[EM] majority rule vs. maximum approval (was: least additional votes)

[James Green-Armytage]

James G-A replying to Forest Simmons, about fundamental Condorcet vs.
approval issues

>James opined that the winner should always come from the Smith set
>because 
>otherwise majority rule is violated more than necessary.
>However, it seems to me that majority is just one form of consensus.
>Max approval is another form.

	Majority rule methods don't aim for consensus. They are used when
consensus is considered impossible/impractical.
>
>Consider (sincere)
>52 A>B>>C
>48 B>C>>A
>Candidate B is the max approval candidate.
>Candidate A is the majority candidate.
>Which is the "consensus" winner?

	Impossible to say. Most likely none of the above. A consensus winner
would have to be accepted by all voters.
>
>I maintain that if the voters had to reach a consensus, as jurors are 
>required to do on important cases, and as cohousing shareholders require 
>for important community decisions, that B would be the more likely 
>consensus candidate.

	It's hard to say. Anyway, I suggest that establishing such a consensus
between 300 million people (for example) would be impossible. Imagine that
just one person stubbornly refused to accept nothing other than something
which nearly everyone else considered to be truly crazy.
>
>I believe that in a system that has caulked up all of the trickle down 
>leaks the democratic ideal of relative equality is better served by the 
>alternative that the most find acceptable, than the option that the bare 
>majority considers best and the rest find intolerable.

	That may be so, but it is hard to determine exactly how "acceptable"
people actually find a particular option. This is the classic
interpersonal comparison of utilities problem. If the majority in your
example above wanted to, they could easily pretend that they found B
intolerable (e.g. by voting A>>B>C), in order to keep their first choice.
	One method that addresses this might be to give voters the option of
voluntarily reducing the weight of particular pairwise preferences. If
they were feeling honest/selfless, some of our 52 voters could give 1/2
strength to their A>B preference, while maintaining whole strength for
their A>C preference and B>C preference. But if the voters in the majority
aren't so chivalrous, there's not much that can be done about it.
>
>In my opinion, the sincere approval winner is usually better for society 
>than the sincere Condorcet Winner when the two are different.

	I don't think that the "sincere" approval winner is as well-defined as
the sincere Condorcet winner, because "approval" is not as well-defined as
preference.
>
>But both of these are elusive candidates because of insincere ballots.

	I argue that the "sincere approval winner" is substantially more elusive
than the sincere Condorcet winner, both for reasons of strategic incentive
and well-definedness as stated above.
>
>Furthermore, I think that unless both the Approval Winner and the 
>Condorcet Winner have chances of winning, there will usually be some 
>incentive to vote insincerely.
>In the above scenario if the CW candidate A is given no chance of
>winning, 
>then A supporters will move B below the approval cutoff, even though they 
>consider A only slightly better than B, whom they consider perfectly 
>acceptable.
>In another example (sincere)
>45 A>>C>B
>30 B>>C>A
>25 C>A>>B
>unless the approval winner A is given some chance of winning, the first 
>faction will reverse the C>B preference and create a cycle that any 
>reasonable Condorcet method would give to A.

	Interesting example! It's kind of like a Mexican standoff... Maybe I'll
have more to say about this later. Of course, if other voters besides the
A voters use strategies of their own, then A will not necessarily win;
there are many possible scenarios, which could result in the election of
any of the three candidates. A may be a likely favorite in that he is the
plurality winner, and the majority coalition that opposes him is not
strong. However, there are plenty of scenarios where B voters could vote
B=A>C, either directly or through some anti-strategy mechanism (e.g.
AERLO, CWP, AWP, CWO, etc.). Also, the C voters could conceivably hand the
result to B, whether on purpose (to punish the A voters) or through a
failed deterrent strategy. 
>
	More thought-provoking examples are always welcome.
>
>It doesn't bother me that Least Additional Votes sometimes picks outside 
>Smith.  So does Approval, and it is one of the best possible public 
>proposals.

	I strongly prefer approval to plurality, but I currently don't prefer it
to equal rankings IRV or good pairwise methods.
>
>In Approval voter strategizing (when not misled by disinformation) tends 
>to get winners from the Smith set.

	Right. So why not use a Smith-efficient method to begin with? This way,
you save a lot of the costs and uncertainties associated with formulating
and coordinating strategy, and you reduce the chances that voters will not
use optimum strategy, leading to a non-Smith-set winner that causes
unambiguous majority regret.
	It's like using single non-transferable vote (SNTV) instead of STV.
Theoretically, with perfect coordination, SNTV will produce the same
results as STV... so why waste all that effort on coordination when you
can use ranked ballots and simulate coordination with a simple algorithm?
>
>I suspect the same would happen with Least Additional Votes.

	Right. Same criticism applies.
...
	In conclusion, I agree that it's logical to be uncomfortable with
majority rule. I agree that super-majorities should be sought more often,
and that democracy should involve more of an attempt to communicate and
find common ground, rather than simply pitting different factions against
each other in a sort of war/team/battle mode. 
	However, if we've reached the point where a decision has to be made one
way or another, and we've accepted the need to use a method where a bare
majority CAN unilaterally determine the result, then we might as well
choose a method that facilitates the process of revealing the actual
majority winners with minimum hassle rather than a method that more
roughly approximates a majority decision after much second-guessing and
outside coordination. Hence, for single-winner purposes where
supermajority requirements are not appropriate, we should choose a
Smith-efficient method (with good anti-strategic protection).
>
my best,
James
fc.antioch.edu/~james_green-armytage/voting.htm