I've argued before
that the uses of the terms "preference" and "sincere preference" on the list
have treated the terms as "undefined terms" but have been applied ambiguously,
which results in some confusion about what when and how they are
applicable.
Within the context
of election-methods list discussions, I suggest the
following:
Let:
V = { all eligible voters
}
A = { all possible
alternatives }
B = { all possible ballot
configurations allowed by a method }
P(v,A) = a subset of
A that represents Voter v's "acceptable alternatives" and
P*(v,A) = {A} - P(v,A), i.e. the complement of P(v,A)
P*(v,A) = {A} - P(v,A), i.e. the complement of P(v,A)
Then a method can be said to be
"preference preserving" if it meets at
least both of these conditions:
1. There exists at least one element of B that includes all members of P(v,A) and no members of P*(v,A) for any member v of V
2. No ballot which conforms to condition 1 contributes to the selection of an alternative in P*(v,A)
1. There exists at least one element of B that includes all members of P(v,A) and no members of P*(v,A) for any member v of V
2. No ballot which conforms to condition 1 contributes to the selection of an alternative in P*(v,A)
Condition 1 is necessary, but not
sufficient. It has implications regarding the types of ballots that can be
supported by a counting method.
Condition 2 is the one that is necessary
as a framework for the "voting strategy" discussions. If there is something
about a method that requires a member of V
to choose a B that does not conform to condition 1, then that is a
measure of how how strategy-sensitive the method is.
Note that
in this approach the only undefined term is "voter v's acceptable alternatives'"
- and this is acceptable because it is determined by the individual voter, not
by the method. We may not know what the term means, but that doesn't matter
because the voter DOES know, and we just acknowledge that.
I
strongly suspect that while both of these are necessary conditions, these are
not SUFFICIENT conditions. Any method more sophisticated than plurality includes
as its counting method some step that alters A and therefore B, and it is the
original A cross B that the voter used to provide input.
So for
the purpose of analyzing election methods, we can assume that a method
satisfying condition 1 can at least be aware of "sincere preferences", and we
can DEFINE "sincere preferences" to be the ballots cast if the method meets
condition 1.
Some
methods meet condition 1 and not condition 2, and those are necessarily NOT
"preference preserving" (which may not be a bad thing, it is just a
fact).
I don't
suggest that this is the only or best way to axiomatize the definition of
"sincere preference", but as far as I know it's the first proposal that isn't
ambiguous.
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