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

[Terry Bouricius]

Greg,

If one limits criteria to the few you selected, Range "looks" good. I will set aside for the moment the fundamental issue of whether mixing different individuals' different scoring standards can convey any real meaning ( the difference in candidate "quality" between candidates you score 8 and 10 may be ten times greater than the difference your neighbor assigns to candidates scored 2 and 10), and just speak about other criteria.

Personally, I agree that the Condorcet-winner criterion is not as significant as it sounds (we may not be looking at a single solid majority, but rather antagonistic divergent majorities). I think the mutual-majority criterion is more significant (and Range violates it).  However, I think the Condorcet-loser criterion is a show stopper. If a candidate would lose in every single one-on-one match up, then that candidate should not win. But such a Condorcet loser can indeed win under Range voting.

I also believe the later-no-harm criterion is of crucial importance, which Range fails. 

Range is more prone to strategic voting manipulation than either IRV or Condorcet (see analysis by James Green-Armytage in his doctoral paper  linked on this list a couple of months ago).

Range is also more prone to spoiler scenarios than IRV or Condorcet-compliant methods, because the score a voter assigns is dependent on what other candidates are, or are not in the race to compare with. 

Beyond the realm of standard criteria, I am also concerned about the effect different voting methods have on candidate campaign behavior, and resulting voter information. Some voting methods discourage candidates from revealing their true positions on controversial issues, if avoiding voter alienation is more crucial than earning first-preference support (this can be true of both Range and Condorcet).

Terry Bouricius

----- Original Message ----- 
  From: Greg Nisbet 
  To: election-methods at lists.electorama.com 
  Sent: Saturday, October 11, 2008 3:01 AM
  Subject: [EM] Range > Condorcet (No idea who started this argument, sorry;I am Gregory Nisbet)


  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*)
  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.

  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.

  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.

  Voter Experience:

  Range Voting (based on the existence of Amazon product ratings, youtube video ratings, 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.

  Understandability:

  Range Voting (I dare anyone to challenge me on this)

  Bayesian Regret:

  Range Voting (same comment)

  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)
       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

  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.

   If I overlooked something or made an error, please tell me; I'm just a high school student.


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