[EM] Range vs Condorcet Overview

[Greg Nisbet]

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.

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.

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

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. 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?

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

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.

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?

RP:

1)      This is a system I initially cited as an example of a reasonable
Condorcet method, it hasn't really been argued about.

Schulze:

1)      Same comment

River:

1)      Same comment

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.

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.

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.

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?

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. 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. 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.

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.

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.

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.

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.

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

There is one exception to this. Clone independence must be evaluated
separately because the simulation would not be especially good at
determining the impacts of strategic nomination.
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