[EM] Re : Condorcet vs Range (Greg Nisbet)

[Kevin Venzke]

Hi Greg,

--- En date de : Sam 11.10.08, Greg Nisbet <gregory.nisbet at gmail.com> a écrit :
>> I suggest Condorcet//Approval with ranking among
>> disapproved candidates
>> disallowed. Though apparently you are adamant about
>> Clone-Winner
>> compliance.
> 
> I merely said that of the methods I am aware of, Schulze,
> River, and RP are
> the best. Condorcet-Approval certainly sounds interesting
> though. I heard
> about another hybrid today that also looks promising. Elect
> the Condorcet
> winner if there is one otherwise default to approval.

That is Condorcet//Approval.

> I think in practice
> this would mostly result in the Approval winner being
> elected anyway.

I suspect that is a minority opinion (that there would *typically* be
Condorcet cycles), unless you just mean that either the Approval winner
would win or else the CW would win and probably simultaneously be the
Approval winner.

> I admit it. I completely overlooked Range-Condorcet hybrids.
> This one,
> http://fc.antioch.edu/~james_green-armytage/cwp13.htm, also
> looks
> interesting by the way. My response to these is largely the
> Bayesian Regret
> argument. As near as I can tell, this preliminary procedure
> will reduce
> overall Bayesian Regret scores.

But that is a superficial analysis that assumes sincerity. You may also
consider that if the preliminary procedure were not there, voters would
not submit the ratings as sincerely.

>> I'm not entirely sure when the ranking of the
>> disapproved candidates would
>> throw out the approval winner. (Which logically it must if
>> it is to be
>> different.) I'll look for it though.

The problem is that if you can rank among disapproved candidates, you
can prevent the would-be CW from winning as CW, and force the result to
be decided based on Approval, without you then having to support the
candidate that you falsely claimed was better than the CW.

>> MMPO fails clone independence rarely; the difficulty with
>> it is its
>> potential to give absurd results failing Woodall's
>> Plurality criterion
>> (is how I would describe it).
> 
> Wouldn't
> MMPO<http://www.mail-archive.com/election-methods-electorama.com@electorama.com/msg06261.html>be
> susceptible to the other arguments as well? At first
> glance, it does
> appear promising.

It would be susceptible. It does not even satisfy Condorcet for one thing.

But Clone-Winner failures under MMPO are not to be expected often,
because it is not intuitive to suppose that when you clone a winner
into three candidates, the greatest opposition to each will come not 
from a rival faction but from each other.

>> > 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?
> 
> I would say it doesn't matter. I'd also say that in
> reality, Range isn't
> better, even if technically it doesn't seem to have
> this problem. So
> it's purely a theoretical concern.
> 
> It may be a theoretical concern, but saying it doesn't
> matter really isn't a
> response. I was wondering how a method failing this could
> be considered to
> truly represent the will of the people when considering
> them as several
> independent groups would lead to unanimous support of a
> different candidate.
> I did not link this argument back to the real world of
> voting; I
> specifically asked for a theoretical justification.

I guess what you are really asking for is an argument that "the will of
the people" is itself not additive and need not obey consistency.

The theoretical justification would have to go directly into the issue 
of cyclical preferences in the population, but I guess you know that.

The reason I'm not very inclined to discuss the theory is that it doesn't
have to matter. I can agree that Bayesian regret is the correct way to 
measure methods, and simultaneously reject additive measures as 
ineffective at minimizing it.

If we have to hold archery contests instead of elections to minimize
Bayesian regret (or whatever the measure is) I basically would recommend
that, and not spend much time discussing why the archery champion is
theoretically the will of the people.

>> > Condorcet methods
>> > are not additive, this calls into question the actual
>> > meaning of being
>> > elected by a Condorcet method.
> 
>> It would, if one did not know what the meaning is. Of
>> course the CW is
>> not selected on some additive reasoning.
> 
> This is my argument. Please defend the concept of a CW
> given its
> non-additive properties.

CW is a majoritarian concept. There are practical arguments in favor of
majoritarianism (dealing with stability of the result, and reduction of
the need for strategy) but the argument on principle, it seems to me, is
majority rule.

You must realize how easy it would be for us to change positions, with me
asking you to defend the concept of Range given its counter-majoritarian
properties. You could properly respond that it isn't clear that such
properties call for a defense.

>> > 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.
> 
>> The reason this is not a satisfying answer is that when a
>> method is a
>> "majority method" this means that the majority
>> does not have to get
>> together before the election, identify themselves as being
>> a majority,
>> and settle on a singular goal.
>> 
>> Otherwise almost every method is a "majority
>> method" in your sense. Plurality is one too.
> 
> First of all, I wasn't suggesting this as an
> alternative definition of the
> majority criterion. Also, in order for a method to escape
> your criticism it
> would have to satisfy FBC and majority at the same time so
> that sincere
> majorities can be identified and rewarded. Please identify
> a method that
> does both of these.

Well, MMPO and my improved C//A method (ICA) can do this.

But I should clarify that I don't propose that a method should be able 
to identify majorities that don't vote sincerely.

>> My point is that a strategic majority will always be
>> rewarded. The majority
>> does not have to organize itself before the election; they
>> just have to
>> individually be unwilling to compromise.

Yes but the criticism is that a sincere majority is not always rewarded.
The response that the majority can prevail by not being sincere, is not
very reassuring given the criticism.

> Another response to this argument:
> 
> What happens if you combine the majority criterion with
> Range Voting. Have
> an initial step to check for a majority winner and then
> proceed with normal
> Range Voting if a majority winner is not found. Presumably
> this would answer
> the argument. Well, not really. It would encourage people
> to vote for a
> compromise candidate in the hopes of guaranteeing them a
> majority and thus
> violate FBC by forcing them to shove their true favorite
> into second place.
> Compliance with the majority criterion would destroy FBC
> compliance. (you
> might be able to make it so that the single vote for a
> candidate to attempt
> to get a majority were separate from the range ballot, but
> this would again violate FBC)

MajFP//Range would satisfy Majority; it could also satisfy FBC as long 
as you are not requiring a strict majority favorite in order to win on 
that basis.

This method is extremely similar to MCA or Bucklin.

Even if it doesn't satisfy FBC, it is still ok according to my criticism,
because if there is a strict majority first preference, the method will
elect this option (irrespective of whether this majority is sincere or
not, even though we only are concerned with the sincere cases).

This is how I define FBC failure: Lowering a candidate tied for the
first preference, will cause one of those preferences to be elected,
when otherwise the winner is a lower candidate.

>> > Understandability:
>> >
>> > Range Voting (I dare anyone to challenge me on this)
>> 
>> Jobst criticizes that the numbers are meaningless. I would
>> not criticize
>> this, except that it does not even seem to be possible to
>> use strategy
>> to come up with a practical meaning of the intermediate
>> ratings.
>> 
>> I could imagine someone perhaps complaining that the
>> meaning of rankings
>> is not clear. (Perhaps they believe real preference
>> rankings are not always
>> transitive.) But when you know what the rankings are
>> supposed to do and
>> when and how to use them effectively under whatever method,
>> you can still
>> figure out the practical meaning of a ranking, even if it
>> does not mirror
>> your real and complete sentiments.
>> 
>> With Range this seems lacking.
> 
> The point of understandability isn't conceptual but
> rather a reference to
> how long it takes to explain to the average person how the
> voting method
> works. Your counterargument does not apply to my original
> point, but I
> explained it badly so it's my fault. Criticizing the
> concepts as
> meaningless, I like that. Especially since that is what I
> was doing with my
> consistency failure remark. You can't have it both
> ways; either
> philosophical attacks are valid or they are not. 
> Let's assume that they are.

Ok. I will read the below section as philosophy.

> You say the magnitude of comparisons is not really
> substantiated by anything
> thus their magnitude shouldn't be considered (as almost
> all Condorcet
> methods actually behave). 

Jobst may say that, but I do not. I think theoretically it is valid to
compare methods based on social utility or Bayesian regret.

When I said that the magnitude of comparisons is not substantiated by
anything (if that is quite what I said), I was speaking in practical
terms.

> I disagree. I say Range Voting
> minimally distorts
> the concept of utility, just as you claim Condorcet methods
> minimally
> distort the concept of decision-making. Two limitations are
> placed on
> allowable votes in range voting, lower and upper bounds,
> (they must be
> integers as well, but this point is not especially
> relevant). This is
> designed to defend the system from dishonest utility
> monsters (e.g.
> Candidate A +1000000000000000000000). I'd say the
> concept of utility is
> intuitive. It is very similar to the concept of money. You
> understand that
> $1 > $.99 and that $45 > $1. It is intuitive that $45
> is much, much better
> than $1 than $1 is than $.99. Range Voting is a single
> dimension of
> comparison. Keeping with the Enlightenment style
> assumptions, human opinions
> should be perfectly transitive and rational, yes. So, a
> preference ballot is
> the most information that a human can be relied upon to
> fill out with 100%
> accuracy assuming they are rational (use of singular they
> to avoid sexism).
> I'd say sacrificing 100% accuracy for the vast amount
> of additional
> information you can gain from a cardinal ballot is worth
> it. Given that it
> seems natural to classify candidate worth along a single
> dimension to most
> people.

I don't disagree with this section.

>> > Bayesian Regret:
>> >
>> > Range Voting (same comment)
>> 
>> This is trivial to dispute unless you claim that everybody
>> is voting
>> sincerely under Range. Or, you claim that Warren's
>> simulations do not
>> have all the limitations that they actually do. In these
>> cases, no, that
>> cannot be disputed, that Range reigns supreme.
> 
> To my knowledge, he used strategic voters as well as well
> as a noise
> generator to represent ignorance. 

However, Warren's strategic voters do not use any actual information,
and in fact in rank ballot methods do not even take into consideration
the rules of the method and usefulness of the strategy.

> I have an idea to
> simulate perfect
> strategy. Organize the voters from early to late, have them
> try maybe 20
> randomly generated votes, whichever one affects the outcome
> most to their
> liking will be selected. It seems like a fair way to test
> strategy. It's
> probably already been done, but I'll write a simulation
> for it later. I
> plead ignorance here; I do not know what the limitations
> are. They seem to
> approximate the behavior of real voters to me. If not,
> please suggest an
> experiment that will.

Numerous simulations have been run, some of them by me. However, I have
never pretended to have a simulation so accurate that I could compare
methods according to utility when ideal strategies and realistic
information simulations are implemented.

The closest I came was a simulation that compared sincere Schulze(wv) to
various scenarios of Approval strategy and information. It probably
won't surprise you that I found that if anything, Schulze was better,
especially as the number of candidates increased.

Potential weaknesses in the study are easy to see, of course.

My most complicated strategy simulation worked like this:
There are 5-8 factions each with a single set of sincere utilities.
Each picks a way to vote (initially sincere).
Many, many polls (each identical in format to the actual election) are
run, each faction voting in their selected way. The difference among the
polls is that for each one, only a random percentage of each faction shows
up to answer. This produces variety in the results.
Afterwards, each faction reviews the results and uses knowledge of
the method to calculate a better vote, assuming that the other factions
will continue to do the same thing.
I personally hard coded what information is collected, and what logic is
used to estimate the value of a given way of voting.
Repeat indefinitely (typically looking for equilibrium to emerge).

Limitations:
The factions vote as though their decision is unlikely to affect the
overall results significantly. That is usually quite wrong.
The factions can't determine the value of conditions within a given
outcome if those conditions never occur in a run of polls.
The factions do not generally know how to create conditions that were
not observed in the last run of polls, even if they did know what
they were worth.
The factions commit "with this therefore because of this" logical
fallacies, creating much burial strategy in the Condorcet method I
implemented.
Every way of voting requires a single score to sort by, but it is
extremely difficult to consolidate scores of different aspects or
likelihoods of different types of conditions, in an apples-to-apples
way.

I implemented strictly ranked MinMax, FPP, Approval, MCA, top-two runoff,
antiplurality, possibly Borda (would have to check), and my "vote for and
against" method.

>> > Ballot expressiveness:
>> 
>> Pure expressiveness is useless. What should be compared
>> instead is the
>> degree of expression possible after rational strategy is
>> employed.
> 
> In order for post-strategy expressiveness to be present,
> pre-strategy
> expressiveness must be present. Please prove that a) all
> the expressiveness
> in Condorcet is preserved post-strategy and 

It isn't. The better Condorcet methods encourage some truncation, if
nothing else. Favorite betrayal incentive in Schulze(wv) is almost nil
(that is a simulation done by me); and you would have to assume vast 
amounts of favorite betrayal to reduce Schulze's collected information to
that of Approval.

>b) None of the range expressiveness is.

I don't think this will be necessary, because even Warren Smith will tell
you that in large elections, a rational strategic Range vote only uses the
extremes.

Someone will argue that voters will not, or should not, cast rational
strategic Range votes. To my mind that would be quite a gamble, to
implement a method with the hope or expectation that voters won't want
to, or won't think to, try to maximize their ability to get the outcomes
that they think are best.

>> > Bottom line:
>> >
>> > Range: You can express apathy, but you take your life
>> in
>> > your hands.
>> 
>> On the contrary, you take your life in your hands when you
>> do not
>> use the min/max ratings. That is why I prefer Approval: Why
>> invite the
>> voter to take their life in their hands when it is totally
>> unnecessary?
>> 
> First of all, non min-max ratings have a defined meaning
> when you rate
> everyone because their averages will change in a way
> consistent with how you
> intended your vote. That is my point. As long as you rate
> everyone, their
> averages will be altered according to your vote. My apathy
> argument (against
> range voting, I might add) is that unless you guess
> accurately what the
> averages for the candidates will be, it could backfire.

I'm not sure I understand. Are you saying that if without your vote,
candidate A's score is 6 and candidate B's score is 7, and you feel
these candidates are equally good, you would ideally want to rate A and
B 6 and 7 respectively?

> Condorcet does a
> great job of isolating apathy as you can specify which
> comparisons
> specifically you are apathetic about (with creative ballot
> design of
> course), but at least the capacity exists. For example, by
> ranking candidate
> B and E the same, you can compare their superposition to
> all other
> candidates but express apathy about which is better. In
> order to emulate
> that behavior in range, you have to give them the same
> exact rating, which
> is functionally equivalent but less tidy thus inviting
> other problems in
> more complicated examples (like the one I gave originally)

Just to be clear: I would have trouble advocating any Condorcet method 
that does not allow equality of ranking. (Inability to truncate would be
unacceptable.)

> I think you mean "in addition", 

As opposed to "on the contrary"; that is possible as I'm not sure I have
understood you.

> the CRV website
> does mention some cases in
> which, for a large electorate pool, intermediate ratings
> are strategic
> because the voting patterns of all voters cannot be
> predicted perfectly,
> thus it is best on average to use intermediate scores.

I don't know what CRV statement you are referring to, but I am curious,
because that is generally backwards. You must have *very* precise 
information about the other voters, in order to calculate a use for 
intermediate ratings. If you have no information at all, you use the zero-
info Approval strategy.

> Later I'll do a, "how
> much do honest voters shoot themselves in the foot?"
> test, but please
> suggest some benchmark nonrange method to compare it to.

Warren has done this, I'm sure you are aware.

I don't think it is interesting. In my opinion you should design the
method so that sincerity and strategy are usually the same thing. Plus
I can't take the answer to this question ("how much do honest voters...")
as a direct argument for the idea that voters would decide to not be
strategic. How much would "not that much" be anyway? One's ability to
affect an election's outcome in any way at all is microscopic to begin
with.

The benchmark method should probably be Schulze(wv), but that is not of
much use to you, since you are not going to be able to simulate Schulze
strategy in a way that will be convincing to everybody. (You might have
more success than Warren though.)

In my opinion a realistic Schulze(wv) strategic vote involves significant
truncation, no favorite betrayal to speak of, but some compression in the
top ranks, and some bullet voting (especially from voters favoring a
frontrunner). Burial possible only in very specific situations, or when 
the ballot forbids truncation.

>> >  If I overlooked something or made an error, please
>> tell
>> > me; I'm just a high
>> > school student.
>> 
>> I wonder if the CRV is your introduction to voting systems?
>> I am a little
>> curious where the Range advocates come from.
> 
> It is part of it. I don't take their statements on
> faith, though. I've
> studied game theory a bit and have the websites that
> advocate various other
> methods: IRV <http://www.fairvote.org/irv/>, Borda
> <http://www.deborda.org/>,
> Condorcet <http://condorcet.org/>, Condorcet (as near
> as I can
> tell)<http://www.barnsdle.demon.co.uk/vote/vote.html>,
> various <http://aceproject.org/>. 

I recommend the barnsdle link.

> Some of the newer
> hybrids such as MPPO,
> majority choice approval and such I am not that well read
> on.

MCA is a Bucklin variant. MMPO is not that new but can be seen as a
primitive way to interpret Condorcet (and of course with being primitive
comes some nice properties).

> Si vous savez
> où je peux en apprendre plus, dites-moi. For some reason,
> I cannot access
> the Electorama pages, it sort of annoys me. 

I am having trouble with the wiki myself, else I would at least link to
the page on my ICA method...

> Anyway, I do
> recognize the
> faults of Range Voting. I mentioned them specifically, like
> the results of
> expressing apathy and exposure to the Burr Dilemma. 
> I do not worship the
> CRV; I merely agree with them on most issues. I come from
> California. I am
> not quite sure if that is the intent of the question. I
> studied politics one
> day on Wikipedia and came across something about PR, I
> think and read all of
> the articles about anything remotely voting related. The
> articles on CRV
> were coherent and, unlike Fairvote or de Borda, did not
> ignore the flaws
> with their own system. I even read some of Saari's work
> before deciding that
> he was advocating Borda with arguments that actually
> support Range Voting
> better. Anyway, IRV and Borda seem pointless, once I

Well, Borda is totally broken for public elections.

With IRV you have Later-no-harm, which in theory should help fix the
Burr dilemma. MMPO satisfies this also. But the property seems to
inevitably create either FB incentive (such as in IRV) or burial incentive
creating an incentive to truncate anyway (in MMPO).

> understood Schulze and
> RP, it became tougher to tell which was better, them or
> Range. I decided
> Range on the grounds of the FBC criterion, ease of use,
> simplicity, and
> sidestepping the crushing limitations of Arrow's
> impossibility theorem. 

This last reasoning is not very strong. Rank methods almost universally
select IIA to sacrifice within Arrow's scheme. Range sacrifices compliance
with the relevant ballot format. But in practical reality this doesn't
obtain anything for Range: if voters so much as normalize their ratings,
let alone use any strategy, Range loses IIA.

The argument is not as strong (because the definitions are not as clear),
but I feel the same way about Clone Independence.

> I don't think I'm a normal Range Voting advocate. I
> have no idea how old any
> of you are, but I imagine you aren't 16.

Probably not many... I guess most have been here a few years

> I realize the game theoretical nature of the arguments used
> to support
> Condorcet methods. It is all based on providing absolute
> certainty to voters
> that their vote will never lead to paradoxical behavior Y
> in method X.

Is this really so? It seems to me there are at least as many such
arguments in favor of Range as Condorcet, such as Participation and FBC.

> I understand the specific ordeals that Condorcet helps to
> diffuse. I think the
> best argument I can possibly think of for supporting Range
> is this. Start
> out with the (very charitable) assumption that the
> properties attributed to
> the Condorcet methods are about equal in value to the ones
> that Range satisfies. Now, there isn't one Condorcet method that
> satisfies all of them,
> in fact the existence of one that does so is impossible.

I'm unclear on which properties you have in mind at this point. What
properties are lacked by Schulze(wv) but possessed by another Condorcet
method? The only useful one I can think of is Mono-add-top.

> At the end of the
> day you are left with a nebulous group of methods that
> satisfy an impressive
> group of criteria some of the time and a simple method that
> satisfies some
> very powerful criteria and can be explained to a small
> child in about three
> minutes. Which would you choose?

If that's how I saw the choices then I'd definitely pick Approval.

Other than FBC I don't really see that Approval or Range satisfy very
powerful criteria though. Participation is a very *strict* and difficult
criterion, but I don't perceive it as highly useful.

I am not very optimistic about any very expressive ballot formats,
actually. Allowing desired voter behavior isn't the same as encouraging it,
and I think simpler ballots are better for the latter.

Kevin Venzke