine you mean here that you use STV to narrow down 
the field to three candidates, and then have IRV among these.

If I were to guess, though, I'd observe that STV has a similar chaos 
problem because of its elimination logic. Usually, to paraphrase 
Schneier, "many seats solve a lot of ills", but here you're going to 
pass the "parliament" directly to IRV, so it might be just as sensitive 
to initial conditions.

Perhaps I'll code up something to check later. For now I'll just say 
that these errors can happen in IRV with three candidates, too. The 
"Nonmonotonicity" and "Vote Splitting" Yee diagrams have only three 
candidates.

> 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...

OTOH, it could lead to a "two and a minor" situation. If the system acts 
as you'd expect when the third party is small, but not when it's large, 
that could form a barrier to the third party's growth. Instead of this 
barrier being at zero (like Plurality), that barrier would be somewhat 
higher, but it would still exist.

>>    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. 

> 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???

There are relatively few serious candidates *now*. If we generalize the 
"effective number of parties" measure to "effective number of 
candidates", where instead of shares of seats you have shares of votes, 
then the first round of the 2007 French Presidential election had a 
result as if there were 4.6 equally strong candidates -- and for all I 
know, there could have been strategy pushing in the direction of lesser 
evils in that particular election. After all, vote splitting led to a 
suboptimal outcome in 2002, and the voters might have decided not to 
fall into that particular trap again.

In 2002, the effective number of candidates for the French Presidential 
election's first round was 8.7. In comparison, for the United States, 
the number for the 2008 Presidential was 2.05, in 2004 it was 2.04, and 
in 1992, Perot brought it up to 2.8.

My point is that just because there are few serious candidates under the 
two-party pressure of Plurality, that does not mean that there will be 
only a few serious candidates under a better system. Patching a system 
that has real trouble with more than two so that it handles three (or 
somewhere between two and three) is looking one step ahead. Shouldn't we 
look further ahead so the method will stand the tests that may cause it 
to otherwise be discarded?

>>    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).

> 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...

That's right. Most good methods (those passing mutual majority not just 
by a contrived patch) would discard that kind of noise, and IRV is one 
of those. If a majority of the people vote

[Serious candidates in some order] > [noise candidates in other order]

then mutual majority will ensure the winner is one of the serious 
candidates. So to the extent there's noise, and the method passes mutual 
majority, only the noise among the serious candidates matter.

I don't think that 3-rank restricted IRV passes mutual majority (or for 
that matter, clone independence) when there are more than three 
candidates, because the majority could be forced to rank just a subset 
of the set they consider serious. See http://rangevoting.org/IRV3.html 
for an example of that.

As for whether 3-IRV prefixed by STV to get the count down to three 
would pass mutual majority, I don't know.

>>>       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.  

I'm just bringing it up as a context for threshold below. If your 
strategy is to use rules in the multi-winner domain to get a better 
single-winner method under the idea that they'd easier gain acceptance, 
that would hold for the concept of a threshold, too. (Though STV usually 
doesn't need a threshold...)

>>    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.

> 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.  

Any limitation is unfair, theoretically speaking. The advantage of a 
threshold vs a clean divide is that it would be more adaptive: it would 
retain all 4 candidates if they all got a fourth of the vote, but only 
two if the rest got below n%.

This might not matter as much, though, if you intend to use STV for the 
first stage -- except possibly from voters reacting to a viable 
candidate being excluded from the second round.

>>     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.

> 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.

As long as the clone problem isn't too severe, probably. I think using 
Borda elections would almost always go wrong, for instance. Its cloning 
problem is just too great.

>>>         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.

> 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.  

Does it work? See my other reply.

>>    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.

> 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.

You could argue the same way in favor of FPTP. You could say that 
eventually, an extrapolitical movement would get tired of the injustices 
that are being made and force the right kind of change, be it campaign 
finance reform, anti-gerrymandering rules, or something entirely different.

You seem to be saying that we only need enough reform to check the 
influence of money, then we can let the Occupiers fix the rest. But if 
we take that further, can't the Occupiers fix the imbalance in power due 
to money, too? It'll take a while, but that fits with what I said about 
periodic release in the other reply.