[EM] some July 4 comments

[Alex Small]

Adam Tarr said:
> - the voters apparently had little prior knowledge of the relative
> position  of the candidates.  Knowing whether your candidate is likely
> to win is  crucial in deciding whether to vote your second choice as
> well.

Good point.  I would really like to see evidence from an Approval election
in which the voters had access to polling data, and the data was taken two
or three times to see how people responded to polls and then to the
subsequent responses of everybody else.

Mr. Hodges said:
>>Saari makes the point that, to get a definite predicted result for AV,
>> you  not only have to specify a profile of voter preferences, you ALSO
>> have to  specify some assumptions about voter behavior in choosing how
>> many  candidates to "approve". I.E in an election with five candidates,
>> in AV  the voter may vote for one, two, three, or four; which will they
>> choose to  do and why? With ONE assumed profile of voter preferences,
>> AV may produce  just about ANY result, depending on how the voters
>> choose to set their  individual thresholds of approval.

Yes.  Approval Voting does not give a result that can be predicted a
priori from ranking information.  Approval Voting requires a different
decision-making process from voters.  If you take it as a postulate that
the outcome MUST be predictable from the voters' preference orders rather
than their absolute ratings of candidates, then Approval is a bad method. 
But who says we must embrace that axiom?

It's worth noting that rated methods, like Approval and CR and MCA, are
not subject to limits espoused in the two most famous "impossibility
theorems" of voting theory:  Arrow's Theorem and the Gibbard-Satterthwaite
Theorem.

Here's a thought on those theorems:

Some people here (including me and Mike Ossipoff, who is no longer posting
here) have observed that Condorcet's paradox is the reason why Condorcet
methods cannot satisfy Arrow's definition of IIAC (Mike's observation) and
Gibbard and Satterthwaite's condition of non-manipulability (my
observation, which I will be happy to defend in later posts, although I'm
sure others have observed this).  We can make good arguments that
Condorcet's paradox is the "reason behind those theorems" and argue that
Condorcet methods are the way to go since they are only plagued by those
paradoxes when the "inevitable source" of those paradoxes occurs.

Some of us have also observed that rated methods are not governed by those
theorems, and hence not susceptible to the problems that have bothered so
many voting theorists.  We can therefore argue that rated methods are the
way to go since they are in some sense free of the problems that have
bothered so many voting theorists.

Finally, Saari has argued that certain geometric properties are the
"reason behind those theorems", and that Borda addresses those geometric
issues.  Because Borda gets at "the heart of the problem" Borda is clearly
the way to go.

In other words, if you conclude "I have a great insight into the source of
the fundamental problems of voting theory!" you can always conclude "We
just need to use methods that recognize and correct for the source of the
problems!"

I think the lesson is that if you let theory be your guide you can justify
just about any voting method out there.  It's better to look at how the
method actually performs, at what actually happens and when.  Saari fails
to do that.



Alex