[EM] Why the concept of "sincere" votes in Range is flawed.

[Abd ul-Rahman Lomax]

At 01:46 AM 11/26/2008, Juho Laatu wrote:
>In the EM discussions people seem to assume
>that at least one should put the cutoff between
>some leading candidates. People seldom talk
>about marking those candidates that one approves
>(I have seen this approach however in some
>mechanically generated ballots for simulations).
>Don't know about real life.

We are much better at making binary comparison choices than at 
generating, ab initio, ratings. Candidates don't have numbers on 
their foreheads.

It's pretty easy, though, to weigh two candidates in one's mind and 
decide which of them is better. Have trouble? Set the problem aside 
and consider them as clones. You will vote the same for them unless, 
later on, you change your mind.

For an individual to have a Condorcet cycle may be possible (this 
would be based on conflicting criteria, at least three criteria must 
generate different results in the important parts of the preference profile.)

In the vast majority of elections, though, most voters have some idea 
of who the frontrunners are. Haven't heard of the candidate? Pretty 
likely to not be a frontrunner! I'd start by classing all unknown 
candidates in the equally-unpreferred set. I really doubt that I'd 
"abstain" even if the method allows it. (It's a bad sign that a voter 
has paid *any* attention doesn't recognize a candidate and have some 
opinion, it almost certainly represents a candidate not yet read for 
prime time. Range would allow such a candidate to show some 
respectable results -- for example, how many voters both rated the 
candidate above zero -- but it is highly debatable that a method 
should ever consider partial abstentions. Vote for one candidate, you 
have voted against all the others unless you explicitly rate them 
otherwise. This makes Range match Plurality and Approval, i.e., it 
fits in with minimal disruption.

So generating a full preference profile, allowing equal ranking, 
isn't difficult. With three serious candidates, I could do it right 
on the ballot. More than three? I'd need some scratch paper.... But, 
really, I could get very close simply by asking myself the question, 
with each candidate, which would I prefer? This candidate or for the 
election to fail to find a majority, and thus need to be repeated in 
some way. If a majority is required, this is a very sophisticated 
criterion. (This also needs some rating to be defined as acceptance 
of that candidate, probably the simplest is above half-rating. Or 
maybe at half exactly, if N in Range N is even. I'd tend to have N be 
odd precisely for this reason. But, on the other hand, I like Range 
10 or Range 100, for familiarity.)

You can forget about, initially, ranking any nonviable candidate, and 
including unrecognized candidates in that is reasonable. So, usually, 
you are only ranking two or *rarely* three candidates. What could be simpler?

Start out by max rating your favorite and min rating the worst.

With two frontrunners, you top rate one, I'd suggest, and bottom rate 
the other. Except that if you have a preferred candidate -- in either 
direction, you *might* pull down the preferred frontrunner one notch, 
to preserve expressed preference order. Remember, though, by 
definition, that preferred candidate is determined by you to not have 
a prayer of winning. If he or she does, this isn't the contingency 
described here. There are only two who could win.

Okay, there are three. That's a little harder. Same strategy: rate 
the best frontrunner at top rating or one notch below if you favorite 
is not one of the three, if you care to risk that minor loss of 
voting strength in the real election, in order to preserve sincere 
preference order expression. In Approval, you don't do this at all, I 
assume, at least I would not advise min rating all frontrunners! 
Unless you don't care about influencing the outcome, which can be 
reasonable. Tweedledum and Tweedledee? Down with them both! I don't care!

But don't, then, complain later, you made your choice. Did you really 
believe Nader when he said that Gore and Bush were the same? Shame on 
you! Ahem. That opinion has nothing to do with voting systems in 
themselves, but only with how we consider strategic voting.

Strategic voting is a way that a voter can improve results from a 
poor method. With Range, while there is a personal improvement from 
avoiding "sincere normalized relative utilities," it is at the cost 
of overall satisfaction. Care about that? Vote *fully sincerely*. Do 
*not* "exaggerate" your vote contrary to your preferences. Otherwise 
vote as people have been voting for a long time: considering the 
election probabilities and shifting voting power accordingly. Range 
allows you to do this without reversing preference. And Approval is a 
Range method.

Further, the improvement from strategic voting is small. If the 
method allows the accurate expression of true, fully sincere relative 
utilities, in fact, voting Approval style -- which is what one does 
in the important races with strategic voting under Range -- has, in 
realistic practical scenarios, *no* improvement over voting 
"sincere." (I've never seen a decent analysis which shows that it 
does, unless the voter has *very* good information about the rest of 
the electorate.) But it may be easier to vote. And low-res Range may 
not allow this sufficiently accurate expression. (This has not been 
adequately studied.)

Preferential voting methods, for you to improve the outcome (which 
may, in fact, improve it overall, this is not necessarily a "selfish" 
move), you must vote reverse preference.

Right. This is what strategic voting used to be defined as. When, 
then, Brams proposed Approval, and published extensively about it as 
"strategy-free," critics figured out ways to pin "vulnerable to 
strategic voting" on it. Of course, these new ways required specific 
definitions to be tailored for the desired result.

The fact is that there is no single sincere vote in Approval. It's 
easy to define an "insincere vote," though, it is one which reverses 
preference. The problem is the middle. If a voter decides that a 
preference that the voter has is below some threshold of 
significance, and thus votes equal preference, is this an "insincere 
vote"? I'd say not. It merely does not express some preference of 
some (relatively) minor maghitude. Given that practical Approval 
voting, for voters who understand it, requires setting, effectively, 
some approval threshold, which will vary with the election 
circumstances -- what we will accept under some circumstances, and 
consider a favorable outcome, we will not accept under others, so 
there is no absolute "Approval" sticker on the forehead of each 
candidate, we only place those stickers in our imagination once we 
understand what is realistically possible. If we are selling 
something, we don't hold out for the million dollar price if there is 
zero chance of getting it, we will accept something much smaller that 
is better than our expectation, and we won't accept something worse 
than our expectation and, probably, to get it over with we'll 
probably accept our expected price and pat ourselves on the back for 
having succeeded. If we get it. These are really bids, not outcomes.

What the voter votes in Approval is a sincere expression classifying 
candidates into two exclusive sets: the "accepted set" and the 
"rejected set." That classification is sincere, unless the voter 
simply does not understand how Approval works; there is no advantage 
to an insincere vote in Approval, defined as one where a voter 
prefers a candidate in the rejected set to one in the accepted one.

To me, this is the only definition of sincere vote in Approval that 
makes sense. It's *fully* sincere from this point of view, and, 
indeed, violating that sincere vote as described, never improves the outcome.

The only question, then, is where the voter sets the Approval 
threshold. It's a judgment, not a matter of sincerity. To maximize 
your personal election power, you must make a sound judgment. You 
must understand the political context, the alternatives. So Approval 
gives an edge in power to voters who understand the situation! Is 
that a bad thing? I don't think so.

However, even the simplest voter, relatively ignorant, knows who 
their favorite is. This is what Carroll realized and published in the 
early 1880s, as the Asset Voting tweak on STV.

So, in approval, vote for your favorite. You can leave it at that! 
The difference in voting power is actually small. As long as you vote 
for a frontrunner, you are pretty safe. If you don't prefer a 
frontrunner, then vote for your favorite. First. And then, if you 
know who the frontrunners are, vote also for your favorite among 
them. Again, even if there are three frontrunners, this is normally 
quite close to expected value.

Presenting Approval as difficult to vote is a radical distortion. By 
definition, most voters will prefer a frontrunner, and, normally it 
makes perfect sense to bullet vote for that candidate. If it is 
majority-required Approval, it is *very* safe, and might actually be 
recommended -- I'd want to study that in more detail.

>FPP (or actually some society that uses FPP) could
>take the stance that voters are expected to pick
>one of the two leading candidates in a two-party
>country, which would make voting sincere.

Yes. They argue that, and they argue that the prior choices made in 
determining the two leading candidates are how the system works. 
There is an obvious failure mode, but it is restrained by a broad 
understanding that the failure mode exists, which *usually* restrains 
minor party candidates and the voters enough to avoid serious problems.

Because of these other situations, Plurality works better in practice 
than in theory. And make a majority requirement, it works much 
better. I.e., runoff. Even better, a little, if write-ins are allowed 
in the runoff (which is the default in California). Top Two Runoff 
probably works better than IRV, for selecting the best winner, 
because voters are more educated in the runoff, and preferential 
turnout probably helps improve results. Is IRV cheaper or more 
convenient? Maybe. It's a trade-off, which is more important?

FairVote will certainly argue that runoffs have lower turnout and 
that this is a Bad Thing. Without actually considering why and the 
likely effect on election quality. FairVote doesn't want us to even 
consider election quality in an objective manner, but only looking at 
specific and relatively rare scenarios where IRV will obviously 
improve results. Over Plurality. Not over true runoff voting, which 
IRV is supposed to simulate, but which it most certainly does not, 
that's clear from the actual evidence from real elections.

>Otherwise not voting for one's favourite minor
>candidate could be seen as an insincere strategic
>decision.

Yes, it can be. And I'd agree. It reverses expressed preference.

It is *very easy* as I have described, to define sincere voting in a 
clear way that makes all strategic Approval voting be a sincere 
expression of voter preference profiles. Amalgamated over many 
voters, it creates a pretty accurate picture of the overall voter 
preferences. That is, the preference order represented in the summed 
Approval votes, voted sincerely in a manner which is easy to describe 
and which makes easy sense, will be quite similar, normally, to that 
which we would get from fully sincere -- but normalized -- Range 
Voting. (That also needs special definition, but I've done that in 
other posts.)

>  In real life I think people generally
>know that one should vote strategically in FPP,
>so from this point of view the society expects a
>simple strategy (don't vote for candidates that
>don't have a chance) to be applied.

Yes. And they would continue to do this with Approval, only they now 
have an additional choice. If it is Bucklin they can have their 
additional choice and express their first preference also.

SU theorists can sometimes go a bit bananas when I suggest that maybe 
if a majority has the same first preference, it's not a bad idea to 
just elect that sucka. Sure, there might be a better winner.

But have you *ever* seen an election where this was true? Where using 
full-blown Range would have produced a better result, where two 
candidates would both have gained a majority with realistic voters. 
It's easy to posit that it could happen. But then look at what real 
voters do and have done for a long time. It ain't gonna happen.

So allowing voters to express their first preference, distinctly, 
which Bucklin does, will make it easier to get implementations, 
maybe. Allow voters to vote multiple choices in first preference if 
they want. That makes the method quite like Approval, only phased in 
in a manner that allows it to satisfy a reasonable interpetation of 
the Majority Criterion. If a majority *votes* exclusive preference, 
and they can, then that candidate will win. But if they *choose* to 
equal rank top, more than one, they are *voluntarily* abstaining from 
those election pairs, and their preference, now not expressed, may 
not prevail. Prior arguments about whether Approval satisfies the 
Majority Criterion or not were based on objections that the equal 
ranking was *forced*, though I argued that this was moot and not part 
of the definition.... But it's not forced in Bucklin and would rarely 
make a difference.

>One interesting feature is protest votes. Many vote
>for minor candidates although they know that their
>vote will be "lost" (in the usual meaning of the
>term that refers only to the outcome of these
>elections). Protest votes do have a meaning outside
>of this narrow interpretation (impacting the
>outcome of this election) though.

Yes. Many do. Nearly all do this, I imagine, knowing what they are 
doing. Here is the utilitarian understanding of that. The value to 
them of "making a statement" is greater than the difference they 
could make by voting. Consider Nader supporters. Suppose they agreed 
with Nader's often expressed position that there was no difference 
between Bush and Gore (nothing worth worrying about, anyway, it 
doesn't mean absolutely no difference, but an insignificant one). So 
they saw no value in voting in the Gore/everyone else pair, and 
instead voted in the Nader/everyone else pair.

It's rational behavior, given their utilities. Were the utilities 
rational? That's really not for us to judge. We assume that voters 
have the right to make the decisions they make. I may consider the 
Nader position morally reprehensible, I may condemn it right and 
left, but it was, indeed, as he claims, his right to run and the 
right of people to vote for him. In Florida, those voters knew that 
they were possibly awarding the victory to Bush, when they could 
prevent it, *and they did not care enough to drop their vote for Nader.*

There are a number of influences on utility that aren't normally 
considered in the simulations that have been done so far. "The desire 
to make a statement," to protest the limited options in an election, 
and so forth, is one. Another is the desire to express a first 
preference, uniquely, so that a party can get vote credits which lead 
to ballot position in future elections, and possibly campaign finance 
funding. In a majority-required election, the desire to either cause 
or prevent a runoff.

(Under Robert's Rules, in spite of what they give as advice to 
voters, not fully ranking candidates in IRV run the way Robert's 
Rules assumes -- majority required or election fails and must be 
redone de novo -- ranking any candidate other than a true favorite 
can harm the true favorite (this includes a favorite not on the 
ballot!), because it may cause the election to complete, where, 
without the vote, there would be majority failure and thus an 
opportunity for the favorite to win. (I'll say what I've said before. 
Later No Harm is another of the voting systems criteria that a good 
method will necessarily violate. Later No Harm depends on true 
candidate elimination, which can prevent a compromise candidate, 
clearly the best choice, from winning. Even if that candidate would, 
in fact, win a runoff against the IRV winner, with over 75% of the 
vote -- as would have happened if Le Pen had gotten just a tad more 
first preference votes and thus was the IRV winner. It was close to 
that. -- the actual scenario would depend on preference distributions 
among other candidates, I merely assert that the possibility wasn't 
remote or by any means unreasonable.)




> >
> > You can easily deny that you have an internal concept of
> > "approval,"
> > but you can also deny that you have an internal transitive
> > ranking
> > of the candidates. Maybe it's harder to believe, but it
> > can't be
> > disproven. (Though, I don't really think it is harder
> > to believe,
> > since "approval" has a plain English meaning.)
>
>It seems that voting method "Approval" has cut its
>ties to English term "approval" (at least at the EM
>list).

Yeah. Here is the problem: "Approve" has two distinct meanings (at 
least). I won't bother looking it up, but the real one, that applies 
to Approval Voting, is "to act to accept, as with "The officer 
approved Fred as a contractor." Does this mean that the officer likes 
Fred. Not necessarily. All we really know is that the officer 
"accepted" Fred. Or "I approved the purchase." It means that I 
accepted that outcome and the associated conditions, not that I like 
them. The other meaning, of course, represents an emotional or 
conceptual state, "I approve of the way McCain conducted himself when 
it became clear that Obama had won." This latter kind of approval, if 
expressed, is perhaps sincere or not. The former kind is not about 
sincerity at all, though we may infer certain relative states from it.

With a rational Approval Vote -- one designed either to simply 
express a favorite or favorites with no regard for strategy at all, 
or to maximize voter power over the result -- we can infer a sincere 
relationship with preference rankings. We can assume, with high 
expectation of accuracy, that the voter prefers all members of the 
set of "approved" candidates to all members of the set of 
"disapproved" candidates. More than that, we can only guess.

With Range, if a voter ranks one candidate higher than another, we 
can assume that the voter prefers that candidate. If the voter ranks 
two candidates equally, we can make no assumption about the voter's 
preference between them. Such a vote simply does not express the 
information. We do know, however, that the voter presumably prefers 
those equally ranked candidates to all lower-ranked candidates on the 
ballot, and, likewise, that the voter prefers all higher ranked 
candidates to the set of equally ranked ones we are considering.

So a Range vote, quite like Approval, expresses sincere preferences, 
but not necessarily all of them.

But every expressed preference is either sincere or useless to the 
voter, it does not maximize the voters' expected satisfaction with the result.

In this sense, every Range vote can be considered to be either 
sincere or a mistake, same as Approval. The difference between Range 
and Approval is, of course, that with Range the voter can express 
many more sincere preferences, should the voter choose to do so, and 
most of them would be harmless at worst. In a sophisticated 
implementation of Range, we could guarantee that any expressed 
preference is harmless, but that is down the road. It is quite hard 
enough to get across the terminally simple concept of cutting loose 
the votes for candidates from each other, so that no longer does the 
vote for one candidate have to depend on the vote for another. So 
that the voter can vote for no realistic candidates (which is kind of 
abstention from powerful voting that can make a statement), for one, 
for more than one up to all but one -- which means "Anyone but Bill"- 
-- or for all, a different kind of abstention, which means -- hey, 
these guys are all great, I'd like to let you know this and let the 
rest of you decide. All of these are sincere in Approval. And, I'm 
claiming, all the rational votes in Range can likewise be considered 
sincere in what they express.

Odd, don't you think, that voting activists who want to conceal what 
might be a significant lower preference (because of later no harm) 
would be offended that, in Range, a voter may conceal some 
*relatively unimportant* preferences. Clearly not the preferences 
that the voter truly cares about.

Critics of Range, I've found, have asserted vulnerability to 
strategic voting without ever clearly defining it. They give examples 
that, sometimes, assume an oxymoron: a weak preference voted as a 
maximally strong one. Why? What's the motivation of the voter? They 
will say, "they want their favorite to win." But *how much* do they 
want their favorite to win? This is the paradox: not much, it is 
asserted. But enough to damage overall outcome, including, quite 
possibly, their own. Guess wrong with such an "exaggerated vote," and 
you could very, very much regret your vote. Why bother, if the 
preference is weak? It's a paradox, and this is the answer:

The voter won't vote an exaggerated preference like that -- except as 
a mistake -- unless the voter has a significant preference. Not a weak one.

Range votes sincerely express a preference list that may be 
incompletely detailed, but it is never out of sequence, allowing that 
more than one candidate in the list may share a position, as if there 
were no preference, but not actually asserting that. A Range Vote -- 
unless we add some special condition -- doesn't indicate preference 
if there has been equal ranking, among those who are equally ranked.

Again, with Approval Voting, we have the very strange situation that 
a bullet vote is considered strategic because, the critic asserts, 
the voter "also approves of another." But, here, the voter has 
expressed a preference, and it, presumably, is a real one. So how is 
this a "strategic vote?" Yet this has been cheerfully asserted by 
experts who should know better. Basically, this critic claims to know 
where the *real* voter approval cutoff is, and denies the voter the 
right to set that at will. Bad idea. Very bad idea.

Yet setting an approval cutoff is a choice, not a sentiment. It does 
not mean that I feel a certain way about candidates above that cutoff 
vs those below it. It means what I've said: that I'm willing to 
accept the election of all those "approved," and prefer all of those 
candidates, any one of them, to every unapproved candidate. How we 
could consider this insincere, once this is seen, is beyond me.

Critics have confused "strategic" in the sense of smart, with 
"strategic" in the voting systems special sense of reversing 
preference -- "voting insincerely" -- in order to improve an outcome. 
Then, because "strategic voting" was long considered a Bad Thing, and 
they managed to describe concealing a preference as being insincere, 
because of a lack of careful thinking about it, they were able to 
attach the Bad Thing label to Approval's response to simple sensible 
voting. Hence my work deconstructing these concepts.

Now, the kicker: so concealing a preference is, if we follow the 
logic of these critics, "insincere." But, now, let's consider the 
Majority Criterion. Does Approval satisfy it. Follow James 
Armytrage-Green, who is not an enemy of Approval but who senses that 
Approval fails MC and he tries to nail down the definitions so that 
this can be clearly shown, because so many pesky students were 
pointing out that, as the criterion was worded, literally, Approval 
could be considered either as passing MC or as not covered by it so 
that passing or failing is meaningless.

The question hinges on what is a sincere vote. No method based on 
preferences can determine a winner based on the preferences if the 
voter conceals a preference that is necessary. I.e., a Condorcet 
compliant method can't find the Condorcet winner if the voters 
conceal or distort the necessary preferences. So it is assumed that 
voters vote "sincerely," in accordance with their true preferences. 
But for Approval to fail the MC, the voters must conceal the crucial 
preference, that of a majority for a single candidate. How can this 
be a "sincere" vote? Well, they have their cake and eat it to. It's 
sincere because it is not insincere. The voter "really does approve" 
of both candidates, but has a preference between them. Perhaps 
someone should inform them about the excluded middle. Not not-A is 
not necessarily A. It might be something else. Something in the 
middle between A and not-A.

In this case, the double vote is "sincere" in one sense, but does not 
fully disclose all preferences. So in the other sense it is 
insincere. It fails to disclose a necessary preference.

James Armytage-Green: 
http://fc.antioch.edu/~james_green-armytage/vm/define.htm#mc


>Majority criterion (MC): If more than half of the voters rank 
>candidate X over every other candidate, then the winner should be candidate X.
>
>Some methods that pass MC: 
><http://fc.antioch.edu/%7Ejames_green-armytage/vm/survey.htm#smith>Smith/minimax, 
><http://fc.antioch.edu/%7Ejames_green-armytage/vm/survey.htm#sd>sequential 
>dropping, 
><http://fc.antioch.edu/%7Ejames_green-armytage/vm/survey.htm#ranked_pairs>ranked 
>pairs, 
><http://fc.antioch.edu/%7Ejames_green-armytage/vm/survey.htm#beatpath>beatpath, 
><http://fc.antioch.edu/%7Ejames_green-armytage/vm/survey.htm#river>river, 
><http://fc.antioch.edu/%7Ejames_green-armytage/cwp13.htm>cardinal 
>pairwise, 
><http://fc.antioch.edu/%7Ejames_green-armytage/vm/survey.htm#minimax>minimax, 
><http://fc.antioch.edu/%7Ejames_green-armytage/vm/survey.htm#plurality>plurality 
><http://fc.antioch.edu/%7Ejames_green-armytage/vm/define.htm#nonrankedcrit>[*], 
><http://fc.antioch.edu/%7Ejames_green-armytage/vm/survey.htm#irv>IRV, 
>  <http://fc.antioch.edu/%7Ejames_green-armytage/vm/survey.htm#runoff>two 
>round runoff
>
>Some methods that fail MC: 
><http://fc.antioch.edu/%7Ejames_green-armytage/vm/survey.htm#approval>approval 
><http://fc.antioch.edu/%7Ejames_green-armytage/vm/define.htm#nonrankedcrit>[*], 
><http://fc.antioch.edu/%7Ejames_green-armytage/vm/survey.htm#cardinal>ratings 
>summation, 
><http://fc.antioch.edu/%7Ejames_green-armytage/vm/survey.htm#borda>Borda

Notice that for the failure of Approval to be true, "rank" as the 
action performed by the voters is *not* that the vote it. It's that 
they somehow sense it, it is that they have internal utilities which 
show it, something other than voting the preference. Because if the 
voters express the preference, if that were what "rank" means, Approval passes.

He has a footnote. He is aware of the problem. But he comes up with a 
strange solution. He's aware that prior understandings of the 
Majority Criterion were problematic as applied to Approval Voting, 
and that new definitions were needed to apply the MC to non-ranked 
methods. And especially to methods which allow equal ranking. That is 
what was not contemplated in the original work.

>Note on criteria definitions for non-ranked methods
>
>        In the interest of simplicity, most definitions on this 
> page, as written above, assume ranked ballots. However, some 
> methods evaluated on this page (i.e. plurality and approval) do not 
> use ranked ballots, and do not allow complete orderings when there 
> are more than two candidates. I apply ranked ballot criteria to 
> non-ranked methods as follows.
>
>1. Change ranking-based wording to preference-based wording. For 
>example, a criterion with the wording "a voter ranks A over B" is 
>changed to "a voter prefers A to B". The wording "a voter ranks A 
>equal to B" is changed to "a voter is indifferent between A and B".
>
>2. Assume that votes are cast sincerely. In order to do this, I 
>provide an operational definition of sincerity for plurality ballots 
>and for approval ballots.
>
>2a. Assume that a sincere vote on a plurality ballot entails voting 
>for one's favorite candidate.
>
>2b. Assume that an insincere vote on an approval ballot entails 
>approving B but not approving A, if the voter prefers A to B, or is 
>indifferent between A and B.
>
>Note: I am not entirely convinced by either of these definitions (in 
>2a or 2b), but they seem to serve our current purpose as well as 
>anything else. Other applications are possible, and strictly 
>speaking it's hard to argue that any single application is 
>definitively correct. One approach is to ignore the possibility of 
>unexpressed preferences and evaluate plurality and approval only 
>with respect to expressed preferences. In that case, they pass just 
>about anything you can think of, but this doesn't tell us very much, 
>or capture the intent of the criteria themselves. Hence, I use the 
>methods above for my tables.
>
>Note also that alternate (more restrictive) definitions for sincere 
>approval voting, such as voting for candidates that provide utility 
>above a certain threshold, or voting for the candidates in the top 
>half of one's ranking, produce the same results for the criteria 
>listed on this page.
>
>        For example, the majority criterion for ranked methods is : 
> "If more than half of the voters rank candidate X over every other 
> candidate, then the winner should be candidate X."
>
>        To apply the majority criterion to non-ranked methods, it 
> can be re-worded as follows: "If more than half of the voters 
> prefer candidate X over every other candidate, and votes are 
> sincere, then the winner should be candidate X."
>
>        For cardinal ratings methods with more possible ratings than 
> candidates, ranked ballot criteria can usually be applied without 
> the need to use preference-based rather than vote-based 
> definitions. For example, the majority criterion can be worded as 
> follows: "If more than half of the voters give candidate X a higher 
> rating than any other candidate, the winner should be candidate X."

Now, the problem is that, of course, the votes are "sincere," but 
they are not a sincere expression of the preference involved in the 
Majority Criterion. They are a *different kind of sincerity.*

This is pretty crazy stuff, actually. Voting systems criteria were 
supposed to be objective criteria, considered desirable, that were 
then applied to all methods, equally. However, if you need to create 
special definitions for each method, by manipulating the definitions 
-- consciously or unconsciously -- you can cause the method to pass 
or fail. In fact, the whole criterion-based method of evaluating 
election methods is flawed, for we can rather easily show that some 
of the criteria are *not* desirable, and that a good method must, 
under some contingencies, violate these criteria. The Majority 
Criterion is one of them. With Approval, it's quite possible to argue 
that Approval passes, but Armytage Green essentially doesn't consider 
that "useful." He's quite aware, I think, that the MC-violating 
winner is quite likely *better* than the majority preference. 
However, in supporting MC violation for Approval -- which he doesn't 
think is an argument against it -- he has enhanced the argument of 
those who confuse MC compliance with majority rule -- and who have 
often used the word "majority rule" in this connection, as if 
"majority rule" were an election criterion, and then they describe 
the Majority Criterion. Majority rule refers to something quite different.

With Range, though, Majority Criterion violation is unavoidable, 
because, with Range, a majority may express their preferences and 
their first preference may fail to win. Hence in educating people 
about Range, it is necessary to confront the assumption that Majority 
Criterion compliance is desirable. It's pretty easy to show it is 
not, that the first preference of a majority can be quite a foolish 
and damaging choice. And that a different choice would likely be 
approved by a majority, explicitly, voting on that narrow question, 
not in a multiple-choice voting system subject to all the 
complexities and paradoxes.

That's majority rule, it refers to the right of a majority to make a 
decision, typically as consent to a proposed action ("motion") with a 
vote that is either Yes or No. The majority can explicitly decide to 
set aside its first preference, because it finds greater value in 
something else (which then is, in fact, its first preference, the 
paradox. I.e., the majority prefers, over the other options, to give 
up its favorite pizza in order to satisfy a higher goal: maximum 
group satisfaction and acceptance. Presumably it does this respecting 
its own preferences and won't do it in order to choose what the 
majority considers a bad pizza, normally.

>In ranking based methods EM people seem to assume
>that voters have some easy to identify transitive
>order of the candidates in their mind (=sincere
>opinion).

Yes. Allow only that where the voter has difficulty choosing between 
two candidates, the voter can equate them. (The voter might also, in 
the quite rare circumstance that the voter recognizes a Condorcet 
cycle in his or her own preferences, recognize the confusion and, 
again, rank them equally, as a set that is preferred to all other 
candidates. I'm not sure I've ever encountered a Condorcet cycle 
personally, but it's theoretically possible, though only by 
considering pairs separately and using different measures for them.

Humans, though, are equipped, instinctively, to use a kind of Range 
Voting. We sure don't construct a Condorcet matrix! And cycles don't 
exist in Range Voting. If it seems that we do, when we try to 
construct the rank order from pairwise comparisons, we need to 
consider all the candidates at once, and pick out the top candidates 
and bottom candidates, if any, then the next ones, etc. In that 
action of picking out the favorites or the worst, we must consider 
all of them at once, thus ensuring that the neural patterns which 
generate our preferences are simultaneously operative. (And the rest, 
when we get to where it is difficult to rank, could go in the middle 
or at the bottom. I won't address this here.)

But, ordinarily, pairwise comparison will work, and is simpler. The 
preferences will be transitive. In the few cases where they are not, 
we need then rely upon natural Range Voting, so to speak. Find the 
favorite. It will be the one with the loudest cheering. (Real voting 
method in Sparta.)

>I find it revealing that there is not much
>discussion on the possibility to cast non-transitive
>votes. Such votes would be strategically more
>efficient than the transitive ones. Use of
>transitive votes seem to reflect the idea that the
>sincere opinion of a rational voter would always be
>transitive. (Well, of course casting non-transitive
>votes would be technically more challenging.)

Indeed. Give the voter three votes and allow the voter to cast them 
in a preferential voting system, creating a condorcet cycle all by 
his or her lonesome. But ... I don't think this is realistically 
necessary, nor do I think it would enhance results, over simply 
approving all members of a Smith set at the top of the voter's 
preferances. (It is reasonable to assume that if a voter has a 
Condorcet cycle in the voter's list, that the voter has more-or-less 
equal preference between them, overall. And, remember, this is just 
one voter's vote. How accurate does it need to be? In Approval, the 
voter would approximate this condition pretty well by approving all 
three, and if that were offensive, then, clearly, the voter has a 
strong preference that should be given priority. The voter has to 
decide which pairwise election was more important.... Which one gave 
the voter chills? Which one made him or her feel like throwing up? 
Excited? Depressed? Etc.

Mostly, though, we do have an internal,transitive preference ranking, 
excepting blocks of candidates who are more-or-less equally 
preferred; such close preferences may shift from moment to moment, 
and because we may think differently about each pair, we could 
discover a Condorcet cycle, hence my discussion above. But I think 
there are sound reasons for a simple resolution being to equate the 
members of such a cycle and abstain from choosing between them. Leave 
that to the other voters, and probably any one of these would be 
reasonable as an acceptable winner (if at the top).

Further, it's unlikely that all three are all frontrunners.... And so 
practical Range Votes won't have the problem. The powerful vote is 
given to frontrunner preference pairs that are outside the Condorcet 
Cycle (i.e, only involve one of them at a time).