[EM] Generalizing "manipulability"

[Kristofer Munsterhjelm]

Jonathan Lundell wrote:
> On Jan 17, 2009, at 4:31 PM, Juho Laatu wrote:
> 
>> The mail contained quite good
>> definitions.
>>
>> I didn't however agree with the
>> referenced part below. I think "sincere"
>> and "zero-knowledge best strategic"
>> ballot need not be the same. For example
>> in Range(0,99) my sincere ballot could
>> be A=50 B=51 but my best strategic vote
>> would be A=0 B=99. Also other methods
>> may have similarly small differences
>> between "sincere" and "zero-knowledge
>> best strategic" ballots.
> 
> My argument is that the Range values (as well as the Approval cutoff 
> point) have meaning only within the method. We know from your example 
> how you rank A vs B, but the actual values are uninterpreted except 
> within the count.
> 
> The term "sincere" is metaphorical at best, even with linear ballots. 
> What I'm arguing is that that metaphor breaks down with non-linear 
> methods, and the appropriate generalization/abstraction of a sincere 
> ballot is a zero-knowledge ballot.

Wouldn't it be stricter than this? Consider Range, for instance. One 
would guess that the best zero info strategy is to vote Approval style 
with the cutoff at some point (mean? not sure). However, it would also 
be reasonable that a sincere ratings ballot would have the property that 
if the sincere ranked ballot of the person in question is A > B, then 
the score of B is lower than that of A; that is, unless the rounding 
effect makes it impossible to give B a lower score than A, or makes it 
impossible to give B a sufficiently slightly lower score than A as the 
voter considers sincere (by whatever metric).