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James Green-Armytage wrote:<br>
<blockquote type="cite"
cite="midfc.005b8ffc00b892e33b9aca00913a0bcb.b89307@mcgregor.edu">
<pre wrap="">I wrote:
</pre>
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<blockquote type="cite">
<pre wrap="">majority criterion: If a majority of the voters prefers all of the members of a given set of candidates over all candidates outside that set, and they vote sincerely, then the winning candidate should come from that set.
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<pre wrap=""><!---->
Ken Johnson wrote:
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<pre wrap="">James - Can you elucidate why this should be a required criterion?
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<pre wrap=""><!---->
Sure. Look at it this way. Let's say that 55% of an electorate are to the
left of the center, and 45% are to the right of center. If a method goes
ahead and elects a right of center candidate anyway, then we know
something has gone wrong. Plurality is problematic for this reason, and so
is approval. </pre>
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What has gone wrong? Consider, for example, a specific CR profile:<br>
55%: A=99, B=100<br>
45%: A=99, B=0<br>
If people vote sincerely, the election goes to candidate A. Of course,
the voters who have a slight preference for B may insincerely give A a
zero rating, so that B wins. This isn't necessarily a good outcome, it
is just an unavoidable consequence of insincerity. But with more
candidates, this result may not be unavoidable. For example, suppose
the CR profile with a third candidate C is as follows,<br>
55%: A=99, B=100, C=0<br>
45%: A=99, B=0, C=100<br>
Now, unless the B supporters know for sure that they are a majority,
they will vote sincerely and the election will go to candidate A, who
has the strong, unanimous approval of all voters. This is arguably not
a bad outcome.<br>
<blockquote type="cite"
cite="midfc.005b8ffc00b892e33b9aca00913a0bcb.b89307@mcgregor.edu">
<pre wrap=""> The goal of single winner voting is majority rule. While majority rule is
fraught with dangers and paradoxes, it is axiomatically preferable to
minority rule. Given two groups of different size with irreconcilable
opinions on a given issue, any value-neutral decision-making rule must
logically chose to execute the wishes of the larger group.
James
</pre>
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It may be that majority rule is preferable, but as illustrated above it
is clearly not self-evident that majority rule is always preferable.
Therefore majority rule should not be posited axiomatically; it needs
to be justified on the basis of a more fundamental statement of "the
goal of single-winner voting".<br>
<br>
Ken Johnson<br>
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