[EM] What is the ideal election method for sincere voters?

[David Cary]

--- Scott Ritchie <scott at open-vote.org> wrote:
 
> This definition bothers me a bit.  We tend to think of "sincere"
> votes as non-strategic, but the method you just described for 
> "voting sincerely" can involve a whole lot of strategy based around
> resizing the sets and setting the approval threshold.

It is important to recognize that sincere and non-strategic are
different concepts which may intermingle differently in different
situations.  It is also important to recognize that there is nothing
inherit in sincerity that requires an election method to have a
unique sincere vote for each voter.  When a voter has multiple
sincere votes for an election method, tactics can be a factor in
which of those sincere votes are actually cast.

I describe a sincere vote as one which reflects as accurately as
possible the person's personal preferences.  The preferences are ones
that are independent of the election method, independent of
information about how other voters will vote, and independent of the
addition of another candidate.  Reflecting those preferences as
accurately as possible is judged relative to the voting limitations
imposed by the election method and to an overall design intent or
other normative specification for voting with the election method.

For ranked ballot election methods, except for maybe issues about how
ties in preferences are handled if ties are not allowed in the voted
rankings, there is a unique sincere vote.  Similarly for plurality
voting.

For approval voting, the issue depends or whether you think people
have an approval preference that is independent of adding an
additional candidate.  If so, each voter has a unique sincere vote. 
If not (and I don't), then there are multiple sincere approval votes,
depending on where an approval threshold is applied.

Assume a voter has preferences that can be represented by a
von-Neumann-Morganstern utility function.  For range voting with
infinite precision, there are infinite sincere votes:  those that
preserve the relative differences in preference strength between the
options.  Distorting the relative differences between preferences by
pushing middle options disproportionately towards the extremes is not
a sincere range vote.  In discrete range voting, some details can get
messier about how to deal with rounding issues.  Multiple sincere
votes are still possible though.  

In discrete range voting with just two rating options, the threshhold
has to be set at the average of the max and min preferences.  That
means a vote could be a sincere approval vote but not a sincere range
vote.  That is not a contradiction, just a result of (what I see as)
the different design intent / normative specification for range vs.
approval voting.

I'll claim that for election methods which allow a voter to have
multiple sincere votes, the only way for such a voter to vote purely
sincerely is for that voter to randomly select, using a uniform
distribution, which sincere vote to cast.

-- David Cary


 
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