> Your fundamental fallacy is that you treat `the voters' as a unified
> entity - which they are not.
I don't see how you could think that, given the text of my last
message on this topic. I explicitly assume the reverse. That is what
it means to say: "Complete honesty is not a stable strategy." The
definition of "stability" there depends on voters making individual
decisions. Similarly with "Nash equilibrium".
> In particular, the situation you fail to cover in your `exhaustive'
> list is the one where _some_ of the voters vote tactically[1]; in
> that situation tactical voters do better than non-tactical ones.
> That is unfair and perverse.
That list was not intended to be exhaustive. It was a list of the
points of agreement between myself and Steve Langasek. If that list
were exhaustive, we would not be disagreeing about anything!
I do agree that it is "unfair and perverse" that voters who vote
"tactically" do better (as measured by their own measure of estimated
self-interest) than voters who vote "non-tactically". Unfortunately,
as Arrow's Theorem shows, this is UNAVOIDABLE in any voting system
that satisfies <technical conditions>. In particular, this is a
property shared by Range Voting, Condorcet, Approval Voting, and
Plurality Voting. The only voting system that does not suffer from
this problem involves telepathy.
> <topic: instructions to voters>
> Condorcet (and indeed conventional STV) do not suffer from this
> problem and this fact is one of their chief advantages.
> It's a special case of the general property of being
> `gaming-resistant' - ie, we want the game implied by the voting
> system to be one where the most effective strategies are the ones
> which are the ones we want the players to adopt. With range voting,
> each individual voter's interests are best served if they only use
> the extremes of the scoring range. The only respect in which this
> is different from approval voting is that the naive voter is given
> the false impression that they might usefully give some candidates
> middling scores. So approval voting is strictly superior to range
> voting - why aren't you plugging it ?
I believe that this was largely addressed in my previous message.
(a) Condorcet is not actually "gaming resistant" in this sense. See
the DH3 pathology for an example.
(b) It is not clear that, under the actual conditions that hold in DPL
elections, pure min/max ballots are actually optimal tactical
Range Voting ballots.
(c) Smith's Range=>Condorcet Theorem also speaks to this issue,
showing that, under certain conditions, fully strategic Range
Voters will elect the honest Condorcet winner.
I will now elaborate on point (b).
Experiments have shown that, in practice, people do use the dynamic
range of Range Voting and do not simply set all their numbers to
max/min. In the Debian context, where we do not have polling data or
other accurate pre-election estimates of the opinions of the
electorate as a whole, pegging all numbers to max/min is typically not
the optimal voting strategy. This is because the correct
game-theoretic-optimal place to put the threshold for pushing numbers
up vs down depends on the other voters. Uncertainty about the other
voters' opinions will cause this threshold to become fuzzy. When that
threshold is fuzzy, the expected optimal values for the numbers on the
ballot become a mixture of min/max, in other words they become
intermediate values.
> Voting tactically is what you call `dishonestly' but I don't agree
> with that value judgement. A voter is not dishonest when they vote
> tactically; they're merely playing the game as it has been set up so
> as best to achieve their aims
I agree: the terms "honest voters" and "dishonest voters" are poorly
chosen. (They were not my choice.) Perhaps better terminology would
be "veridical ballots" and "tactical ballots". And, one property that
would be desirable in a voting system would be that optimal tactical
ballots would in fact also be veridical.
Unfortunately this property is not actually attainable. (Arrow's
Theorem etc.)
However, Range Voting does have a big advantage over Condorcet in
precisely this regard.
To explain, let me define a new term: I will call a ballot
"anti-veridical" if it contains a reversal, meaning that in the ballot
the voter claims to prefer B to A even though they actually prefer A
to B. (Warren Smith uses the term "semi-honest".)
With Range Voting, as you point out, highly tactical voting (given
good pre-election knowledge of the opinion of the electorate) degrades
the system to Approval Voting. That isn't veridical, but it isn't
anti-veridical either. In fact, there are no circumstances in which a
rational (in the game theoretic sense of that term) Range Voting voter
will cast an anti-veridical ballot. On the other hand, with
Condorcet, highly tactical voting leads rational (in the above sense)
voters to cast highly anti-veridical ballots. This in turn can lead
to horrible counter-intuitive election outcomes, like candidate C
winning even though all voters prefer A to C and all voters also
prefer B to C. That cannot happen with Range Voting.
> With range voting, each individual voter's interests are best served
> if they only use the extremes of the scoring range.
That isn't always true - see above.
> The only respect in which this is different from approval voting is
> that the naive voter is given the false impression that they might
> usefully give some candidates middling scores. So approval voting
> is strictly superior to range voting - why aren't you plugging it ?
For two reasons. One is the above: optimal Range Voting ballots
aren't always pegged at min/max, due to a number of factors:
uncertainty about the other voters, intrinsic voter honesty, and also
a desire to express one's own uncertainty. The other is that it is
good to provide voters with more expressive power, so they can more
accurately express their opinions should they so desire. As to why
they might so desire, here are a few reasons. The DPL elections are
iterated, so if we regard saturating all number to min/max as
"defecting" then the iteration may discourage defecting. The ballots
are made public, and intermediate values (and veridical ballots) will
probably be seen as "looking good" for Debian, which would also lead a
rational Debian voter to cast a more veridical ballot. There is also
a natural human tendency towards honesty and generosity, which in this
case would manifest as not casting zeros for people who don't really
"deserve" a zero.
All of this ability to cast a nuanced ballot---in other words, the
expressive power of a range voting ballot---would be thrown away with
approval voting. And some of it is thrown away with Condorcet.
--
Barak A. Pearlmutter
Hamilton Institute & Dept Comp Sci, NUI Maynooth, Co. Kildare, Ireland
http://www.bcl.hamilton.ie/~barak/
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