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

[Kristofer Munsterhjelm]

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.

> 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.

> 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).

> 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.

> 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.

> 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).

> 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.

>      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.

> 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.

>  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.