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Abd ul-Rahman Lomax wrote:<br>
<blockquote type="cite">
<pre wrap="">As written, AV satisfies the MC, and the arguments I see
on this, so far, do not really address the issue.</pre>
</blockquote>
What issue? Since you don't support the "MC", why do you even care if
it does<br>
or not?<br>
<br>
<blockquote type="cite">
<pre wrap="">Show me a proof
that AV does not satisfy the MC, but Plurality does.
To do so, you must define "strictly prefer."</pre>
</blockquote>
"Strictly prefer" means exclusively prefer. The "Majority Criterion" (I
don't like this name<br>
because Woodall uses it to refer to Majority for Solid Coalitions. I
prefer "Majority Favourite"<br>
or "Majority for a single candidate") means that if more than half the
voters prefer X to all<br>
other candidates, then X must win".<br>
<br>
What Approval in effect does is ask the voter to divide the candidates
into two sets at his/her<br>
discretion (technically one of these sets may even be empty) and then
tell us which set s/he prefers<br>
to the other. Only if the voter's preferred set happens to have one
member can we infer which<br>
candidate that voter prefers to all others.<br>
<br>
So really since the method doesn't ask the voter which candidate is
their exclusive favourite, it<br>
has no way of "knowing" who is the favourite of the majority is and so
of course can't and doesn't<br>
meet Majority Favourite/MC.<br>
<br>
Abd isn't the first sophist to try to argue that if a voter puts more
than one candidate in his/her <br>
preferred set, that must mean that he/she means to rank them all
equally in first place and so<br>
therefore if a majority don't put X alone in their preferred set X
can't be the majority favourite.<br>
<br>
(But that is like me gluing your legs together and then pretending that
you only have one leg.)<br>
<br>
<blockquote type="cite">
<pre wrap="">These voters, who have elected to use Approval
in this way, have abstained from indicating the "strict preference"
which is part of the Criterion, and therefore they are not party of
the "majority."</pre>
</blockquote>
The criterion doesn't stipulate that the majority have to be willing to
pay a price or engage in <br>
some perhaps risky strategy to express their strict preference for X
above all others.<br>
<br>
<blockquote type="cite">
<blockquote type="cite">
<pre wrap="">It is not accurate or honest to ignore voter preference or treat it as
irrelevant when the ballot does not allow it to be expressed!
</pre>
</blockquote>
<pre wrap=""><!---->
Does Plurality allow the expression of preference? How?
</pre>
</blockquote>
The only "preference" the criterion is concerned with is the first one,
and that is the one that FPP<br>
allows voters to express. Making the comparison with Approval, if the
voters are constrained to<br>
put a single candidate in their "preferred set", then of course that
candidate is their clearly voted<br>
strict favourite.<br>
<br>
<br>
Chris Benham<br>
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