[EM] Condorcet How? Abd

[Kevin Venzke]

Hi Abd,

--- En date de : Lun 12.4.10, Abd ul-Rahman Lomax <abd at lomaxdesign.com> a écrit :
> De: Abd ul-Rahman Lomax <abd at lomaxdesign.com>
> Objet: Re: [EM] Condorcet  How? Abd
> À: "Kevin Venzke" <stepjak at yahoo.fr>, election-methods at electorama.com
> Date: Lundi 12 avril 2010, 10h30
> At 12:56 PM 4/11/2010, Kevin Venzke
> wrote:
> > --- En date de : Dim 11.4.10, Abd ul-Rahman Lomax
> > <abd at lomaxdesign.com>
> a écrit :
> >>> In a given election yes, it is easy to miss
> the mark. But in
> >>> general,
> >>> aiming for the median voter is the most
> reliable. (That is
> >>> assuming you don't know utilities, which I'm
> really not sure you
> >>> showed how to find.) To see this, you assume
> utility is based on
> >>> issue space distance, and that the voters
> aren't distributed
> >>> unevenly.
> >> 
> >> I didn't show how to find utilities, I only showed
> various
> >> possibilities consistent with the votes.
> 
> Actually, I did follow an algorithm. I'd say it's
> reasonable. No claim
> that it is definitive. Obviously, how people will vote may
> depend on
> how the votes will be counted. But less than we might
> think

Ok.

> > Yes, and my response is what can I possibly do with
> that? You used one
> > method that was rather Borda-like in character. One
> can't evaluate
> > methods
> > using a Borda-like criterion or you'll end up
> advocating something
> > Borda-like.
> 
> The algorithm was not "Borda-like" because it did not
> prohibit equal
> ranking bottom. It's true that I did not use equal utility
> top,
> because there was no information to justify it.

It is rather positional even if it isn't Borda.

> >> To study voting system performance, I'm saying,
> one must
> >> *start* from utilities, not from preference order
> without
> >> preference strength information. Voter behavior is
> not
> >> predictable without preference strength
> information.
> >> Strategy, in general, doesn't make sense without
> an
> >> understanding of preference strength.
> > 
> > We sort of have been doing this when Juho questions
> the story behind
> > my
> > scenarios.
> 
> Yes. But the long-time use of voting systems criteria that
> depend
> solely on preference order is a hard habit to break. And
> the whole
> discussion of "strategy" has been often off the point. The
> use of
> "strategy" (as being about the idea that people will bullet
> vote to gain some
> advantage, which is assumed to be improper) neglects that a
> bullet
> vote reflects a strong preference. The voter wants their
> favorite to
> win, strongly enough that the voter suppresses the
> expression of remaining preferences.

I'm willing to say that truncation indicates a strong preference against
the truncated, but to accord extra importance to a bullet vote strikes me
as extremely harmful, if the method will actually respect that. You'll 
force people to just bullet vote for the better frontrunner. (Or use
equal ranking, perhaps.)

> IRV encourages this lower expression, because it doesn't
> require a true majority, but it "eliminates" candidates,
> hence lower preference votes will only be counted if your
> more preferred candidate is eliminated.
> 
> In other words, in a non-LNH method like Bucklin, A>B
> means that you actually are willing to elect B, enough to
> risk the possibility that B beats your favorite, A. With
> higher preference strength, you will vote only for A.
> Whereas with IRV, A>B (>C) tells us nothing about the
> preference strength of A>B, nor, in fact, about the
> strength of B>C. It only tells us that some preference
> exists.

Yes, but notice that *all things being equal* it is preferable if voting
A>B doesn't risk changing the winner from A to B. To the greatest extent
possible.

> >>> Thus when you have a situation where every
> voter
> >>> chimed in on some question, and they didn't do
> that for any other
> >>> question, you shouldexpect (on average) a
> utility problem when the
> >>> outcome goes against the majority opinion.
> >> 
> >> I'll agree that this is the "norm." However, it
> can go
> >> drastically wrong.
> >> 
> >> How can we detect the exceptions?
> > 
> > Right, that's the question.
> 
> In order to detect the exceptions, and use that
> information, we must risk some level of error in that. Let's
> be clear about something.
> 
> Suppose a set of voters has, for a complete candidate set,
> internal absolute utilities. We can imagine a set of voters
> all with the same resources financially. They have, however,
> various degrees of interest in politics and who wins
> elections. The utility is the "value" of the election of a
> candidate to the voter, and may be negative. Assuming that
> all voters have equal resources, the positive value is what
> the voter would pay to be assured that the candidate would
> win, and a negative value is what the voter would find
> adequate as compensation if a disapproved candidate wins.
> 
> Can we agree that the ideal winner of an election is the
> one which would maximize the sum of utilities of the voters?
> Note that these are *not* normalized utilities, and that if
> there were a Clarke tax or the like, collecting from those
> who assigned positive values and paying this to those with
> negative values, such that the benefit of the election is
> equalized across all voters, the best candidate would
> represent maximized value for *all* voters, not just those
> whose preferred candidates won.

For the sake of argument I'm willing to agree that this is the ideal
winner of an election.

> These utilities, except in certain narrow situations,
> cannot be directly determined. We can only infer them, to
> some degree, by voter behavior in elections and, as well,
> with respect to campaign donations and responses to polls.
> But it is not necessary to know them in order to use, in
> simulations, such a social preference profile to predict
> voter behavior under various voting systems, and to compare
> performance.
> 
> Okay?

Possibly...

> This is roughly Warren Smith's approach, of course, though
> details may certainly differ.
> 
> The Majority Criterion require majority preferences to
> prevail, at a point where the majority may not have
> sufficient information to choose the social utility winner,
> assuming that the majority would want to do so. In fully
> discussed deliberative election, a serious "utility error"
> may be detected and avoided through two means: abstention by
> voters with low preference strength, and, as well, a posible
> deliberate choice by voters to please those with stronger
> preferences, i.e., socially cooperative behavior. In top-two
> runoff, if the primary fails to forward the social utility
> winner to the runoff, and if the error is large, and if
> write-ins are allowed in the runoff (which makes it closer
> to deliberative process), a write-in might well win. If the
> runoff voting method is such that a write-in candidacy
> doesn't need to create a spoiler effect, this can be
> facilitated.

Ok, I read this.

> I consider it an unresolved question, how common it would
> be in real elections that picking a majority preference will
> cause utility error. (Bayesian regret in Warren's work.) But
> I'm sure it happens. How much damage is done, I don't know.
> But it could be significant. And the scenario we have been
> working on does show this.

How common, I do not know.

> >> Sure, the majority criterion and the condorcet
> criterion
> >> are usually a sign of good performance, but it is
> obvious
> >> that exceptions exist, and we should not denigrate
> a voting
> >> system if it, under an exception condition, it
> violates the
> >> criteria!
> > 
> > I wouldn't, no. But I would presumably have some model
> that explains
> > why violation of the criterion worked.
> 
> Sure. Now, let's assume that the votes given as the
> election scenario were sincere, and reflected sincere
> preferences. Shouldn't we start there?

I do start there. It's only when people don't believe me that I seem to
deviate from this.

> From the classic study of preference, it has been assumed
> that a bullet vote is strategic, not sincere. It is assumed
> that if the voter votes just for A, instead of, say, A>B,
> the voter does have a preference between B and C, and is
> suppressing that to gain advantage. However, that is not a
> realistic assumption.

I am not able to discuss that outside the context of a particular
method. I would not presume anything about the meaning of A vs A>B
without knowing what the incentives are. Your IRV vs Bucklin comparison
is quite adequate to see this.

> Suppose a voter is only familiar with A and "approves" of
> A, will be pleased to see A election, and has no opinion
> about either B or C. The voter, then, assigns no value to
> the election of B or C, but does assign value to the
> election of A. The bullet vote for A is a perfect expression
> of the voter's preferences. 

With you so far.

> Suppose we shift this to a
> situation where the voter does have some preference between
> B and C, but it is small. If C is elected the voter will
> emigrate, if B is elected, the voter will merely make sure
> that there is enough money to buy a ticket, and that the
> voter can emigrate quickly! In IRV, rationally, the voter
> should rank B. But in systems that are collecting utility
> information, the utility of B is small and speculative.
> (It's negative in the system I proposed).

Yes, I don't expect to see a lower preference in this case for B when
the method is WV. Personally I expect I would not rank much lower than 
my approval cutoff (in the same election run as Approval).

> In a full-on Range voting system, with high resolution, the
> voter would indeed show a preference for B. But only in the
> second scenario. In the first the value for B is zero. The
> voter, by bullet voting, is totally abstaining from all
> other pairwise elections. (I'll neglect average range, which
> I consider politically foolish as a proposal, requiring
> judgement about something where we have only air to build
> on.)
> 
> I took the proposed votes, and inferred from them what
> votes would be equivalent expressions of preference in, not
> Borda, but Bucklin, specifically 3-rank Bucklin-ER, and I've
> come to the (tentative) conclusion that rational votes in
> Bucklin-ER are actually sincere range votes, particularly if
> a majority is required or there is further process. For
> 3-rank Bucklin ER, the votes would be Range 4, with possible
> ratings of 0, 2, 3, 4, and midrange represents approval
> cutoff. That's why rating 1 is missing, it is a disapproved
> rating.
> 
> (In a more sophisticated Bucklin system, rating 1 would be
> allowed, and could be used to determine ballot configuration
> in a runoff. This would encourage, a little, bumping up, to
> a rating of 1, an only-disapproved-a-little candidate.)

Hm I'm not sure what you were getting at with the last three paragraphs.
I assume all you want to say is that it's not likely for A to give a
lower preference to B or C.

> >> I was just pointing out that the outcome you
> claimed was
> >> obviously bad wasn't. It might be that, on
> average, this
> >> outcome would be poorer than the other,
> > 
> > Yes, I'm afraid that's what I call "bad." If I didn't
> call this
> > "bad" I would also have to be pretty undecided about
> the resolution of most
> > two-candidate FPP elections.
> 
> Actually, if the Bayesian regret was low, using "bad" would
> be hyperbole.

I never have the Bayesian regret, so I would be silenced completely if I
had to base my judgment on that.

> Two-candidate elections are not the kind of
> scenario considered here. I do not believe that choosing the
> majority preference is an error in two-candidate elections,
> on average, and the incidence may be rare. We don't have a
> two-candidate election, the campaign was not over two
> candidates, it was over three, and it was very close. 

However, we have exactly one full-majority opinion, and if we remove
C it is hard to imagine why that should disappear.

So you go on:

> These
> are conditions where, in fact, utility error may be much
> more common, if we require the Condorcet criterion. The
> election does not fail the majority criterion. If we require
> a majority, the election simply fails. Now, take results
> like that and require a runoff between A and B. Who will
> win? Most voting systems students will assume that B will
> win, based on the votes in the first election. However, we
> know that in one-third of runoff elections, and these were
> not as close as this election, there is a "comeback." That
> means that in two-thirds there is not. Usually, the
> plurality winner goes on to win the election. 

Yes but you could probably make much stronger rules if you knew the
rankings behind the runoff votes. For example it could very well be
that in most cases the other candidates (second place onwards) are not
united against the frontrunner. While in other cases, they could be.

> Note that it
> only takes a very small amount of shift among the B and C
> voters to allow A to win, perhaps some lower turnout (which
> tests preference strength). In a real runoff with initial
> votes as described, A will almost certainly win.

However, I think it would be pretty unfair to decide an election based on
this guess.

> We know, from the bullet voting, that the preference of the
> A voters is strong, it is less likely to shift in a direct
> campaign between A and B.
> 
> And, as I hope I show, the simplest analysis of likely
> normalized utility profiles shows that A is, indeed, the
> range winner (Range 4). That is the center, not the
> extremes.

Yes but I have trouble seeing why to use the "simplest analysis of likely
normalized utility profiles."

> This kind of thinking leads me to conclude that plurality
> is a better voting system than we often think. We dislike
> plurality because of the breakdowns, not because of the
> normal function!

FPP is better than normally thought, I think. But I certainly don't agree
that A would be the expected winner if this were an FPP election. At
least, it would be more likely that there would not be three candidates.

> >> but it was not a truly bad outcome,
> >> under reasonable assumptions of likely
> >> utility, the first utility scenario I gave, which
> used Range
> >> 2 utilities, i.e., normalized and rounded off so
> as to make
> >> all the votes sincere and sensible. The bullet
> voters then
> >> had equal bottom utilities for the other
> candidates, and
> >> those who ranked had stepped utilities. Simple.
> And showing
> >> that A was, indeed (with these assumptions, which
> seem
> >> middle-of-the-road to me), the utility maximizer,
> by a
> >> fairly good margin!
> > 
> > This was the Borda-like thing I mentioned above.
> 
> Borda is Range with what is, in the end, a bizarre
> assumption. Use a Borda ballot and stop discarding "illegal
> votes," but count them rationally, i.e., allow equal ranking
> and therefore empty ranks, and keep the rank values the
> same, and it is a Range ballot. Since the only difference
> between Borda and Range is this, the system I used was
> Range, not Borda.

Yes but Range is not normally used on rank ballots whereas Borda is,
thus the similarity. Either way the positional analysis produces some
alarming incentives, if the method will follow it.

> >> You can make a contrary assumption, that the A
> voters were
> >> "strategic." That they "really" would be happy
> with B. I'm
> >> assuming, instead, that their votes would be
> sincere. And
> >> likewise the votes of the other voters.
> >> 
> >> Look, A *almost* has a majority in first
> preference. I'm
> >> very suspicious of claims that an election outcome
> is
> >> "terrible" if it depends on some close-shave
> majority that
> >> failed.
> > 
> > You are really missing my complaint then. According to
> your stepped
> > utility analysis C voters don't like B that much at
> all. If they know
> > that the method interprets such votes that way, then
> it is really bad
> > to vote sincerely for C.
> 
> We don't know how much they like B. We know that they like
> B more than A, that's all. So I inferred the middle
> assumption, that their utility for B was midway between that
> for A and C. That gives equal wiggle room in both
> directions.

Haha. There is no wiggle room, you have cemented it. You may have had
wiggle room in deciding where to cement it, but if there is an error
you are committed to it.

> What you are doing now, Kevin, is criticizing the original
> votes, which were the assumption.

I don't follow. I am criticizing your assumptions about the original
votes.

> And, it seems, you are
> criticizing as well, possible (unstated) ballot limitations.
> Clearly, the ballot allows equal ranking bottom, but it
> seems you assume it does not allow equal ranking top. 

Please assume that the ballot allows equal top.

I am hardly going to blame the C voters for not using equal-ranking
for C and B. I am trying to get accurate information from them.

(Again, if it's truly hopeless to have a rank ballot, we can use Approval.)

> I assumed, instead, that an expressed preference had real
> value, was not merely forced by the ballot. I gave it a
> middle value, neither extreme. Could you suggest an analysis
> more likely to be accurate?

What kind of analysis do you have in mind?

1. I don't want C voters to have to be insincere. Your response is 
seemingly that the C voters should do something else if they care so much.

2. There is a full majority for B vs. A. The median voter thinks B is
better than A. From where can we get an assumption that the voters are
distributed in such a way that we shouldn't base a utility guess on the
median position? I'm sure we can come up with one but I guess it would be
extremely speculative.

> > I initially read your last paragraph with disbelief.
> In my
> > interpretation,
> > C and his votes are just noise. The task of the
> election method is
> > to pick
> > the right candidate between A and B, just as it would
> be in FPP
> > (where C
> > would probably have died off pre-election). To be
> unable to do this is
> > quite useless in my view.
> 
> If that is the task of the election method, why is C on the
> ballot?

C wanted to try to win.

> Suppose that C is *not* on the ballot, suppose that
> C was a write-in. If that's true, then C would very likely
> be the utility winner. Not A or B.

You're probably right.

> What is the "right candidate" between A and B and why are
> we limited to that?

A vs B is the contest that everyone participated in. That's the race you
get when you take out the other candidate. In this scenario it happens
to work out as nicely as that*.

[*When I wrote this entire post I forgot that we are considering the
scenario with near-clones. In that scenario it's less obvious that C
is mere noise.]

> I agree, it is likely that the right
> candidate is either A or B, but it is not at all impossible
> that it is C. 

Well, without the write-in idea I personally doubt it.

> With my middle-of-the road assumptions, I came
> up with A as the utility maximizer, and B and C not that far
> apart from each other. From pure preference, sure, it looks
> like C is noise. If, in fact, to the C voters, B and C are
> almost equally prefered, C is indeed noise, and the "sincere
> vote" for C is indeed strategically foolish. 

But it does not need to be.

> Indeed, if B
> and C were to agree on who runs, and it would probably be B,
> then all the campaigning would be dedicated to B instead of
> split, and the likely result would be an increase in B
> support, and it's already close.
> 
> But from the voting preferences given and reasonable
> assumptions about the normalized utility profiles behind
> them, A is the best winner! So criticizing a voting system
> because it gives A the victory with those votes is
> backwards.

Not sure why "backwards," but yes, if you use your assumptions, then A
ought to win.

> I would claim that, ideally, no election would
> ever terminate the process with other than a manifest
> condorcet winner, this would always go back to the voters,
> as is normal with deliberative election process, which never
> elects without a majority of the votes supporting the
> winner. But there is no condorcet winner in the election
> being studied, because, while B beats A 51:49, C beats B
> 27:24, and A beats C 49:46.
> 
> So, since there was no majority for A, this election,
> ideally, would go back. For practical reasons, it might
> not.

Personally I would send it back as B vs C. I don't see any reason to retry
the A-B contest; the only way that could change is if we have a cycle of
full majorities, but we'll never know that if we only do two rounds.

Of course you could assume that boredom of going to the polls could
reverse the A-B defeat.

> > --- En date de : Dim 11.4.10, Abd ul-Rahman Lomax
> > <abd at lomaxdesign.com>
> a écrit :
> >>> This should rather say, if I proposed
> utilities behind
> >> the scenario, I
> >>> could make those utilities say anything I
> wanted.
> >> 
> >> I pointed out some extremes, which reveal as the
> ideal
> >> winner A, B, or C. In other words, you are
> apparently
> >> agreeing with me.
> > 
> > Yes.
> > 
> >> However, I believe that I showed that a
> >> middle-of-the road assumption about underlying
> utilities,
> >> with stated assumptions that were not designed to
> make it
> >> turn out some particular way, A could indeed be
> the best
> >> winner.
> > 
> > Yes you did.
> 
> Here, you accept it, but I want to make sure that was not
> accidental. I wrote "could be." I'll make that stronger.
> "Likely is."

A could be the best winner in one given election, that's what I meant.

> >> (I did not set out to "prove" that A was the best
> winner,
> >> but rather just to attempt to infer utilities from
> the
> >> voting patterns, which didn't allow me to assume
> equal
> >> ranking except at the bottom).
> >> 
> >> The matter hinges on the A voters, who are, after
> all,
> >> almost a majority. Why did none of them rank B or
> C? The
> >> only reasonable assumption is that they have
> strong
> >> preference, and that's what ices it.
> > 
> > I'm happy to say that A voters have a strong
> preference, but why
> > should only the A voters get to benefit from this? Are
> you saying the other
> > voters don't have a strong preference against A?
> 
> No, they do, and they are given full credit ("benefit") for
> it. The problem is that they don't explicitly agree on
> strong preference *for* B or C.

Ah, there we disagree, since I find the strong preference in the
truncation.

> I was not analyzing the votes from the point of view of
> strategy in the voting system used, and I don't really know
> what that system is. 

Well, it's quite fine to determine (un)desired strategy first, and pick 
a suitable method to fit that.

> I was assuming, in fact, sincere votes,
> votes that express preferences accurately. If the 51% did,
> in fact, have strong preference for both B and C over A,
> they therefore had weak preference between B and C. (That is
> the restriction that comes from normalization, the
> assumption that all voters have the same range of
> preferences. One person, one vote.)

It's nice that Approval doesn't do this.

> If they have weak preference between B and C, in Range 4,
> they would rationally vote max rating for both. But you have
> 5% of voters who vote contrary to that, because they bullet
> vote for B. The linchpin voters are the C voters. If the
> method is plurality, their strategy is obvious, if they want
> to improve the outcome. But what if some of them, say,
> anything over 1% of total voters, have weak preference for B
> over A? They will prefer to express their clear preference
> for C to betraying their favorite, and that is real voter
> behavior. It was Nader's message in 2000, and, obviously,
> many voters bought it.

It is unfortunate that the election method worked that way.

> In IRV, their strategy is also obvious. IRV works with an
> election like this, unless. Unless enough C voters abstain
> from ranking B. Some will. And there you go, IRV is likely,
> still, to give this to A! Only a Condorcet method will give
> it to B, narrowly.

The idea (as this is originally also meant to be an IRV scenario) is that
B is eliminated and does not transfer enough (or any) preferences to C to
permit a defeat of A, so that C's second preferences are completely 
wasted.

Only some Condorcet methods give it to B. Also Bucklin gives it to B.
I tend to think Approval would give it to B.

I would say the thing in common with B-electing methods is that they
have a concept, that truncated candidates are particularly rejected.

> >> This is the classic
> >> reason to violate the Condorcet or Majority
> criteria: a
> >> strong preference of a minority, particularly when
> the
> >> margin is thin.
> >> 
> >> If, in fact, B and C were true clones, with only
> minor
> >> preference between them, the assumption of a
> significant
> >> reduction of utility between them (which is the
> other factor
> >> that lowers the rating for B and C) would fail.
> >> 
> >> If the method allowed equal ranking, we'd see that
> in the
> >> votes, and B might win. The A votes would be the
> same, the B
> >> bullet voters would be the same, but the other B
> and C
> >> voters would equal rank B and C. Because of the B
> bullet
> >> voters, B would win by a small majority.
> >> 
> >> So my result for A could be an artifact of the
> voting
> >> system not allowing equal ranking. I used Range 2,
> which
> >> doesn't give a lot of room for "creative
> interpretation."
> >> That was much easier with Range 10, as I showed.
> With Range
> >> 2, there wasn't any other reasonable way to
> interpret the
> >> votes.
> > 
> > It's possible that with equal ranking it would be
> different, but if we
> > are not going to ask a method to behave unless voters
> use equal
> > ranking, I guess we could just use Approval.
> 
> Approval is Not Bad, but this would be the problem: what
> about the C voters? Approval would not allow them to express
> their preference for C, and if it is strong, some of them
> will not express it, and A will win.

Yes.

> So, in fact, Bucklin.

Eh. Bucklin doesn't provide much protection from lower preferences.

> > 49 A
> > 5 B
> > 19 B>C
> > 27 C>B
> 
> B wins, assuming these are the votes. Bucklin is an
> approval method.
> 
> However, the election scenario is unrealistic, because we
> have almost half of the voters voting monolithically, and
> then the other half does so as well. For these voting
> patterns to arise, the election must be highly partisan.

I don't really understand your point (we could easily throw some noise
in to make it less monolithic) but I'm happy to say the election is 
partisan.

> Non-partisan voters do not vote like this. In a real
> election, some of the non-partisan voters who prefer A would
> also approve, at lower rank, of B or C. And vice-versa.

Well, I'm not so sure about that for Bucklin. If the A voters have a
strong preference, partisan or not, it doesn't make good strategic sense
to give second preferences.

> For the rest of this post, I will repeat the utility
> analysis, which is Range 4, with the approval cutoff being
> 2. A rating of 2 represents indifference between the
> election of the candidate and the expected outcome.
> 
> 49 A was analyzed as A=4, B and C are 0. This was overly
> pessimistic. If I'm going to be "central," I should rate
> them as 1, i.e., the middle disapproval rating. This is an
> average, some voters might rate B or C as zero, some as
> "almost 2".
> 
> 5 B likewise.
> 
> 19 B>C This is analyzed as B= 4, C = 3. This is
> accurate, because the actual voter rating would be in the
> range of 2 to 4, so I'll assume that the mean is 3. A,
> however, should be considered to be 1, for the same reason
> as with the A voters with regard to B and C.
> 
> 27 C>B likewise.
> 
> So, the new analysis:
> 
>                
> A       B   
>    C
> 49 A            4 
>      1       1
> 5 B         
>    1       4 
>      1
> 19 B>C          1   
>    4       3
> 27 C>B          1   
>    3       4
> 
> totals          247 
>    157     170
> 
> Notice this phenomenon: the social preference order matches
> the first preference order. This, I suspect, is very common.
> This is why plurality voting is a decent method!

Haha, that's not why I would say it's a decent method. It's decent because
it is so primitive that political players have to figure out almost 
everything prior to the vote. If there were no pressure to weed out the
sure-losers, FPP would be a mess.

> What would happen if a majority were required? Suppose that
> the runoff is between the top two candidates, using an
> analysis like what I just did, which assumes that
> preferences are spread such that they average as I
> indicated. The runoff would be between A and C, not A and B,
> and that is probably the best. After all, C beats B
> pairwise.

I disagreed with this above. All the candidates are beaten pairwise, so
unless you give A priority for having the most first preferences (which
is not something I would agree to!), for me A is the last one who should
participate.

But sure, if we use your utility estimates, or Borda or anything 
positional, then we are obligated to keep A in there.

However, in my view a runoff between A and C is a disaster. Assuming the
original votes are sincere, A will win, exactly the result that gives C
voters incentives to be insincere. (It just takes longer to get there.)

[And again I need to note that I had in mind the version of this scenario
where C doesn't receive second preferences.

In the near-clone scenario some of my interpretation loses its meaning.
As I've said elsewhere I'm a little less passionate about the near-clone
scenario because I think it is hopeless. But even so, there are different
degrees of hopelessness. You still have a median voter in that scenario,
and I'm not happy to see him overruled.]

Kevin Venzke