[EM] Sincere Zero Info Range/Approval Voting

Forest Simmons fsimmons at pcc.edu
Sat Nov 7 21:48:20 PST 2020

Robert Bristow-Johnson asked how to know whether or not to approve one's
second choice. He was talking sincere non strategic voting.

Andy Jennings answered how to do that by considering whether or not you
would prefer the candidate in question to a coin flip between your top and
bottom ranked candidates.

Toby Pereira gave another approach ... first rate each candidate on a scale
0 to 100% and then go from there. He made the point that sometimes the
easiest way to rank is to rate or grade or score first and then sort the
candidates according to their scores.

Andy's idea can be generalized for sincere ratings by imagining a spinner
instead of a coin flip in order to model a Bernoulli random variable with
success probability p not limited to 50%.

For example a spinner with 3/4 of the disc area shaded blue and the rest
shaded red could be used  for modeling a Bernoulli random variable with
parameter p equal to 75%.

To keep things simple let's suppose the name of your top candidate is Blue
and the name of your bottom candidate is Red.

Suppose your choice is between ending up with candidate X on the one hand,
or on the other hand getting Blue or Red respectively depending on which
color the spinner chooses.

 If it makes no difference to you, then your sincere rating for candidate X
is 75%. Otherwise adjust the green and red percentages until you are
indifferent between letting the spinner choose between Green and Red as
opposed to just going with candidate X. Your sincere rating for candidate X
is the percentage of green area in the adjusted spinner.

Next how to convert your zero-info ratings into optimum zero-info strategy
approvals: find the average of all of these ratings and approve the
candidates that you rated higher than that average.

Perfect info optimum strategy is more complicated because it not only
depends on the sincere ratings but also on the probabilities for each pair
of candidates being tied for first place. These probabilities are extremely
hard to estimate in practice for two reasons: first as we saw in the recent
election, polls are not very accurate, and second for most pairs of
candidates the polls do not try to measure the probability of a first-place
tie between them.  On top of that the formulas are very sensitive to these
estimates which means that it is very easy for disinformation to invalidate
the approval recommendations.

You might ask, what about optimal range voting strategy? It turns out that
optimal Range strategy is the same as optimal Approval strategy, whether in
the zero information environment or the perfect information environment.
Intelligent rational range voters would never need to rate any candidate
strictly between 0 and 100%. They would be perfectly happy with approval
ballots ... no use wasting perfectly good score ballots on them!

It seems to me that these considerations lead to the conclusion that in
high-stakes elections with several candidates, it is not totally honest to
claim that either Range voting or Approval voting is entirely voter
friendly to unsophisticated voters  without some voter empowerment of the
kind suggested in the voter friendly implementation of approval that we
suggested under the heading Yes/?/No.

What about Majority Judgement? For the sake of argument let's say that
optimal strategy for all practical purposes (unlike in the case of Range
voting) is basically the same for zero info and perfect info voting. For
many voters it could still be a daunting task to assign a grade to each and
every candidate as required by the method. So why not allow the use of
question marks and designated proxies to resolve those question marks where
the voters are unsure? Why not make voting as voter friendly as possible?
So what if computers have to carry an extra Matrix to keep track of how
many grades for candidate i are to be assigned by candidate j ?  They can
take it .... it is more important to make it even slightly easier for the
voter than to make it much easier for the computer. Let's make those
computers earn their keep!

... or so it seems to me...

Peace to All!

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