[EM] Re: Election-methods Digest, Vol 3, Issue 18

[Alex Small]

Paul Kislanko wrote:
>Prove that you can infer my pair-wise choices from my ranked ballot, if you
>want to use my ranked ballot to populate a pair-wise matrix.
>
>It can't be done. So just allow the voters to explicitly input their pair-wise preferences.
>
>This is not rocket science.

Um, OK.
 
Let's that your particular preference order amonst N candidates happens to be:
 
C_1>C_2>...>C_N-1>C_N
 
where I have conveniently assigned the candidates names (well, numbers) derived from your preference order, just to keep the notation simple.

I can infer that in a contest between candidates C_i and C_j you prefer candidate C_i if i<j, and you prefer candidate j if i>j.
 
Now, let's suppose that you indicated indifference between some candidates (i.e. you ranked them equally), so that some of the ">" signs above should be changed to "=" signs.  Well, I think we can all see how you'd vote in those pairwise contests:  You'd abstain.
 
This isn't rocket science.
 
Now, you might say "Oh, but my ranked ballot doesn't represent my true preferences.  In truth my preferences are cyclic."
 
OK, well, let's sit down and chat.  I say to you "Paul, which candidate do you most want to win?"  You ponder it and then you give me an answer.  If you don't then you haven't made up your mind and you won't be voting in this election.  Or at least I assume you won't be voting, because you don't seem sure whom you want.
 
Anyway, you give me an answer.  You say "I'll take candidate C_1, please."

Then I turn to you and say "OK, but what if candidate C_1 dropped out of the race after tearfully admitting to being the governor of New Jersey?  Whom do you want then?"  And you deliberate over it, but in the end you admit that you would take candidate C_2.
 
Well, we now know 2 entries in your preference order.  C_1>C_2>all others.
 
So then we come up with some reason why C_2 will drop out as well.  And I ask whom you want instead.  You say C_3.  So now we know that your preference is C_1>C_2>C_3>all others.  We continue this for all N candidates and get a preference order.
 
You can say what you want about cyclic preferences, but I maintain that I've just described a procedure for elucidating your preferences, and I've described a procedure for elucidating your pairwise preferences from your ordinal preferences.
 
 
>OK, I give up. This board is too hard to use and there's no one on it who
>cares about any opinion but their own. 

With regard to caring about the opinions of others, I think you just described, to some extent, every internet forum I've ever seen.
 
 
 
Alex

		
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