New sw method: "extreme scale"

[Steve Eppley]

Mike Saari wrote:
-snip-
> Actually, instead of a scale up to 1000 (variable depending on the
> #s of voters/candidates), you might do better with a scale up to
> 1.0, with unlimited levels of gradation, i.e. .5, .75, .997, .99834
> etc.

But those votes would be difficult for voters to enter using
current voting booth technology.  Just as the pure "extreme scale"
numbers would be difficult to vote.

A more practical data entry format without this problem would be to
allow voters to use two preference orders which correspond to the
extremes of the scale:
   Most Preferred:   A>B>C
   Least Preferred:  Z<Y<X
The tally algorithm could take these votes and translate them into
the extreme scale (or use them for some different tally algorithm we
haven't yet explored).  

Another advantage of this format would be to make it hard for voters
to vote "wrong" (nonstrategically)--they wouldn't be able to express
votes like scale/2.  So majorities won't have to be as "strategically
smart" to elect the best compromise they can elect.  They'd just have
to learn from the pre-election polls (which presumably would provide
the preference orders of the sample population) how far they need to
compromise.  

They might still sometimes compromise "too far" or "not far enough",
compared to other methods like Condorcet, and elect a candidate less
optimal than an omniscient majority might elect.  But I think the
more interesting question is whether this method has a spoiler
dilemma which would deter candidates from competing.  If a potential
spoiler believes his/her supporters will be willing to rate the
"lesser evil" compromise in the top section of the scale when
necessary to defeat a "greater evil", then it seems to me that 
s/he won't be deterred.

-snip-
> I also note that the system as described doesn't distinguish
> "actively opposed" from "lack of interest" toward a given
> candidate.  Hence I prefer a plus-and-minus scale. 

Mike has confused the properties of the voting method with the
properties of the set of choices the group places on the ballot.

There are really only relative preferences; popular constructs like
"absolute opposition" are mythical.  (Essentially journalistic
shorthands.)  A voter may be indifferent *between* alternatives, 
but not *to* an alternative.  A voter may strongly prefer some
alternative more than another, but can't support or oppose an
alternative in isolation.  What's important is to make sure all the
vital alternatives are choices on the ballot, so all the vital
relative preferences can be voted.

If there are additional alternatives like "keep the status quo",
"hold a new election", or "let some other entity decide" then these
alternatives should be choices on the ballot so the voters can
explicitly rank or rate them alongside the other choices.  (See also
the related comments at the end of my reply today to "Approval-Ranking
Method (ARM)".) 

I prefer the voters not be misled by chimerical constructs, even if
they are popular misconceptions.  Hence my use of "most preferred"
and "least preferred" in the sample format above, and my preference
against a plus-and-minus scale.  In accordance with Arrow's
"completeness" and "universal domain" axioms, *all* the possible
outcomes should be choices on the ballot.  Including outcomes like 
"keep the status quo", "hold a new election", etc.--whichever 
alternatives the group considers relevant.

If Mike as a voter wants to "actively oppose" some choices, he could
simply put those choices at the bottom section of the scale, and put
the choice(s) like "keep the status quo" at the top section of the
scale.  (Similarly with a ranked ballot method: he could rank "keep 
the status quo" ahead of choices he "opposes.")  If none of those 
special choices is on the ballot, then it's because the group
disagreed with Mike about the importance of being able to express
what he thinks is vital.  In other words, it's not a limitation of
the ballot method which would prevent voters from expressing what
Mike thinks is vital; it would be a decision by the group that those
expressions are *not* vital and that those special alternatives are
not acceptible outcomes.  

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)