[EM] Approval-Completed Condorcet Redux

[Alex Small]

This method could be interesting from a strategic standpoint.  Forest
pointed out that strong FBC can be satisfied with certain types of hybrid
ballots.  Conversely, a while ago somebody (Adam?) pointed out that
standard Approval-completed Condorcet can give strong incentives for
insincere voting.  Where does this method fall on that continuum?

(As a reminder, the Approval-Condorcet hybrid discussed in this thread
elects the approval winner UNLESS (1) there's a CW and (2) the number of
people preferring the CW to the aproval winner exceeds the approval
winner's approval rating.  "Standard" approval-completed Condorcet elects
the CW whenever he exists, and the approval winner otherwise.)

Also, let's give this approval-Condorcet hybrid a name.  I suggest
"Condorcet-Enhanced Approval"


Suppose there's a Condorcet Winner:

In most Condorcet implementations, if you don't like the CW your only
strategic recourse is to insincerely rank somebody else ahead of the CW,
and hope that (1) this creates a cycle and (2) it elects somebody whom you
prefer to the CW _and_ the person you insincerely ranked ahead of him.

In "standard" approval-completed Condorcet it's quite easy to determine
whether you'll like the outcome of the completion procedure.  Changing
your rankings doesn't change anybody's approval rating.  The
cause-and-effect relationship between insincere strategies and election
outcomes is clear.  Informed voters can vote insincerely with very little
fear.

However, in the Condorcet-Enhanced Approval, a cycle may not be necessary
to change the outcome.  If you prefer the approval winner to the CW, but
you didn't approve the approval winner, then increasing the approval
winner's approval rating may suffice to elect him rather than the CW.

Or, if you prefer the CW to the approval winner, you've already done
everything you can to enhance the CW's pairwise victory over the approval
winner.  Your only strategic recourse is to withdraw support from the
approval winner if you'd approved him as well as the CW.

So, when there's a CW, Condorcet-Enhanced Approval presents fewer
incentives for insincere ranking.



Suppose there's no CW:

The approval winner is elected.  If you decide you'd rather elect somebody
other than him, you can pursue two different strategies, and normally you
can pursue them in parallel:

1)  Withdraw approval from the approval winner, and approve other people
whom you prefer to him.  The strategic calculus here is the same as in any
ordinary approval election, and it's independent of which
approval/Condorcet hybrid we use.

2)  You can try to elect candidate C (whom you prefer to the approval
winer) by insincerely promoting him ahead of candidates who currently
defeat him pairwise.  This strategy is more likely to work for you in
"standard" approval-completed Condorcet, because being the CW isn't always
good enough to guarantee victory.

So, when there's no CW, Condorcet-Enhanced Approval presents fewer
incentives for insincere ranking when compared with standard
Approval-Completed Condorcet.

Overall, Condorcet-Enhanced Approval gives fewer incentives for insincere
ranking than Approval-Completed Condorcet.  However, it does not eliminate
incentives for insincere ranking.  Neither method gives any incentive for
insincere approval ratings when voters have sufficient information. 
Moreover, this method makes progress toward solving the "Turkey Problem"
(to the extent that I understand/recall the original definition of the
"Turkey Problem").  Finally, it offers simple and compelling rationales
for the winner in each scenario, whereas some Condorcet implementations
have no easily understood rationales.

Overall, I like it, but I don't know that the improvement over standard
approval is sufficient to justify the cost of voting machines that accept
ranked ballots.


Alex Small

matt matt said:
> This is mostly Approval with a little CW as illustrated by defining it
> thus:
>
> 1) If the Approval and Condorcet winners differ then the CW is elected
> when the votes preferring the CW to the Approval winner exceed the
> Approval winner's approval count total. 2) Otherwise the Approval winner
> is elected.
>
> Anyone know the probability that there will be different CW and Approval
> winners?  Less than 1/4?  With more candidates the probability that
> there will be a CW winner presumably decreases while the probability
> that given a CW the CW and Approval winners will be different increases.
>  So maybe it is better to evaluate this method by comparing it to
> Approval than comparing it with CW.
>
> So, contrary to what Kevin says, this method does appear to ameliorate
> the CW turkey problem since Approval avoids that problem and this method
> is mostly Approval.
>
> From: Kevin Venzke <stepjak at yahoo.fr>
> Date:  Sun, 22 Jun 2003 05:05:19 +0200 (CEST)
>
> "I thought briefly about this method, and decided I wasn't clear on what
> it would be good for." [cut]
> "Has anyone come up with a more interesting scenario?"
>
> On Wed, 18 Jun 2003, Alex Small wrote:
>
> "Somebody on another mailing list has put forth an interesting
> Approval-Condorcet hybrid.  I throw it out for consideration.  I know
> some people here have done careful analyses of strategy in standard
> Approval-Completed Condorcet, I'm curious what people think of this: 1)
> Everybody submits a ranked ballot, equal rankings allowed, and also
> indicates yes/no for each candidate. 2)  If there is no Condorcet Winner
> then elect the Approval winner. 3)  If there is a CW, and he also has
> the highest approval, elect him. 4)  If the Approval and Condorcet
> winners differ, compare the Approval winner's approval rating with the
> number of people who prefer the CW to the Approval winner." [cut]
>
>
>
>
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