[EM] Why it doesn't matter if prefer means anything

[Jobst Heitzig]

Dear Mike!

You insist that it doesn't matter what prefer means and simultaneously define this:
> Definition of sincere voting:
> 
> A voter votes sincerely if s/he doesn't falsify a preference, or fail to 
> vote every preference that the balloting system in use would have allowed 
> him/her to vote in addition to the preferences that s/he actually did vote.
> 
> [end of definition of sincere voting]

Now let us consider a situation with three candidates A,B,C and a voter with preferences A>B,B>C,C>A 
(which is surely allowed by you since you pose no restrictions on what preferences one might have).
With your definition, there is no way for this voter to vote "sincerely" on, say, an approval ballot: 
(i) approving noone or all three, she "fails to vote every preference that the balloting system in use would have allowed her to vote in addition to the preferences that s/he actually did vote" since the system allows her to vote A>B by approving A but not B.
(ii) approving one or two candidates, say only A or A and B, she falsifies a preference A>C.
Also, there is no "sincere" way of voting on a standard ranked ballot:
(iii) ranking no-one or all three tied for top is like (i)
(iv) ranking only one candidate, or two tied for top, is like (ii)
(v) ranking A>B>C or A>C>B falsifies A>C

What do you think of this is light of the obvious requirement that the system should provide every voter with at least one sincere way of voting?

Yous, Jobst

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