[EM] A note on Approval strategy A.

[Rob LeGrand]

Forest wrote:
> 2 %  approve A only.
> 25 % approve both A and B
> 23 % approve C only.
>
> But note that (in the sample) every ballot that approves B also
> approves A.  If this is a real feature of the population, it will be
> impossible for B to get more approval than A.
>
> I think I would put my approval cutoff on the C side of A.

I would too, if I were convinced that the correlation was a real feature
of the population.  It depends on what your model of the electorate is
like.  If you have a model based solely on distributing the candidates'
expected vote totals, you'll want to use something in the style of
strategy A.  If you create a distribution based solely on the ballots
themselves (so that the numbers of different ballots are independent of
one another), you'll get something quite different.  Here's a more
dramatic example:

30% approve A and B
20% approve C and D

Say you rank the candidates A>B>C>D.  Strategy A would recommend voting
only for A.  But the ballot-distribution approach would recommend voting
for both A and C, skipping B.  The only approval strategy I know of that
takes as input only vote totals and ever skips is Warren Smith's
moving-average strategy.

> If nothing else, it is easy to approximate the winning (and tie for
> first place) probabilities by repeated Montecarlo simulations based on
> the distribution of the approval ballot profiles in the poll.

I'm working on using a similar kind of idea to develop an objective way
to evaluate plurality, approval and Borda strategies for use with DSV.

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

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