[EM] Re: Election-methods digest, Vol 1 #517 - 3 msgs
Ken Johnson
kjinnovation at earthlink.net
Wed Feb 25 21:52:36 PST 2004
> Message: 3
> Date: Wed, 25 Feb 2004 01:15:41 +0000
> From: "MIKE OSSIPOFF" <nkklrp at hotmail.com>
> Subject: [EM] There's nothing wrong with Average Rating.
>
>
> ...
>
> CR is strategically equiovalent to Approval: In CR, you maximize your
> expectation by giving maximum points to those candidates for whom
> you'd vote in Approval, and giving minimum points to the rest.
>
> That's one reason why CR isn't emphasized much here, because it's
> strategically equivalent to the simpler Approval method.
>
Chris Benham has been trying to explain this to me in an offline
discussion, but I still don't get it. Suppose my preference ranking
(inferred from my "sincere" CR ratings) is A > B > C. Naturally, I
should strategically give A the highest possible rating and C the
lowest. If I know A will beat C, I should give B the lowest rating to
ensure that A wins over B. If I know C will beat A, I should rate B
highest so that C does not win over B. But if I don't know which of A or
C will come out ahead, my strategy options are more complicated. If I
give B a low rating, this increases A's chance of winning, but it also
increases C's chance of winning. If I raise B's rating to shut out C, I
also run the risk that A will lose. It's not clear to me that the best
compromise strategy wouldn't be to give B an intermediate rating
somewhere between A and C.
In my view, strategy is basically a game of judging probabilities and
weighing tradeoffs. If you were to formulate the objective of voting
strategy mathematically (has anyone done this?), you would probably find
that for the above case the optimum strategy can be defined in terms of
a function giving your optimum B rating as a function of your sincere
candidate ratings and your estimated probability distributions for the
aggregate group ratings. Whatever the form of this function, my guess is
that it would be continuous. (For simplicity, I assume rating levels are
not discretized.) Furthermore, the function range covers the high and
low rating limits (as demonstrated above), so for any intermediate
rating level there will be some condition under which your optimum B
rating is at that level, implying that CR is not strategically
equivalent to Approval.
On the other hand, it may be that the optimum-rating function looks more
and more like a discontinuity as the number of voters increases, so I
could be wrong - maybe CR does reduce effectively to Approval for large
voting populations. I don't know. Furthermore, if the optimum CR
strategy is so horrendously complicated that it can't be stated in plain
English terms that the average voter can understand, that alone may be
sufficient grounds for eschewing CR in favor of Approval.
Comments?
Ken Johnson
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