[EM] minimizing voter despair

[Forest Simmons]

One of the reasons citizens don't vote is voter apathy born of despair:
"What good will it do, none of the candidates have my interest in mind."

A major objective of election reform is to  overcome this despair.

Let Pij be the subjective probability in the mind of the i-th voter that
the j-th candidate will be more helpful than harmful to his/her interests
if elected.  Similarly, let Qij represent the subjective probability in
the mind of the i-th voter that the j-th candidate will be more harmful
than helpful.  For purposes of polling the population, we might arrange
for the voter to adjust two complementary sectors in a pie chart until the
two areas seem to be in proportion to the two probabilities to ensure
consistency:  Pij + Qij = 1. 

For any voter i, the product of Qij over all j's in a subset of candidates
represents the probability that all of the candidates in that subset would
be more harmful than helpful (assuming independence ,etc.)  In any case,
that product would be a measure of the despair that voter i would feel if
that subset of candidates should be the winning subset. 

If that despair is large, then the voter will tend to feel
disenfranchised.

The complementary value, one minus the despair product, would represent
the hope that at least one of the members of the subset would be more
helpful than harmful.

A natural objective would be to minimize the total despair, or
equivalently, to maximize the total hope.

The total despair could be thought of as an estimate of the number of
voters that would believe that every one of their representatives was apt 
to neglect their interests, while the total hope would be the expected
number of voters that would believe that they had at least one
representative who would look out for their interests.

Could voters be trusted to vote their sincere subjective probabilities? Or
would they try to manipulate the results by voting insincerely?  If so,
would insincere voting backfire on them?  If so, could they be convinced
of that?

It seems to me that there might be a "tragedy of the commons" dilemma
here.  The voters know that if they all stick to their agreement to vote
their honest probabilities, the outcome for the group will be best, but if
most vote their honest probabilities, a group of like minded citizens can
do better by defecting from the agreement by exaggerating their
probabilities to the extremes. However, if everyone defects, most voters
will be worse off, because if everyone defects, only the minority
hard to please voters will be benefited. This is because when everyone
votes only zeros and ones, maximizing the (distorted) hope total is the
same as maximizing the number of voters that have at least one approved
representative, which gives all importance to the first layer of
representation, which in turn, tends to benefit the voters with the fewest
number of potential layers, the ones that are used to voter despair.

So defecting from the general good would hurt the majority worse than the
minority.  Is that poetic justice?

Seriously, I'm not proposing this as a practical voting method.  But it
could be one tool for gauging the effectiveness of other methods in
maximizing hope and minimizing despair.


This is an example of what I meant when I said there could be valuable
theoretical uses for higher resolution methods. 


Forest