[EM] Approval-Competed Condorcet... "more" strategy-free?

[Adam Tarr]

Hello everyone.  I was just playing around with my/Forest's/Demorep's 
Approval-Completed Condorcet idea again.  Once again, the idea is to use a 
graded ballot (ABCDEF, for example). If there was not a Condorcet winner, 
then the candidate with the most approval votes (A's, B's, and C's in the 
case of ABCDEF ballots) wins the election.

I like this approach more than Forest's 5 grade-ballot (A,B,C,D,F) since it 
has one more slot, but moreover it has an even number of slots which seems 
to make the approved/disapproved break more intuitive.  Blake expressed a 
concern that people might feel a need to distribute the candidates in 
separate slots.  I doubt this, especially since the majority of public 
elections lack that many popular candidates at this point.

I think that if you give people a ballot that looks like grades, they will 
tend to assign candidates grades that reflect their cardinal rankings for 
those candidates, provided they don't have strategic incentive to do 
otherwise.  If lack of slots becomes a problem, we could switch to 1-10 
rankings.  If a tendency to spread the candidates out tends to skew the 
results, we could go with the "none of the below" candidate in ranked 
ballots.  But for the time being, I think the 6-slot ballot would do fine, 
and if I were to advocate this method I'd go with the 6-slot ballot.

At any rate, I was just looking at how well this technique responds to 
certain strategic voting scenarios.  In an earlier message (March 20) I 
suggested that Approval Completed Condorcet ("ACC" from here on out) passes 
SFC and SDSC from Mike's criterion.  It doesn't pass the "Generalized" 
versions unless one slips in a Smith set requirement explicitly, which I 
argued against in that message.

I'm now going to compare ACC to margins and winning votes Condorcet 
methods, using the example that has become my signature example on this 
list.  The following are the sincere preferences of my example electorate:

49: Bush>Gore>Nader
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader>Gore>Bush

If everyone votes sincerely, then Gore is the Condorcet winner.  The 
problem arises when the Bush voters swap Nader and Gore on their ballots 
(in margins they can achieve the same effect by truncating, but I'll ignore 
that for this analysis).  So the new "preferences" are

49: Bush>Nader>Gore
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader>Gore>Bush

In margins-based methods, the only way for Gore to still win the election 
is for the Nader voters to bury Nader behind Gore.  The stable equilibrium 
ballots become:

49: Bush>Nader>Gore
12: Gore>Bush>Nader
39: Gore>Nader>Bush

And this allows Gore to still carry the election.  This sort of equilibrium 
is what Mike is talking about when he says that margins methods are 
"falsifying".

In winning votes methods, the Nader camp can vote equal first-place 
rankings rather than swap Gore and Nader entirely.  The stable result is 
therefore:

49: Bush>Nader>Gore
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader=Gore>Bush

In ACC... we first have to define where the approval cutoffs on the ballots 
are.  Since the approval tally is only used to break cyclic ties, clearly 
the Bush camp has no incentive to Approve of anyone except Bush.  I'm going 
to make the assumption that since Gore and Bush are the apparent front 
runners in this race (the only two with a decent shot at election), every 
voter will approve one and not the other.  This is the logical approval 
cutoff to use, based on the approval strategy threads that have been 
circulating on the list of late.  So the ballots could look something like 
this:  (>> denotes approval cutoff)

49: Bush>>Nader>Gore
12: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush

In this case, Gore wins the approval runoff 51-49-33.  So not only did ACC 
avoid the need for defensive order-reversal like margins methods, but it 
avoided the need for defensive equal-ranking like winning votes 
methods.  This is a super result: totally strategy-free voting for the 
majority side.

There is a dark side to this result, though.  Say that some of the 
Gore>Bush>Nader voters were extremely non-strategic and decided to approve 
both Bush and Gore.  So the votes now look like:

49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush

Now, Bush wins the approval runoff 55-51-33.  This is where ACC's favorite 
betrayal scenario comes in.  Since Bush wins the approval vote, the only 
way the majority can guarantee a Gore win is to make Gore the initial 
Condorcet winner, which requires that the Nader camp vote Gore in first place:

49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
33: Gore>Nader>>Bush

So this is more or less the same as the margins method equilibrium.

In summary, if the voters are fairly logical in the placement of their 
approval cutoff, then ACC seems almost uniquely free of strategy 
considerations.  If the underlying approval votes do not back up the 
sincere Condorcet winner, however, then ACC becomes just as vulnerable to 
strategic manipulation as the margins methods are, if not more so.

Comments?

-Adam