[EM] Re: ruminations on ordinal and cardinal information

[Araucaria Araucana]

On 20 Mar 2005 at 01:38 PST, Jobst Heitzig wrote:
> Dear Russ!
>
> I completely agree with what you wrote!
>
> Just like you, I think that
> [Russ Paielli wrote earlier:]
>> an "ideal" election method must integrate both ordinal and cardinal
>> information, and the cardinal information should be simple approval
>> (yes/no for each candidate).
>
> I would even go so far to claim that the ideal election should also give
> special relevance to a third kind of information: "direct" support.
>
> For example by using Random Ballot to choose from a small set of most
> acceptable candidates such as Forest's P.
>
> Or, a new idea, if you find randomization inacceptable, by electing the
> member of P with the most direct support!
>
> Yours, Jobst

Hi Jobst,

To summarize: the approval-augmented method on the table is ranked
ballots plus approval cutoff (by whatever means), then eliminating
Approval-consistent defeated candidates (see
http://wiki.electorama.com/wiki/Techniques_of_method_design#Defeats_and_defeat_strength
for Jobst's definitions of defeat strength).  The set of candidates
remaining is denoted as P.

Those advocating a deterministic method ("Direct Majority Choice")
propose picking the pairwise winner from P.  This is Condorcet and
Smith-efficient.

Since you (and Forest) feel that picking the least-approved member of
P is counterintuitive, you're proposing picking the winner from P
based on either Random Ballot or maximum Direct Support.

I disagree.

First point: High Approval score indicates broad consent that the
candidate is minimally acceptable.  But it doesn't indicate highest
preference.

The main effect of Approval in DMC is to use it to discount the
pairwise defeats of candidates with less widespread support.  But it
is still possible for a minority block of voters to express
"lesser-of-evil" preference among candidates approved by the majority.
This helps avoid the polarizing potential of IRV picking the 'core
support among the majority' winner (IRVists' secret agenda?).

Approval Cutoff also has an effect similar to AERLO/ATLO, which we
should also consider strongly desirable -- we want to encourage voters
to express a preference between approved candidates without fear of
hurting on or the other.  If you end up ignoring that preference,
you're no better off than with straight Approval.

Second point: In the USA, at least, it may be more desirable for the
pairwise winner to have lower approval.  This seems paradoxical, but
it tends to keep the winner from making overly radical changes.  The
US founders distrusted government enough that they put in checks and
balances to make the process *less* efficient.

Thirdly, choosing the Direct Support winner from P will tend to
discourage a more generous approval cutoff and encourage bullet
cutoffs.  You're right back with something little better than
Plurality again.

Consider your DMC tie problem:

       1 A>>B>C
       1 B>>C>A
       1 C>>A>B
       3 A=B=C

This means the electorate is polarized three ways:

http://wiki.electorama.com/wiki/Voting_paradox

With DMC, however, a fourth candidate will see the opportunity and
step in to fill the center -- if not in that election, then in a
future one:

       1 A>>D>B>C
       1 B>>D>C>A
       1 C>>D>A>B
       3 A=B=C=D

One of the goals of a new voting system is that we want to give the
best candidates an opportunity to win without being eliminated in
runoffs.  In this case, D would lose the approval and direct support
races, but would be the best compromise candidate wherever the cutoff
line is placed.

Ted
-- 
araucaria dot araucana at gmail dot com