# [EM] Re: Election-methods digest, Vol 1 #517 - 3 msgs

Adam Tarr atarr at purdue.edu
Wed Feb 25 22:48:02 PST 2004

```Ken Johnson wrote:

>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.

My intuition is that that would be the case.  Basically, it comes down to
this.  After some, possibly messy, calculations, you will derive some
expected utility for voting for candidate B.  If that expected utility is
positive, then you should maximize your utility by giving B 100.  If that
expected utility is negative, you should maximize your utility by giving B
0.  Only when that expected utility is zero (i.e. your feelings toward B
are exactly equal to your expectation of the election outcome) does a vote
between zero and 100 make sense - of course you can put B anywhere in that
case.

Your mention of "large voting populations" is crucial, since it allows me
to assume that the marginal utility for an additional ranking point given
to candidate B remains constant through the entire 0->100 range.  On a
small committee, this may not be the case, so it's possible (I'm not sure)
that intermediate rankings make sense in that case.

>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.

Well, I don't see CR strategy as much trickier than approval, which has
some relatively simple strategies that work well.  The best simple strategy
I know of is to approve your favorite of the top two candidates, plus
anyone you like more than the front-runner.  That said, it is more
strategically tricky than winning votes Condorcet (just rank the candidates).

The issue with CR is that some voters will treat it like approval voting,
while others will use lots of intermediate rankings, and may not even put
their favorite at 100 and their least favorite at zero.  CR gives the
voters a chance to shoot themselves in the foot in a way that approval does
not.  That said, as Mike pointed out, CR may be an easier sell, due to
people's familiarity with CR in the Olympics and such.

-Adam

```

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