[EM] Approval Voting vs Instant Runoff Voting

[Bart Ingles]

LAYTON Craig wrote:
> 
>   [...]  Utility is relevant, perhaps even the most
> important factor in evaluating electoral systems.  But there isn't just the
> kind of dis-utility you get from a candidate you don't like winning, there's
> also the kind of dis-utility you get when the contest is close, you have a
> voting system highly vulnerable to vote splitting and strategy, voters
> aren't sure how to vote, and those who don't do the right thing (ie voted
> A>B=C instead of A=B>C)feel cheated (quite rightly).  They think that their
> vote didn't count, and if only they voted differently they could change the
> outcome.  It's like finding out your vote has been declared invalid.

With approval the risks and tradeoffs are clear and obvious.  While a
voter might regret  using a voting strategy which didn't produce the
preferred outcome, I doubt that this would be nearly as bad as the
disappointment experienced by a voter in a ranked system, who voted
believing that sincere ranking was all that was required, and then later
finds out that he should have used a different strategy.

Suppose you have a partial-info Condorcet election, where in a
head-to-head pairing between candidates A and C, A is given a 30% chance
of winning vs. C's 70%.  Candidate B is between the other two in policy
space, and could be considered a possible sincere Condorcet winner
provided neither A or C has a first-choice majority.

                 Candidate (utility)
           ----------------------------------
Group 1    A(1.0)        B(<.30)       C(0.0)

Group 2    C(1.0)        B(<.70)       C(0.0)


For group 1, the expected utility of the AC contest is 0.3.  The utility
of a sure B win for this group is less than 0.3.  Group 1 is better off
bullet voting for A, even if it can otherwise guarantee a win for B by
voting sincerely.

For group 2, the expected utility of the AC contest is 0.7.  Group 2
should bullet vote whenever B's utility is less than 0.7.

This was using group strategy; individual pivotal voter strategy would
require estimates of the probabilities of ties among the candidates,
which in turn requires some assumptions about the voters' likely
approach to strategy.


If the group 2 bullet-votes and A subsequently wins, then these voters
may regret using the optimal strategy, just as they might under approval
voting.  I doubt they would feel "cheated", though, since they had to
have known they were were making a calculated gamble.

But what if the group 2 voters rank sincerely resulting in a B win, and
then find out that C would have won if they had bullet-voted?  Further,
what if B's utility to these voters was not merely < 0.7 , but
substantially lower, say 0.1?  If they had previously been assured that
they couldn't go wrong by voting sincerely, then they may well feel
"cheated".  


>   [...]  But, if you (or
> anyone else) actually prefer Approval over Condorcet, then I'd be really
> interested in seeing the arguments.  The few I have seen that actually
> compare the two certainly caught my attention.  Despite the fact that it is
> perhaps the most interesting division on this mailing list, people haven't
> been particularly willing to come down on either side.  And, lets face it,
> some of the Condorcet advocates will be much better at defending their
> position than I.

Reasons to support Approval over Condorcet:

1) The worst-case "low-utility Condorcet winner" scenario, as
illustrated above, and which I have posted many times in the past. 
Strategic voting may mitigate this problem, but so far there doesn't
seem to be much consensus that this is generally the case.  To me, a
good average is not sufficient; it's also important to avoid the
worst-case situations (if you were about to take an airline flight,
which would you prefer -- one which had a high frequency of minor
problems but no serious ones, or would you prefer one in which
everything ran smoothly except for the occasional crash?)

2) Craig's regret dis-utility argument suggests another reason to
support Approval over Condorcet -- I had previously thought of this more
as a negation of Condorcet's supposed advantages over Approval, but the
possibility of "feeling cheated" with ranked systems might actually be
another point in Approval's favor.

3) The usual cost and simplicity arguments, plus the fact that it's
possible to institute pilot tests of approval voting without investing
in either the equipment or personnel required to handle ranked voting.

4) Approval's simplicity means that it can be used anywhere in the
world, in any jurisdiction capable of conducting elections of any other
kind.  If I'm going to expend time and energy trying to get a reform
enacted, I would rather support a reform that can be applied rapidly and
universally, and not just in selected, relatively wealthy jurisdictions.

Bart Ingles