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Scott Ritchie wrote:<br>
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<pre wrap="">On Wed, 2006-12-13 at 21:06 +1030, Chris Benham wrote:
</pre>
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<pre wrap="">Scott Ritchie wrote:
</pre>
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<pre wrap="">I was thinking about corporate elections today, and how under some
voting systems an individual would want to strategically vote by
submitting multiple, different ballots. I soon realized that this was
generalizable to multiple voters with identical preferences in any
election.
Basically, something like "If a group of voters share the same
preferences, then their optimal strategy should be to vote in exactly
the same way."
</pre>
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<pre wrap="">Scott,
Are you referring to 0-info. strategy, or to informed strategy?
Chris Benham
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<pre wrap=""><!---->
Good point. STV is only violated with informed strategy, I think
(though I may be wrong), while SNTV may be violated with 0 info.
Does "size of the electorate and of my group" count as information for
our purposes, or is information just the preferences of other voters?</pre>
</blockquote>
"Our" purposes? This criterion is *your* idea! :) But if it refers to
informed strategy, I don't see the<br>
point of limiting the type of information. <br>
<br>
Maybe you can have more than one version of the criterion, varying
according to to the amount and type<br>
of information this "group of voters" has.<br>
<br>
Assuming this faction is perfectly informed and coordinated, methods
like IRV that fail mono-raise and are<br>
vulnerable to the Pushover strategy certainly fail this criterion.<br>
<br>
Also "Approval Margins Sort"(AMS) aka "Approval-Sorted Margins" fails
it.<br>
<br>
<a class="moz-txt-link-freetext" href="http://wiki.electorama.com/wiki/Approval_Sorted_Margins">http://wiki.electorama.com/wiki/Approval_Sorted_Margins</a><br>
<br>
Suppose the voting intentions are:<br>
44: A|>B<br>
46: B| <br>
07: C|>A<br>
03: C>B|<br>
<br>
AMS is a Condorcet method that uses ranked ballots with approval
cutoffs (signified by | ).<br>
On these votes A is the CW and wins. Assuming that only the 46 B voters
are informed and strategy minded,<br>
what can they do to make B win the election?<br>
<br>
If they all vote the same way they can't elect B, but if 30 of them
vote B>C| and the other 16 vote B|>C, then<br>
B wins.<br>
<br>
44: A|>B<br>
16: B|>C<br>
30: B>C|<br>
07: C|>A<br>
03: C>B|<br>
<br>
Now the approval order is B49, A44, C40.<br>
A>B and C>A. The "approval margin" between A,C (4) is smaller
that that between B,A(5) so the first <br>
"correction" to our order of candidates is for A and C to swap
positions to give B49, C40, A44.<br>
This order is now in harmony with the pairwise defeats (B>C>A) so
B wins.<br>
<br>
If instead the 46B supporters had all voted B|>C then A would
have won, and if they'd all voted B>C|<br>
C would have won.<br>
<br>
Note that this strategising couldn't have worked with DMC (my
favourite in this genre) because it has an<br>
anti-burial property (I call "Approval Dominant Mutual Third Burial
Resistance") that says that if there are<br>
three candidates XYZ, and X wins and is exclusively approved on more
than a third of the ballots, then changing<br>
some ballots from Y>X to Y>Z can't change the winner to Y.<br>
<br>
<a class="moz-txt-link-freetext" href="http://wiki.electorama.com/wiki/Definite_Majority_Choice">http://wiki.electorama.com/wiki/Definite_Majority_Choice</a><br>
<br>
Chris Benham<br>
<br>
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