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James G-A,<br>
Yes, I goofed. You wrote (Tue.Aug.31):<br>
<blockquote type="cite">
<pre>I don't understand how B got an automated approval score of 55. When I
did it, I got a score of 15 instead of 55. Here are the ballots again:
><i>
</i>45: A 100 > B 0 = C 0
10: B 100 > A 90 > C 0
5: B 100 > C 90 > A 0
40: C 100 > B 40 > A 0
><i>
</i> When you say "rate above average", what exactly do you mean? By
"average", do you mean the average of all the possible ratings, i.e. 50?
Do you mean the arithmetic mean of all the candidates marked on that
ballot? Or do you mean the median of all the candidates marked on the
ballot. I'm guessing it's the arithmetic mean of the candidates. If so,
let's take one of the people who voted C100>B40>A0. The arithmetic mean of
the candidates on this ballot is 46.67. So, only candidate C is rated
above the mean.</pre>
</blockquote>
CB: Yes, by "average" I mean the arithmetic mean of the Schwartz-set members
on the ballot ("marked" or not, unmarked are rated zero).<br>
Your calculations are correct. The "automated" approval scores are A55,
B15, C45. Using the margins between these scores to rank<br>
the pairwise results, we get C>B +30, A>C +10, B>A -10, giving
the final order A>C>B. <br>
A easily wins, and so the A voters' Burying (by truncation) succeeds. Looking
at the sincere votes on which a above example is based:<br>
<blockquote type="cite">
<pre>45: A 100 > B 0 = C 0
10: B 100 > A 90 > C 0
5: B 100 > C 90 > A 0
40: C 100 > B 40 > A 0</pre>
</blockquote>
If I was going to continue to defend AAM, I would say that this result
(A winning) is not so bad, because A is the highest sincere social<br>
utility winner (and B is the lowest).<br>
<br>
I previously wrote that Blake Cretney's Sincere Expectation Criterion (SEC)
is a weaker version of the No Zero-Information Strategy<br>
criterion/standard, which says that with no information or guess about how
others might vote, the voters best "strategy" is to give a full<br>
sincere ranking.<br>
I think NZIS (but not SEC) is incompatible with Non-Drastic Defense,
because if a majority (who agree in preferring some<br>
individual candidadate to some other individual candidate) can block the
election of the undesired candidate by voting all the candidates they prefer
to that candidate in equal-first place (but otherwise maybe not), then it
probably follows that if the zero-information voter has sufficiently large
gap in hir ratings, that voter will be better off insincerely voting all
the candidates above the gap in equal-first place (hoping to be part of a
majority that does likewise).<br>
Probably any method that meets Symetric Completion (or has Later-no-harm
and Later-no-help in balance) and fails NDF meets NZIS.<br>
Lots of ordinary methods, like FPP, IRV, TTR, Borda (either with truncation
not allowed or the ballots in-effect symetrically completed) all meet it.<br>
<br>
Chris Benham<br>
<pre>
</pre>
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