[EM] Generalizing "manipulability"

[Abd ul-Rahman Lomax]

At 01:38 AM 1/18/2009, Juho Laatu wrote:
>I don't quite see why ranking based
>methods (Range, Approval) would not
>follow the same principles/definitions
>as rating based methods. The sincere
>message of the voter was above that she
>only slightly prefers B over A but the
>strategic vote indicated that she finds
>B to be maximally better than A (or
>that in order to make B win she better
>vote this way).

That is an *interpretation* of a Range vote. In fact, they are just 
votes, and the voter casts them according to the voter's 
understanding of what's best. This has been part of my point: Range 
votes don't "indicate" preference strength, as such. Consider 
Approval, which is a Range method. If the voter votes A=B>>C=D, what 
does this tell us? We can infer some preferences from it, to be sure, 
and those preferences are probably accurate, because Approval never 
rewards a truly insincere vote. But does this vote "indicate" that 
the voter has no preference between A and B, nor between C and D? Of 
course not!

Now, a Range vote. But the voter votes Approval style. What does this 
tell us about the voter preferences? *Nothing more and nothing less.* 
The voter chose to vote that way for what reason? We don't know!!!

They are votes, not sentiments. Voters may choose to express relative 
preference, in Range, with some fineness of expression, but they may 
also choose not to make refined expressions, and all these votes are 
sincere, i.e., they imply no preferences that we cannot reasonably 
infer from them with a general understanding that the voter had no 
incentive to show preferences opposite to the actual.

(Now, there is a kind of insincere voting that voters may engage in, 
but it isn't really rewarded, and voters will only do it when they 
expect it to be moot. And they may do this kind of insincere voting 
with any method whatever.)