[EM] Re: "Weighted Pairwise" proposal (Oops!)

[Chris Benham]

James G-A,
Yes,  I  goofed.  You wrote  (Tue.Aug.31):

>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: 
>>
>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
>>
>	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.
>
CB: Yes, by "average" I mean the arithmetic mean of  the Schwartz-set 
members on the ballot  ("marked" or not, unmarked are rated zero).
Your calculations are correct. The "automated" approval scores are  A55, 
 B15, C45.   Using the margins between these scores to rank
the pairwise results, we get  C>B +30,  A>C +10,  B>A -10, giving the 
final order  A>C>B.  
A easily wins, and so the A voters'  Burying (by truncation) succeeds. 
Looking at the sincere votes on which a above example is based:

>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
>
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
utility winner (and B is the lowest).

I previously wrote that Blake Cretney's  Sincere Expectation Criterion 
(SEC) is a weaker version of  the No Zero-Information Strategy
criterion/standard, which says that with no information or guess about 
how others might vote, the voters best  "strategy" is to give a full
sincere ranking.
I  think NZIS  (but not SEC) is  incompatible with Non-Drastic Defense, 
because if  a majority (who agree in preferring some
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).
Probably any method  that meets Symetric Completion (or has 
Later-no-harm and Later-no-help in balance)  and fails NDF meets NZIS.
Lots of ordinary methods, like FPP, IRV, TTR,  Borda (either with 
truncation not allowed or the ballots in-effect symetrically completed) 
all meet it.

Chris Benham





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