[EM] James, your 6-candidate example

[James Green-Armytage]

James Green-Armytage replying to Mike Ossipoff...

James:
>My earlier example could probably be conceived of as a spatial model in
>three dimensions
Mike:
>Not necessarily, unless that's what it was gotten from.
James:
>, but perhaps you would like one in two dimensions
Mike:
>The example that you give is in one dimension.

	Yes, you're right; I meant 2D and 1D rather than 3D and 2D.

Mike:
>I don't know of any errors, except for one big one: I didn't say that no
>one 
>could take victory from the CW and give it to A unless A has a sincere 
>plurality. I said that _the A voters_ can't take victory from from the CW 
>and give it to A unless A has a sincere Plurality.
>
	So, by "A voters", you meant voters who rank A in first place, rather
than voters who prefer A to the CW. In that case, you're right; I didn't
realize that you had placed this restriction on the set of candidates who
can perform the burying strategy. In that case, my 1-dimensional example
doesn't fit your restriction, as you say.
	However, I suggest that this restriction is not a very useful one. My
reasoning is as follows: If we are worried about a burying strategy
("offensive order reversal") in favor of candidate and A against the
sincere CW, the voters whom we should worry about are all of the voters
who prefer A to the CW. Whether A is their first choice or not is
irrelevant to whether the strategy is in their interest. Hence, A may not
be the plurality winner, but a successful burying strategy by those who
prefer A to the sincere CW is still possible, even in a 1-dimensional
example.

Mike:
>One thing for sure is that the guarantee holds when there are 3
>candidates, 
>and B, the CW, is between A & C, in the sense that I defined.
>That also means that it always holds when there are 3 candidates and 1 
>dimension. 

	I think that you're correct here, given the restriction noted above.

>I don't know in what sense, if any, something like my guarantee applies
>with 
>more than 1 issue dimension.

	Nor do I.
>
Mike, you wrote (in part):
>just repeating already-answered statements
...
>your pages of repetition. 
...
>continually repeating answered statements 
...
>slogging through your long repetition
...
>repetition of already-answered statements
...
>
>your repeated (and repeated and repeated...) statements 
...
>after that I won't reply to repetition from you.
>
	It strikes me as ironic that you repeat yourself so much in one diatribe
about my supposed repetitiveness.
	Anyway, for the record, I think that you're totally wrong when you assert
that my e-mails to you on the topic of voter strategy are nothing but
mindless repetition of points that you have long ago defeated. However, if
that is in fact your perception, I agree with you that our discussion is
not likely to be a satisfying or productive one.
	My perception is as follows: In the message that you so vehemently
complain about, I replied directly and earnestly to the salient points
that you had made in your preceding message, and my primary arguments are
unique to that message. Here are links to the two messages side by side,
in case anyone would like to have a verify one point of view or the other:
http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-April/015562.html
http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-April/015591.html
	I'm quite sure that there are points in my e-mail that you have not
answered yet. As for the points that you feel you have answered
satisfactorily, feel free to leave them alone, or refer me to a specific
posting (via link or date) in lieu of retyping a reply.
	
Sincerely,
James Green-Armytage