[EM] Range vs Condorcet Overview

[Kevin Venzke]

Hi Greg,

--- En date de : Dim 12.10.08, Greg Nisbet <gregory.nisbet at gmail.com> a écrit :
> De: Greg Nisbet <gregory.nisbet at gmail.com>
> Objet: [EM] Range vs Condorcet Overview
> À: election-methods at lists.electorama.com
> Date: Dimanche 12 Octobre 2008, 15h25
> I'll attempt to organize the Range Voting vs Condorcet
> debate somewhat.
> 
> >From what I can see, the following methods have been
> proposed/have some
> argument defending them/are reasonably good representatives
> of the groups
> being considered:
> 
> Range Voting:
> 
> There are two types of arguments against this system:
> 
> 1)      Ratings themselves are
> useless/unreasonable/illogical/not indicative
> of reality
> 
> 2)      Nothing survives post-strategy, so any benefit of
> Range Voting is
> lost anyway as it reverts to approval. The zero-info
> strategy is approval.

The zero-info strategy is the same as the zero-info Approval strategy.
I think that is the same as what you meant.

> 3)      Range Voting isn't a majority method.
> 
> My response typically is:
> 
> 1)      The meaning of the vote is substantiated by the
> system. People vote
> to achieve a particular outcome. With Range Voting, the
> different scores
> have an at-least partway predictable impact on the election
> (same as any
> other system). People can tell what is good for the
> candidates and by how
> much. Every reasonable voting system preserves this
> important feature. As a
> consequence of the votes influence result effect, the
> different scores now
> have meaning.

This is true, but it would be nice if the scores could also reflect
something more psychological, as rankings usually do.

> a.       The concept of comparing candidates along a single
> dimension is
> more intuitive and hence more meaningful to voters than
> making O(n^2) binary
> decisions

Rank ballots do this anyway; intransitive rankings are usually not
allowed on them.

> 2)      In order for this to be true, the utility gain from
> having one's
> favorite candidate in office must exceed the relative
> benefit of choosing
> between the competitors. To the extent which this is true
> in reality, the
> results will resemble approval.

Actually they will resemble FPP

> The real question here is:
> if each voter
> strongly prefers their favorite candidate set to the set of
> everyone else,
> would a non-approval style election really help?

I don't understand why you are discussing a "favorite candidate." You
don't have to settle on one favorite candidate.

> a.       Does zero-info in this case mean a) lack of info
> about of the
> behavior of other voters 

This.

> or b) (a) and lack of info about
> other candidates
> as well? Either way, if the problem can be ameliorated by
> adding info, then
> add info.

This is unrealistic unless you can reduce the number of voters to about
four.

> 3)      Any majority can impose its will.
> 
> a.       It is a majority method if you reject the ranked
> ballot conception
> of what a majority is. If you regard someone who voted
> Alice 60% and Bob
> 100% as belonging 60% to the Alice camp and 100% to the Bob
> camp, then Range
> Voting is a majority method. If you interpret the same data
> as meaning I
> support Bob, failing Bob, I support Alice… then it
> isn't.

Well, the latter is what the critics say. And of course they are not
being completely arbitrary in using that meaning.

Also "failing Bob, I support Alice" is not even allowed in Range. It
makes no effort to simulate conditional votes. If it did, it would
probably collect more information.

> b.      Is this behavior even a good thing? If the majority
> isn't exercising
> its influence and a compromise candidate is elected
> instead, do you really
> want a polarizing candidate or a compromise one?

The problem is that if you do not guarantee the majority that they will
get their favorite if they vote sincerely, then they will stop telling
you who their compromise choices are.

That is basically exactly why Range degenerates into Approval when voters
use rational strategy: Because there are no guarantees about how the
information they submit will be used, strategic voters are forced to
commit to their goals prior to voting, instead of letting the election
method handle things for them.

> MMPO:
> 
>                 Seeing as Electorama is down and I
> can't find an actual
> description of how this system works, I am stuck making
> generic arguments
> against it. If someone could explain it to me, that would
> be great. From
> what I can tell, it is a variant of Minmax that satisfies
> FBC, but neither
> Clone nor Condorcet.  My best guess is that it takes the
> biggest loss for
> each candidate, and picks the candidate with the smallest
> biggest loss. That
> is what I have gathered from its name,
> MinMaxPairwiseOpposition.

Yes, that is correct.
 
> If that is the case, then my responses to this are that the
> myopic view of
> what is your biggest loss has profound impacts on strategic
> nomination.
> Cloning becomes extremely powerful.  By nominating an
> additional candidate,
> my biggest loss won't go down if my party is even
> slightly organized, but my
> opponent's can. I'm not quite sure how this teaming
> incentive compares to,
> say, Borda, but I imagine it to be fairly substantial
> nonetheless.

No, you have it backwards. Cloning can only hurt you. If you clone
yourself, how on earth does that gather more votes against the opposition?
You have exactly the same number of votes on your side as before.

> Condorcet-Approval:
> 
>                 Ok, so I inadvertently described this one.
> I assumed it was
> more complicated than a simple two-step process.
> 
>                 My arguments against this system:
> 
> 1)      The Bayesian Regret Data
> http://rangevoting.org/StratHonMix.htmlsuggests the
> Condorcet winner
> is usually good for society and that Range
> selects the Condorcet winner more often than Condorcet
> efficient methods do.
> If one compares Condorcet-Approval to just Approval,
> Approval chose the
> utility-based Condorcet winner 655 more times. In fact, all
> of the
> Condorcet-efficient methods selected the true CW winner
> 10342 times. This
> suggests that obeying the nominal property can cause the
> system to elect
> fewer actual CWs.

That page still greatly annoys me as it quotes me and then does not
respond to the concern I described.

I can't remember what "true utility-based CW" means, but I suspect it's
a euphemism for something else.

I already explained why the simulations of strategic voters are unusable.
I also see in another post that you are already proposing a simulation 
that would be light years beyond what CRV has used.

> 2)      Let's pretend there are two ballots here, one
> ranked and one rated.
> Does the ranked ballot have any influence on the rated
> ballot or vice versa
> or are they separate? E.g. would it be possible for me to
> disapprove of the
> person I voted best in the Condorcet section or approve of
> the first and
> third best but not the second best?

I do not think that should be possible, for strategy reasons. It would
also be too complex to be a good thing to present to voters.

> ICA:
> 
> Hmm so this is ICA:
> 
> *3e. ICA
> <http://wiki.electorama.com/wiki/Improved_Condorcet_Approval>*:
> 
>    1. (Same as for MDDA.)
>    2. Again as in MDDA, a voter implicitly *approves* every
> candidate whom
>    he explicitly ranks.
>    3. Let v[a,b] signify the number of voters ranking
> candidate *a* above
>    candidate *b*, and let t[a,b] signify the number of
> voters ranking *a*and
>    *b* equally at the top of the ranking (possibly tied
> with other
>    candidates).
>    4. Define a set *S* of candidates, which contains every
> candidate *x* for
>    whom there is no other candidate *y* such that
> v[x,y]+t[x,y]<v[y,x].
>    5. If *S* is empty, then let *S* contain all the
> candidates.
>    6. Elect the candidate in *S* with the greatest approval
> 
> This description appears to suggest that the candidates
> that are not ranked
> are automatically disapproved of. I'll follow the link
> to variant forms of
> ICA, but just as a quick question: If you can't decide
> among candidates you
> disapprove of, how do you know if the optimal strategy is
> to approve of the
> candidate at the bottom or to disapprove of the candidate
> entirely.
> 
> Let me explain this dilemma:
> 
> A 1
> B 2
> C 3
> D X
> E X
> F X
> 
> That is my ballot so far. How do I know whether it is in my
> best interest to
> bottom-approve D (making it 4) or disapprove of it
> entirely.

Well, you never know for sure, in any method, what you must do. But you
must consider how you want your vote to be counted in the event of a
cycle. If you vote all but the last candidate, your vote almost will not
count, in that event.

You could simply use Approval strategy to decide who to rank. That's pretty
much what I would do.

> In my opinion
> this is worse than Range Voting's rate as zero or give
> intermediate score
> dilemma because you are comparing apples and oranges. 

Range doesn't even have that dilemma. It has the same dilemma that
Approval has.

> If my
> understanding of
> this method is correct, then if you want to have any impact
> at all on the D
> vs E or D vs F subelection, you must rank it 4.

Yes.

> The variant forms cannot be accessed to a SQL error. Great.
> 
> At last some good news, apparently the Google caches still
> work so
> Electorama can still be accessed yay!
> 
> Majority-Range:
> 
> This is one hybrid I suggested.
> 
> My description was vague; there are at least four possible
> ways to do this.
> 
> 1)      Include a super-99 option. It counts the same as 99
> for the range
> portion but is capable of being used to construct a
> majority. One Super-99
> is allowed
> 
> 2)      Same as (1) but multiple super-99s are allowed
> 
> 3)      You are given one supplementary vote; it is counted
> for the majority
> thing before anything.
> 
> 4)      Multiple supplementary votes.
> 
> The argument over this is whether it satisfies FBC or not.
> 2 and 4 clearly
> satisfy FBC, but not majority, in fact they turn the method
> into essentially
> approval. 1 and 3 satisfy majority, but not FBC. Here is
> why, it is
> conceivably in my best interest to give my supervote to a
> front runner
> compromise candidate rather than my true favorite.

I do not agree that 2 and 4 fail majority. If a majority vote for a
strict first preference, then that candidate will win. It is possible
that this does reduce the method to Approval, and that is in fact why
I am not a big fan of MCA or Bucklin.

> Cardinal Condorcet
> http://fc.antioch.edu/~james_green-armytage/cwp13.htm:
> 
> This method is another hybrid.
> 
> The advantages of this method are similar to both Range and
> Condorcet.
> 
> First of all it is a Condorcet efficient method, meaning
> the CW as reflected
> by the voters will be chosen. This specific tiebreaker uses
> the magnitude of
> comparisons in order to decide which to drop.
> 
> This method has the advantages of both worlds. The CW
> comparisons means that
> voters are never forced to abandon preferences regarding
> particular
> candidates for fear of diluting the power of the vote. It
> also means that
> voters get some sort of direction as to which comparisons
> they feel more
> strongly about. This method was never really attacked.
> Mentioning it was,
> but whatever.

I think I criticized once that the method seemed indecisive. I can't 
remember.

I also don't remember any demonstration (either way) that the rating
component really was protected from exaggeration.

> Framing the debate:
> 
> Debating the specific merits of Range Voting or Condorcet
> Method X is
> meaningless unless we can agree on some kind of metric.

Each merit is a metric. You need a metric for the merits ;)

> Debates about which properties are important don't
> really lead anywhere.
> There are a few we can probably agree upon. Let's see
> how often it satisfies
> those properties. I advocate moving away from a binary
> framework and
> focusing on how often certain properties are satisfied.

This is extremely difficult. Aside from the issue of having to simulate
strategy in an agreed-upon way, you have to decide how you are going
to generate the voters and the candidates. Will any nomination strategy
be present or are the candidates random?

Some simulations generate each voter independently, meaning virtually
none of the scenarios resemble a real world election.

> I like the Bayesian Regret metric because it's nice and
> quantifiable.
> Apparently there are some issues with previous simulations.
> I proposed a
> method for simulating strategy for any method about forty
> minutes ago.

I saw it. Did you have any thoughts on mine? I hoped to convey some of
the difficulties involved. Chances are you will come up with a sound idea,
but once implemented, there will be huge problems that can't simply be
patched over.

> I think Bayesian Regret is the way to settle this, once the
> simulation's
> lumps have been smoothed out.

Personally I would love to be able to score methods according to social
utility, and not have to doubt those scores.

Kevin Venzke