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).
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