[EM] Is there a criterion for identical voters casting identical ballots?

[Chris Benham]

Scott Ritchie wrote:

>On Wed, 2006-12-13 at 21:06 +1030, Chris Benham wrote:
>  
>
>>Scott Ritchie wrote:
>>
>>    
>>
>>>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."
>>> 
>>>
>>>      
>>>
>>Scott,
>>Are you referring to 0-info. strategy, or to informed strategy?
>>
>>Chris Benham
>>    
>>
>
>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?
>
"Our" purposes? This criterion is *your* idea! :)  But if it refers to 
informed strategy, I don't see the
point of limiting the type of  information.

Maybe you can have more than one version of the criterion, varying 
according to to the amount and type
of information this "group of voters" has.

Assuming this faction is perfectly informed and coordinated, methods 
like IRV that fail mono-raise and are
vulnerable to the Pushover strategy certainly fail this criterion.

Also "Approval Margins Sort"(AMS) aka "Approval-Sorted Margins" fails it.

http://wiki.electorama.com/wiki/Approval_Sorted_Margins

Suppose the voting intentions are:
44: A|>B
46: B| 
07: C|>A
03: C>B|

AMS is a Condorcet method that uses ranked ballots with approval cutoffs 
(signified by | ).
On these votes A is the CW and wins. Assuming that only the 46 B voters 
are informed and strategy minded,
what can they do to make B win the election?

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
B wins.

44: A|>B
16: B|>C
30: B>C|
07: C|>A
03: C>B|

Now the approval order is  B49,  A44,  C40.
A>B and C>A. The "approval margin" between A,C (4) is smaller that that 
between B,A(5) so the first
"correction" to our order of candidates is for A and C to swap positions 
to give  B49, C40, A44.
This order is now in harmony with the pairwise defeats (B>C>A) so B wins.

If instead the 46B supporters had all voted  B|>C  then  A would have 
won, and if they'd all voted B>C|
C would have won.

Note that this strategising couldn't have worked  with  DMC  (my 
favourite  in this genre) because  it  has  an
anti-burial property  (I call  "Approval Dominant Mutual Third Burial 
Resistance") that says that if there are
three candidates XYZ, and X wins and is exclusively approved on more 
than a third of the ballots, then changing
some ballots from Y>X to Y>Z can't change the winner to Y.

http://wiki.electorama.com/wiki/Definite_Majority_Choice

Chris Benham

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