More Standards

[Bart Ingles]

I've been out of town for several days, sorry if the next few replies
are excessively outdated.


Blake Cretney wrote:
>  [...]
> In more complicated examples, not everyone even agrees on what
> majority rule means.  In fact, we all seem to have our own
> definitions to fit whatever method we advocate.  And it is impossible
> to prove that anyone's definition is wrong.  People can define words
> any way they wish.
> 
> Our arguments take on the character of scriptural debates, where
> people all agree that a particular phrase must be true, but
> disagree widely on what it means.  When I say that
> I support majority rule, I do so because I think that the
> majority will give the best guess for the best candidate, and
> my argument for majority rule frames my definition of it.  I
> would be interested to hear arguments for majority rule that
> do not derive it from the search for best candidate.
> 
> So, I think that best guess for best candidate is in fact a
> more realistic goal than a direct search for arbitrarily
> defined majority rule.

I agree that the term "majority" is not generally useful for comparing
different systems, since the term means something different in each
case.  An exception may be when the methods are related, as with Runoff
vs. IRO or Approval vs. Bucklin. 

> 
> [...]
> Perhaps even more obvious is the argument against methods that
> are reverse-inconsistent.  That is, consider a method that says
> the  best candidate is candidate X for some ballots.  Now reverse
> the candidate order on all ballots, so they are now ordered to
> determine the worst candidate.  If the worst candidate is found
> to also be X, the method is reverse-inconsistent.  That is, it
> can't possibly be right both ways because it contradicts itself.

This test seems to assume that "best candidate" and "worst candidate"
are equally valid ways of ranking candidates.  I wouldn't expect this to
be the case, however.

Determinations of "worst candidate" may be more emotion-based, and/or
may simply indicate the greatest tactical threat to the "best
candidate".  I imagine the two would be completely intertwined for many
people.  This is why on this issue I lean toward methods that either
drop the lower rankings (i.e. forced truncation) or that rarely make use
of lower rankings (such as IRO or Approval).

Even if the voters are completely sincere and rational, then to the
extent that they vote along ideological or partisan lines the "best
candidates" will be the same as the "worst candidates" when looking at
the raw returns.  For example, suppose two major factions of equal size
vote ABCD and DCBA for purely ideological or partisan reasons.  You end
up with candidates A and D, who are tied for both first and last place. 
In this case, all this really means is that you have redundant
information in the last half of the list.

In this example, if you use the "for" votes while attempting to count
the lower rankings against a candidate, you are in effect subtracting
this redundant information from itself.  The meaningful infomation (i.e.
the strongest preferences from the majority of voters) tends to cancel
out, leaving a combination of minority preferences and near-random
garbage as the result.

Where there is redundant information, I would prefer to use the
"cleanest copy", i.e. that with the least emotion & strategy involved.

Bart Ingles