[EM] Range > Condorcet (No idea who started this argument, sorry; I am Gregory Nisbet)

[Greg Nisbet]

On Wed, Oct 15, 2008 at 3:09 PM, Kristofer Munsterhjelm <
km-elmet at broadpark.no> wrote:

> Greg Nisbet wrote:
>
>> Reasons why Range is better and always will be.
>> I would like to end the truce.
>>  I'll be generous to the Condorcet camp and assume they suggest something
>> reasonable like RP, Schulze or River.
>>  Property Related:
>> favorite betrayal, participation and consistency.
>> Implications:
>> 1) It is always good to vote and it is always good to rate your favorite
>> candidate 100. The only Condorcet method to satisfy favorite betrayal is an
>> obscure variant of Minmax which I'll ignore because of its glaring flaws
>> (clone dependence *cough*)
>>
>
> MMPO's greatest flaw isn't clone dependence but indefensible Plurality
> failure. Consider this case (by Kevin Venzke):
>
> 9999 A > B = C
>   1 A = C > B
>   1 B = C > A
> 9999 B > A = C
>
> C wins.
>
> Also, MMPO isn't technically a Condorcet method, since it doesn't pass
> Condorcet. Here's another example, also by Venzke:
>
> 30 B>C=A
> 19 A=B>C
> 51 A=C>B
>
> The Condorcet Winner is C, but A wins in MMPO.
>
> If you like Range, this may be to your advantage, since you could say that
> instead of there being only one Condorcet method that satisfies FBC, there
> are none at all, or if there is, that this method must be very obscure
> indeed.
>

Before writing this, I knew there were about five versions of Minmax, all
possessing different properties. I think there is one version that satisfies
CW but not CLoser and various other weird combinations of properties such as
that. On the topic of whether there is a method that satisfies both
Condorcet and FBC.
http://osdir.com/ml/politics.election-methods/2002-11/msg00020.html claims
that any majority method will violate FBC. Think of it this way, any
majority method without equal rankings will always encourage betrayal so
that a compromise candidate will get the majoirty thereby sparing you
potenial loss. Anything with equal rankings cannot be a majority method b/c
simultaneous majorities will form and only one will win, hence allowing a
candidate with a "majority" to in fact lose. You are right. Until a few days
ago, I didn't know that much about MinMax, I just remembered hearing
something about a MinMax variation that obeyed FBC and later-no-harm. I
assumed it was a Condorcet method, incorrectly.

>
> 2) How does it make sense to be able to divide a region into two
>> constituencies each electing A if B is the actual winner? Condorcet methods
>> are not additive, this calls into question the actual meaning of being
>> elected by a Condorcet method.
>>
>
> I'd consider this problem similar to Simpson's paradox of the means, where
> one can have trends that go one way for the means of two separate groups,
> but where this trend reverses if the groups are aggregated. It's
> unintuitive, but doesn't invalidate the use of means in statistics.


ONE CRUCIAL DIFFERENCE: Simpsons paradox relies on comparing fractions with
different denominators to mask statistics. (I know it isn't necessarily
fractions, it is just different results compared against each other that are
weighted differently in the final average, but 'denominator' is easier to
say/explain than this sentence.)

Here is why that analogy fails:
We are not using different districts for each candidate.

Let's say I can divide country X two ways. Into Y1 and Y2 and into Z1 and Z2

The consistency criterion states that if I divide my country into Y1 and Y2
and both of them are a victory for candidate A and B wins this IS a
violation of the consistency criterion.

Now let's say that for candidate A I divide it into Y1 and Y2 and for
Candidate B I divide into Z1 and Z2. In addition to this division not making
sense, let's say A did manage to win twice (however that work work). B wins.
This DOES NOT constitute a violation of the consistency criterion. The
regions you are dividing the country into have exactly the same weight for
every single candidate.

The Simpson's paradox is impossible if I am always comparing data of like
weights.

>
>
> answers to potentital majority rule counterarguments:
>> 1) Range voting isn't a majority method.
>> answer: any majority can impose their will if they choose to exercise it.
>> concession: it is true that Condorcet methods solve the Burr Dilemma
>> fairly well because parties can simultaneously compete for majorities and
>> swap second place votes. Range Voting can at best allow voters to
>> differentiate between better and worse candidates by one point. So Range's
>> ability to emulate this behavior is competitive.
>>  I am not aware of another anti-range voting property one could claim that
>> is applicable to cardinal methods.
>>
>
> This is really a question of whether a candidate loved by 49% and
> considered kinda okay by 51% should win when compared to a candidate hated
> by the 49% and considered slightly better than the first by the 51%. A
> strict interpretation of the majority criterion says that the second
> candidate should win. The spirit of cardinal methods is that the first
> candidate should win, even though it's possible to make cardinal methods
> that pass strict Majority.
>
> Another argument against Range as a cardinal method might be that it
> suffers from compression incentive (with complete knowledge, the best
> strategy is to, for each candidate, either maximize or minimize the rating
> given). Something like, say, a Condorcet method where rating A 100 and B 20
> gives A>B 80 points would not be as susceptible to this (though it would
> probably be vulnerable to other strategies).
>

This is called Cardinal Condorcet or something like that and is detailed
here: http://fc.antioch.edu/~james_green-armytage/cwp13.htm

Compression is a problem. A makeshift attempt to avoid it might cause more
harm than good though. The fact of the matter is that Range at least allows
voters to express this.

>
> Computational Complexity (time):
>> Range O(c*v)
>> RP O(c^2*v+c^3) #c^2*v = constucting matrix; c^3 finding local maximum or
>> generating implications c^2 many times.
>>  Range Voting is more scalable.
>>
>
> I don't think this is much of a concern. With modern computers, voters will
> have trouble ranking all the candidates long before the computers that do
> the counting would exhaust CPU processing power, and that'll hold as long as
> the complexity is a reasonably sized polynomial.


Yes this is true. Computational complexity is just another random advantage
I can claim for Range Voting, so I will. It is more relevant in elections
with hand counts because the difficulties associated with a pairwise matrix
and whatnot do not have to be dealt with.

>
>
> Voter Experience:
>>  Range Voting (based on the existence of Amazon product ratings, youtube
>> video ratings, hotornot.com <http://hotornot.com>, the number of movies
>> rated out of stars.) I cannot find a single instance of Condorcet methods
>> besides elections in various open source communities. It doesn't qualify as
>> mainstream.
>>
>
> http://en.oreilly.com/oscon2008/public/schedule/detail/3230 mentions that
> MTV uses Schulze, internally. The French Wikipedia, as well as the Wikimedia
> Foundation in general, also uses Schulze. The Wikipedia article on the
> Schulze method also lists some other organizations that, while small, are
> not communities organized around open source.
>

Congratulations, it has some usage. Range Voting is still vastly for
familiar to most people.

>
>
> Understandability:
>>  Range Voting (I dare anyone to challenge me on this)
>>  Bayesian Regret:
>>  Range Voting (same comment)
>>
>
> Granted, though DSV methods based on Range do better (and may help with the
> compression incentive - I'm not sure, though). If they help sufficiently
> that one doesn't have to min-max in order to get the most voting power, it
> would keep Range from degrading to Approval and thus (absent other problems)
> fix the "Nader-Gore-Bush" problem (where Nader voters don't know whether
> they should approve Nader and Gore or just Nader).
>

Not quite sure what this has to do with the text it is in response to, but
whatever. The Nader Gore Bush problem is an issue, Range Voting doesn't use
any type of conditional vote (I don't think that Xs count as a conditional
vote), so this will, of course influence results. I did admit that Range
Voting was susceptible to the Burr Dilemma, but the ability to give subtlely
different votes can combat this.

>
>
> Ballot expressiveness:
>>      For elections with less than 100 candidates Range voting is more
>> expressive
>>    (If anyone thinks about advocating Condorcet for large numbers of
>> candidates, think again. Sorting candidates is an O(nlogn) problem. AND
>> that's only if you have O(logn) memory available, otherwise its O(n^2). In
>> short, you would need to be a genius or have large amounts of time on your
>> hands to do this properly. Range Voting does not have this problem)
>>
>
> Heap sort is n log n with constant space overhead. Also, there's nothing
> stopping you from using a rated ballot where the ratings are reduced to rank
> votes - perhaps with a cardinal strength backup to resolve ties. The
> computer analogy of this would be a radix sort - by invalidating an
> assumption (comparison sort is the only way to sort), you can break
> seemingly impenetrable barriers.


Rated rank ballots, eh? That isn't a bad idea. I would recommend an initial
score and a tiebreaker value.

>
>
>     Expressing apathy: Okay Condorceties, you got me. voter ignorance in
>> Schulze and RP can be expressed with (somewhat) less bias than Range
>> Votings- X marks. For those of you who don't believe me, consider the
>> following thought experiment: I rate Candidate A 70 (which I consider a good
>> score) and express apathy about Candidate B. I may think 70 is a damn good
>> score, but this might hurt my cause. I'll call this apathy-participation
>> failure. In contrast, apathy in Schulze and RP is strictly worse (to the
>> extent that participation failure allows) than support over ANY candidate.
>> Think of it this way, let ~ be the apathy comparison; (A > B) > (A ~ B) > (A
>> < B) in RP and Schulze. Now, the argument could be made for Range Voting
>> that (A = 100 B = 0) > (A = X B = 0) > (A = 0 B = 100), but this neglects
>> some important points. In Schulze and RP I am expressing apathy about A
>> SINGLE COMPARISON. This means I can leave the choice of, say, the two best
>> members of my party to the members of my party. I can still vote them
>> superior to all others without bothering to make an internal ranking.
>> Strictly speaking, Range Voting also somewhat has this property: I could
>> vote both 100, but the comparison is less explicit and less isolatable and
>> hence less expressive in this sense.
>>  e.g. A = 100, B = 80, C = X, D = 60, E = 0
>> If I like A more than B, like C less than B, but am apathetic about C vs D
>> I am out of luck. Depending on C's average so far, my ballot could influence
>> the result any number of ways. I need to anticipate in advance what the
>> average is LIKELY to be.
>>  So... bottom line on apathy.
>>  Bottom line:
>>  Schulze and RP: Precise expression on what exactly it is that you are
>> apathetic about in such a way that it doesn't spill over into other
>> comparisons.
>>  Range: You can express apathy, but you take your life in your hands. On
>> the other hand, your ballot is more expressive
>>
>
> Perhaps this could be improved by using Warren's "range plus no opinion"
> ballot. If you express no opinion, no score is added to the average, so your
> vote has absolutely no effect on the candidate in question, which would make
> sense if you truly have no opinion about that candidate.


Xs are range plus no opinion. I was using Warren's option in the previous
example. I was saying that rating someone a 60 and someone an X can turn out
any number of ways. I have no idea what the average will be in advance, so I
cannot tell what an X will do.

>
>
> Bottom Bottom line:
>> Range voting is better for expressiveness (taken as a whole)
>> Condorcet is better for isolating comparisons, but is less expressive with
>> each comparison.
>>  Most of these arguments favor Range Voting, there are two (and only two)
>> that do not:
>> 1) the result of apathy can be unpredicatble in RV
>> 2) a passive majority (one that doesn't exercise its majoritarian might)
>> is not assured victory.
>>  The rest of the arguments favor Range Voting. Range Voting is victorious.
>>
>
> What worries me with regards to RV / cardinal ratings (beyond the
> majoritarian situation, where I'm not certain if a method failing Majority
> is a good one) is the dynamics. A reasonable degradation chain might go like
> this: First range voters find out that they can maximize their power by
> voting approval-style. Then Range reduces to Approval. At that point, voters
> basically have to strategize in order to vote effectively. Some basic
> strategies (frontrunner plus, or the Approval A strategy) might be used, but
> the point is that voters shouldn't have to do this, and it appears that
> while approval (and Range) may seem simpler than Condorcet at the "front
> end", they lose at the "back end" as the voters have to calculate their
> ballots before voting.


Approval isn't a particularly bad method, so backsliding might be tolerable,
if it occurs at all. Anyway, all voting systems are susceptible to dishonest
voters. The Gibbard-Satterthwaite theorem guarantees this. Anyway, this
argument mentions nothing of the quality of the post-strategy winners.

>
>
>  If I overlooked something or made an error, please tell me; I'm just a
>> high school student.
>>
>
> Alright, I've tried to do so.


Gregory Nisbet
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