The "problem" with circularity (was Re: Reply to Blake Cretney)

[Bart Ingles]

Steve Eppley wrote:
> [snip]
> I advise Blake to use the terminology "voters' circular preferences"
> rather than Donald's "circular ties" to make it clearer that
> circularity, when it occurs, is an attribute of the voters and not an
> artifact of some methods.

No individual voter can have "circular preferences", but I agree that
"circular tie" is a misnomer as well.  "Circular defeats" might be
better, or maybe something using the terms "deadlock" or "gridlock".

It's hard to believe that "rock-paper-scissors" (or Ali-Frazier-Foreman)
is such a big mystery.  Although the mere fact that such circular
defeats can exist in a voting method makes me want to question the
results of such a method, even in situations not involving circular
defeats.


> [snip]
> I think it's much less important, and not really valid, to try to 
> identify which one of the top cycle is "best" as long as one of them 
> gets elected.  (Recall the discussion about the merits of the 
> Smith//Random method.)  It's far more important to use a voting 
> method which minimizes incentives for voters to strategize, for 
> potential candidates to not compete, and for parties to want to 
> nominate only one candidate.  If it minimizes those incentives, it 
> will also elect one of the top cycle.

More on this below.


> [snip]
> > [Donald wrote:]
> > We are justified in reducing the lower choices because the voters
> > themselves value the lower choices less than their most preferred choice.
> -snip-
> 
> Donald has apparently confused "utility" with "utility differences."
> (An "absolute" with a "relative.")  A preference is a comparison
> between two alternatives.  The expression "I like Ike" really means
> "I prefer Ike to Adlai."  Support and opposition are relative.
> 
> Just because a voter prefers a favorite (A) more than a compromise
> (B) does NOT mean his/her relative preference for B rather than C is
> in some way weaker than other voters' preference for B rather than C.
> It's possible for the "B>C" preference of an ABC voter to be just as
> strong as, or stronger than, the "B>C" preference of a BAC voter.

The point is, it's also possible for the reverse to be true.  I can't
speak for Donald, but my objection is not that the "B>C" preference is
always, or even usually, weaker than the "A>B" preference.  My objection
is that it COULD be weaker, and when that happens the method is capable
of electing a candidate with very little actual public support (in terms
of average or aggregate ratings).

IRV has a similar, nearly opposite problem.  When it eliminates a
candidate, it in effect assumes that ranking differences between that
candidate and candidates higher in a voter's rankings are nontrivial. 
When incorrect, it can allow a low-rated candidate to win after
higher-rated candidates are eliminated.

While Approval is probably no better than ranked methods at picking the
absolute best from a group of high-rated candidates, it appears to be
much better than ranked methods at eliminating extremely low-rated
candidates.  Just as Steve believes that which of the top-cycle
candidates is chosen is not important, I believe that which of two or
three "high utility" candidates is chosen is less important than whether
or not extremely low-utility candidates can be reliably eliminated.

> [snip]
> Information about the strength of voters' preferences is entirely
> lacking from preference order ballots.  One should avoid the urge to
> jump to "intuitive" conclusions about other meanings "inferrable"
> from an order of preference.  Preferences are relative, not absolute,
> and rankings contain no information about preference intensities.
> (Sadly, methods which ask voters to express their intensities or
> utility differences invariably create strong incentives for voters to
> exaggerate.)

I agree with everything in the above paragraph.  Unfortunately, ranked
methods do indeed infer meaning from preference orders.

> One thing we can say for sure is that a voter whose preference order
> is ABC wants to be able to vote ABC and have that counted as a full
> strength vote for B over C when that's needed to defeat C.

Right.  But that doesn't mean he should necessarily be able to do so. 
By requiring a voter to either reject B or vote B equal to his favorite,
you can avoid counting trivial difference.

> [snip]
> My humble offering is to move the complexity out of the method, into
> the laps of the dominant or near-dominant candidates (or the laps of
> the sponsors of dominant ballot propositions, when we vote on rival
> propositions).  Simply precede Instant Runoff (or plain Condorcet)
> with two simple steps:
> 
>    1. After the voters cast their preference order ballots, publish
>       the preference orders (electronically, on the internet).
> 
>    2. After step 1 is performed, allow candidates a short period of
>       time (perhaps a week) to voluntarily withdraw from contention
>       before the final result is tallied.  (No candidate can be
>       forced to be a spoiler.)
> 
>    3. Tally the preference orders using Instant Runoff (or plain
>       Condorcet), ignoring rankings of the withdrawn candidates.
> 
> To use Bruce Anderson's syntax, this method is named JITW//IRV (or
> JITW//Condorcet).  JITW stands for "just-in-time withdrawal."
> [snip]

I can't go along with JITW, but I had an idea for a sort of pre-arranged
withdrawal when thinking about how to adapt Approval to work with open
primaries.

The method involved choosing an overall Approval winner, who was by
definition the winner for his party, and then dropping all other
candidates belonging to the same party as the winner.  You would then
choose another Approval winner, who is by definition the winner for
another party, etc. until all candidates are either chosen as a party
winner or eliminated.

If you expand the definition of party to allow independent candidates to
form ad-hoc "parties" for a single election, you would have what amounts
to a withdrawal agreement under this method.  You could even allow
parties to "join", in effect run as a single party.

I think the only way I could support candidate withdrawal would be if
the conditions for withdrawal were agreed to and publicized in advance
of the election, and were binding.

Bart