[EM] Approval Strategy

[fsimmons at pcc.edu]

Mike,

I agree that the gut feelings for the hope and fear terms are more important than subjective estimates of the 
individual factors in these products.

Also, going back to what you metioned before about the value of showing support for losers that you like 
better than the winner (given they have the chance of the proverbial snowflake), I think that this is perhaps 
the main rationale for extending approval all of the way down to the candidate most likely to win (and 
include that candidate only if the runner up is below it).  [That's another way to state strategy A.]

Of course, LeGrand also has strategy B, C, etc. 

Joe's strategy in the zero information case reduces to "approve exactly half of the candidates and flip a 
coin if the number isn't even."  Obviously this is not as good as the gut feeling method for the candidates 
near the approval cutoff.

Also the validity of using strategies based on maximizing expected outcomes depends on the opportunity 
for repeated play.  Arguably there are cases where this consideration cannot be entirely compensated for 
by adjusting the utilities.  Unquantifiable gut feelings are doubly important in these copntexts.

And I like Jobst's idea of calling the zero-info method described below "the honest approval strategy." 

Jobst wrote
>Forest wrote:
>> Now for the interesting part:  if you use this strategy on your approval ballot, the expected number of 
>> candidates that you would approve is simply the sum of the probabilities of your approving the 
individual 
>> candiates, i.e. the total score of all the candidates on your score ballot divided by the maximum possible 
>> score (100 in the example).  Suppose that there are n candidates, and that the expected number that 
you 
>> will approve is k.  Then instead of going through the random number rigamarole, just approve your top 
k 
>> candidates.

>So we could justifiably call this strategy the "honest" approval
>strategy, since if preferences are sufficiently mixed and all voters use
>this strategy, the outcome is the same as the one with sincere Range
>ballots, i.e., the option with the highest total rating.