[EM] Some myths about voting methods

[Warren Smith]

>>> From an information science perspective it is clear that a preferential
>>> ballot have more information than an approval ballot.

>> and range ballots still more.

>Not, if you count the effect of tactical voting: range ballot effectively becomes an >approval ballot.

--let me refute some errors/myths here.   In a 3-candidate election, there are
6=3! possible rank-order votes.   However, there are 8=2^3 possible
approval-style votes.  Since 8>6, we see the approval voting ballots
provided more, not less,
info, than the preferential ballot.

Now you may say "but two of those approval ballot types, namely
all-yes and all-no, were silly."  In that case there are only 6 kinds
of non-silly approval ballot (6=8-2).
Then still, approval provided SAME info as preferential ballot.  Not
correct to say
"it is clear that a preferential ballot has more information than an
approval ballot."

Now consider tactics.  If in a 3-way race between Dem, Repub, and
Nader, the votes
are tactical, then the number of approval ballot types is 4, namely the sets
of approved candidates are
  {Dem, Nader},  {Dem}, {Repub}, and {Repub, Nader}
which is 4 options.   In contrast, with preferential ballot, the
number of possible
exaggerated-tactical-style votes is
   {Dem > Nader > Repub}  and  {Repub > Nader > Dem}
which is only 2 options.

So approval has more, not less, info than a preferential ballot in
this election with
tactical voters.

In a 4-way race, the approval #tactical ballots would be 8, while the
preferential
#tactical ballots would be 4.

So again,  approval has more, not less, info than a preferential
ballot in this election with
tactical voters.

In a 5-way race,  the approval #tactical ballots would be 16, while
the preferential
#tactical ballots would be 12.

So again,  approval has more, not less, info than a preferential
ballot in this election with
tactical voters.  Your tactics argument, in these cases, was exactly wrong.

And range voting always provides at least as much info on a ballot
than approval.

> Nash equilibria...

--"Nash equilibria" are an attempt to salvage game theory in N-player
games with N>2.
But it works badly for voting purposes.
My usual example is, suppose everybody realizes Adolf Hitler is the
worst candidate but still (idiotically) everybody votes for Hitler,
who wins.
OK, this election is a Nash equilibrium representing, in the sense of
Nash equilibria,
"best voting strategy" for all.

What we conclude from this example, is game theory and Nash
equilibria, simply do not work well when applied to voting.
Please do not use Nash equilibria or game theory in voting theory
arguments, at least unless you have understood this first and hence
are working VERY cautiously.

--Finally:
earlier, Arpad had claimed that "in a game-theoretic sense" the "best
strategy" for
Schulze beatpath Condorcet voting, was "cooperation."
I do not know what that meant, so I cannot comment on it.   But in
view of the above
I'm dubious it makes much sense.


-- 
Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
"endorse" as 1st step)
and
math.temple.edu/~wds/homepage/works.html