At 08:30 PM 6/27/2013, Benjamin Grant wrote:
Something else came up while I was analyzing
some voting methods. If you have a
disproportionate number of political leaning in
an election, some voting systems go awry.
I didn't know what this meant when I first read
it, and there is a grammatical error contributing
to that. Benjamin, would you mind proof-reading
your posts? Yes, some people can't do that, and
if you can't, okay, but ... just understand that
you lessen the number of people who will read
what you write if the lead paragraph is incomprehensible.
Then I guessed what it mean. And that guess was
wrong. In fact, reading the further explanation,
the introduction just doesn't make sense. It means something else.
There may be a criterion for this, this is what I mean.
Condorcet criterion, for starters. The nameless
Range Criterion (i.e, maximized expressed social
utility.) Some voting systems don't collect enough data to handle this.
Lets say that you have three total
candidates. one is conservative, two are
liberal, none are moderate. If the majority of
the electorate is conservative, then it may make
sense that a conservative gets chosen. However,
in some systems say one in which each voter
gets one positive vote and one negative vote to
cast having more candidates of a particular
wing can hurt you. Continuing this example, if
we run Gore/Nader/Bush, both Gore and Nader
supporters give their negative votes to Bush,
casting their positive votes for their own candidate.
Standard vote-splitting problem.
If Gore supporters are 36%, and they vote Gore
+1, Nader 0, Bush -1; and Nader supporters are
10%, and they vote Gore:0, Nader +1, Bush -1;
and Bush supporters are the remaining 54% and
they vote Gore -1, Nader 0, Bush +1
Nader wins. Even though 54% of the people voted
for Bush. Even though only 10% voted for Nader.
The stated votes are *insane.* Not that this
matters, people propose insane voting patterns
all the time, to make this or that point. It
would help to recognize it. ("I am making up this
insane voting pattern just to show how the system would handle it.")
That is, the stated problem is "too many voters
in one wing." But the voting patterns establish
Nader as in the center. You simply *said* that
Nader was "in the same wing," but then you did
not have the voters vote that way.
Of course, you can define a "Wing" any way you
like, by placing the "center" where you choose.
Voting that way, as in the example, we have this situation:
36% of the voters, Gore supporters: Nader is
closer to them than Bush. Consisent with Nader
being Center, not completely consistent with
Nader being Left. (for some Gore supporters,
Nader, if to the left, would be futher from them
than Bush. But if there is a wide enough gap
between the Gore and Nader factions, it could
happen that all Gore voters would vote this way. But they are in a minority.)
10% of voters, Nader supporters: Gore is closer
to them than Bush. Consistent with Nader being
Left, not consistent with Nader being Center.
Center factions will split on who is closer, Left or Right.
54% of voters: Nader is closer to them than Gore.
Not consistent with Nader being Left, consistent with Nader being Center.
From the voting pattern, it's conclusive: Nader
is in the center, as viewed by the majority, and
consistently with the rest of the votes, in spite
of the stated claim that there is no center candidate.
There is a problem with +/- range voting, having
to do with the 0 default that is often assumed.
But we can look at this election as Range 2, by
adding a value of 1 to all votes, and considering
that there were no abstentions. We have a
situation where *every voter* rates Nader as
midrange -- election expectation -- or better.
Nader will win this election in Range, and this
is an example where Condorcet compliance would
damage social utility. I have suggested that it
is defective to accept this result without the
explicit consent of a majority, and, in this
case, if a midrange rating is openly an approval
rating, *every voter has consented.*
The example does not show any problem except in
the analysis as being a "wing" problem. It *looks
like* a Majority Criterion failure, except that,
by giving a half-vote to Nader, the majority
waived its majority rights, that was not the
"exclusive preference" that the majority
criterion requires. The majority approved both
Bush *and* Nader. And *everyone* approved Nader.
So why would one think Bush should win?
There is an answer to that, and it would be a
belief in the Condorcet Criterion as what I used
to call it, the Queen of Voting Systems Criteria.
Is this a thing? Kind of the opposite of the
spoiler effect that having many like-minded
candidates actually increases the chance that
one of them might win, even if their opposition is more numerous?
The example does not show anything about
"like-minded candidates." Rather, it shows how we
casn make up things, express them, and it all
looks sensible to us, because we see only a small
percentage of what is actually in front of our
eyes, as we became socialized and "experienced."
There is a way out of this trap, but few are
interested in it. It can threaten our *identity.*
Most of us would rather be right than happy.
Does this only happen with negative votes? Or
can it happen with other methods?
The example shows no effect from negative votes.
That was noise that helped you to remain
confused, Benjamin. The exact same "issue" would
appear with Range 2, i.e,. votes of 2,1,0, and it
could appear with any Range system. It's a *feature*, not a bug.
The violation is of the Condorcet criterion,
because Bush wins all the pairwise elections.
That's because the Criterion pays no attention to
preference strength. A situation like that
described shows the breakdown of the Criterion,
it can occur where a majority has weak
preferences whereas a minority has strong
preferences. If that is *actually the case,* not
just some artifact of defective strategy, then
social utility is optimized by the violation of
the Criterion in favor of the range winner.
The essential error here was to treat a Range
(Score) election as if it were a ranked election,
because every voter *strictly ranks* the
candidates, using the three available ratings.
That won't happen. If the real situation is that
the left-right axis is occupied by, Left to
Right, Nader, Gore, Bush, then, if voters vote
based on axis position, no Bush voters (the
majority in this model! -- not in real life in
2000) will min-rate Nader, since they would
prefer Gore to Nader; and if, for strategic
reasons (sane if Bush and Gore are frontrunners),
they min-rate Gore, they would *also min-rate*
Nader. Otherwise they would min-rate Nader and
mid-rate Gore. Not mid-rate Nader, ever.
But voters don't vote exclusively based on a
single axis, that is another general problem with many analyses.
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