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

Paul Kislanko kislanko at airmail.net
Mon Sep 6 18:14:05 PDT 2004




From: election-methods-electorama.com-bounces at electorama.com
[mailto:election-methods-electorama.com-bounces at electorama.com] On Behalf Of
Alex Small
Sent: Monday, September 06, 2004 7:46 PM
To: election-methods-electorama.com at electorama.com
Subject: [EM] Re: Election-methods Digest, Vol 3, Issue 18


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




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.


===== you are not allowed to infer that ======= 


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.


Correct, but now we don't get to sit down and have that chat. 


Infer from my original ballot what I would have said if we did get to
discuss it after my first choice is eliminated WITHOUT asking me. You can't.


The question was not "who did I want to win", it was "what is my ranked
ballot", and obviously who I wanted to win was my first choice. The
assumption that my second choice for first would be the second on my ranked
warranted, because just as you said, if you'd asked me a second time I
might've given an answer that was different from C_2 on my first ballot.


 That's all I (and Jobst) have been trying to say. The ranked ballot does
not necessarily reflect an individual's pair-wise preferences. If we had
that little chat, and you told my first choice was unavailable and asked me
who my choice was given that, I'd integrate issues over remaining candidates
and come up with an answer, but there is no particular reason to assume that
it would be the same answer as the one listed in position 2 on my original
ranked ballot. 


Now, if the vote-counting is IRV, I would know to fill out the ranked ballot
as if we'd had that chat. But if the vote-counting is a Condorcet-based
system that depends upon pair-wise comparisons, I have to know a lot more
than who my 2nd-favorite choice is. In IRV, I would be happy with A>B>C>D>E
because that integrates all my issues over all candidates' positions
exactly. But in a Condorcet-based system I'd be less than happy with the B>E
inference on at least one issue.


I don't see how it creates a problem for any method that depends upon
pair-wise comparisons to count the votes to allow voters to explicitly state
pair-wise preferences. To just say voters are stupid and must conform to the
method to make the method easier to analyze just strikes me as academic



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