More Standards

[Blake Cretney]

On Fri, 30 Oct 1998 11:14:41   Bart Ingles wrote:
>I've been out of town for several days, sorry if the next few replies
>are excessively outdated.
>
>
>Blake Cretney wrote:
>> [...]
>> 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.

This has only happened because there is a tie in the sense of exactly
equal support for both factions.  Obviously, reverse-consistency can
not hold in a tie, for example
50 A B
50 B A
No method could pick either A or B as the winner in either direction.
Since in a tie situation, a method can't claim to be picking the best
candidate, the problem with reverse-consistency does not apply.

Reverse-consistency applies where the method picks a single winner
and does so non-randomly.  Of course, if a method was designed to
avoid reverse-inconsistency by having more random results, it could
be criticized for that too.

To answer your comments in a more general way, however, I would suggest
that there are two main premises for the reverse-consistent argument.
- That it is meaningful to say that a particular candidate is the
best guess for best candidate, based on the ballots.
- That the voters if asked to rank candidates from best to worst would
give reversed rankings from those if asked to rank worst to best.

The second requirement isn't quite as strong as requiring that voters
are reasonable and sincere, since many unreasonable insincere ways of
voting will reverse as well.

However, it may well be that some other standard, perhaps one involving
strategy resistance is both more important and irreconcilable with
this standard.  It is possible that we may have to advocate a method
that does not respond as well when people are reasonable and sincere,
in order to have it work better when they are not.  This standard,
then, just points out a necessary sacrifice.

I, however, don't think is the case, and have responded further in the
"reveling the majority winner" thread.

BTW, for something more concrete, here's an example of AV (IRO) violating 
reverse-consistency:

25 B A C
35 A C B
40 C B A
B is eliminated, A wins

25 C A B
35 B C A
40 A B C
C is eliminated, A wins

---
Blake


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