[EM] Re: Cardinal Ratings vs. Approval Voting (vs. IRV)

[Rob LeGrand]

Bill Lewis Clark wrote:
> Suppose voter preferences are as follows:
>
> A>B>C, approve AB -- 30%
> A>B>C, approve A  -- 21%
> C>B>A, approve BC -- 25%
> C>B>A, approve C  -- 24%

But the voters who approved A and B aren't using their optimal strategy. 
They could achieve a better result by approving only A.

CR and AV are strategically equivalent, which means that voters' using
optimal strategy in AV leads to the same winner as voters' using optimal
strategy in CR.  In other words, it only makes sense to vote cardinal
ratings at the extremes.  Show me a CR election in which some voters vote
cardinal ratings somewhere between the extremes and I'll show you how they
all could do at least as well by voting only at the extremes.

> A>B>C, A:2, B:1, C:0 -- 30%
> A>B>C, A:2, B:0, C:0 -- 21%
> C>B>A, A:0, B:1, C:2 -- 25%
> C>B>A, A:0, B:0, C:2 -- 24%

Here the A voters who vote 1 for B could do at least as well by voting 0
for B.  In fact, by doing so, they'd remove the possibility that the C
voters could elect B by voting 2 for B, which would be an improvement from
their point of view.

=====
Rob LeGrand, psephologist
rob at approvalvoting.org
Citizens for Approval Voting
http://www.approvalvoting.org/

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