[EM] Sincere Zero Info Range/Approval Voting

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[EM] Sincere Zero Info Range/Approval Voting

Forest Simmons
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!

Forest















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