New sw method: "extreme scale"

[Steve Eppley]

Demorep wrote:
-snip-
> Good luck to many voters to avoid making errors in the number of
> millions or billions of ratings that they give to each candidate.

I agree that the large numbers could present problems, if the voters 
have to enter those numbers when they vote.  But there are several 
shorthand formats which could be used.

Perhaps it would be easier to vote with fewer errors if ballots also
offer shorthands for big numbers, such as "MAX-2" or "M-2" or "-2"
which could all mean "999,999,999,998":
   A=M
   B=M-1
   Y=1
   Z=0

Or perhaps the ballot could provide for two sets of preference 
orders:
   Most Preferred:   A>B
   Least Preferred:  Z<Y
and the tally algorithm can translate these into the extreme scale 
ratings.  This format would also make it harder for voters to vote 
"wrong" (nonstrategically).

> There is also the factor of *if the voter knows s/he is part of a
> smart majority*.  A slight error in estimating the size of the smart
> majority might cause a major strategic error.

Yes.  The Yes/No voting method which Demorep advocates suffers 
the identical strategy problem, if my understanding is correct. 
(Demorep's method also offers a special tactic to the voters who
wouldn't mind letting the "none of the above" alternative "win.") 
But the term "major" is subjective; would it be a disaster for
society when these errors are made, or just a disappointment for 
the majority?

If one is more concerned with getting good preference order info from
the voters than on whether a so-called "second-best" choice sometimes
wins, one needn't consider these strategy errors to be a significant
problem--as long as analysts can't credibly infer more than
preference orders from the ballots, and as long as potential 
candidates aren't deterred from competing.

What I'd like to know is whether potential candidates would be 
deterred from competing, for fear of being a spoiler, by this method.

> Example-
>   49 A= 1000
>   48 B= 1000
>    1 C= 1000
>      B=  500
>    1 C= 1000
>      B=  499
> A= 49,000, B= 48,999, C= 2,000
> A wins. B's average is 979.88.

Each voter can rate every candidate, but Demorep has shown most
voters rating only one candidate.  I assume he meant the following:
   49:  A= 1000,  B=    0,  C=    0
   48:  A=    0,  B= 1000,  C=    0
    1:  A=    0,  B=  500,  C= 1000
    1:  A=    0,  B=  499,  C= 1000

The two voters who rated B around 500 haven't followed the suggested 
game plan of voting only near-extremes.  That's okay, if they want 
their votes to be interpreted as rating B midway between A and C.
But those two votes look like bad strategy given the polling data,
since C appears to be a sure loser.  If I'm correct in assuming 
that Demorep has these two voters rating A=0, it would make strategic 
sense for them to rate B=999, not B=500.

Using Demorep's Approval+Rankings method, the voters would have
encountered the identical strategy dilemmas and B could be defeated 
there as well:
   49:  A=Yes  B=No      C=No       A>B=C
   47:  A=No   B=Yes     C=No       B>A=C
    3:  A=No   B=abstain C=Yes      C>B>A
(I've changed only one voter here from the above example.  Without 
this change, Demorep's example would have both A and B teetering 
exactly tied and both with approval=disapproval=49.  Since ties 
are unlikely, a double tie certainly isn't a plausible example.)

If the two voters in Demorep's example were "strategically smarter", 
taking into account the tight race between A and B and the 
unlikelihood of C winning, the votes would have been:
   49:  A= 1000,  B=    0,  C=    0
   48:  A=    0,  B= 1000,  C=    0
    1:  A=    0,  B=  999,  C= 1000
    1:  A=    0,  B=  999,  C= 1000
          -----     -----     -----
          49000     49998      2000
   B wins.  (Majority rule is served.)

Even if the two voters weren't "strategically smart", their
important preference order info is preserved.  Candidate A could win,
as Demorep pointed out, but with society so split between A and B
there's no objective reason to believe that A will really be a much
better choice than B.  And the majority preference for B over A will
be clear, so A can't credibly claim an unwarranted mandate.  

> Mr. Eppley's proposal seems to be a variant of Borda's method.

Not at all.  Borda's method scores each candidate by how many 
other candidates it outranked.  (For instance, with the vote ABC
Borda's method gives A 2 points, B 1 point, and C 0 points.)  

Borda's method creates incentives for voters to misrepresent their
preference orders, but "extreme scale" doesn't, if my understanding 
of it is correct.

If one of candidates B and C is the likely winner, and the voter
prefers B more than C, than Borda's method creates a clear incentive
for the voter to rank B first and C last: BAC.   But with the
"extreme scale" method, the voter can rate A=1000, B=999, C=0.
There's no need to rate B higher than A to avoid electing C.

> I point out again that nice examples can be thought up in any
> method but that not so nice Arrow strategic voting possibilities
> must be brought up.

I agree.  Condorcet performs much better on strategy issues than
"extreme scale", or Demorep's method, or Instant Runoff.  But 
the algorithm in "extreme scale" might be easier for the voters to 
understand, so in my opinion it's worth exploring.

> Mr. Eppley's proposal again brings out the fact that even second
> choices might be very weak relatively on the +100 percent for to
> -100 percent against scale (and the tendancy to vote the + or -
> extremes). 

The term "weak" isn't defined.   Assuming my guess of what Demorep
meant is correct, then I agree in part.  A second choice might be
nearly as distant from the voter's views as a last choice, etc.

But unlike other rated ballot methods, the "extreme scale" method
doesn't attach much subjective significance to the absolute ratings.
So what if a ballot rates A=1000, B=1, C=0?  *The method takes for 
granted that most ratings will be strategically voted.*  The vote 
{A=1000 B=1 C=0} does NOT imply that the voter considers B to be a
"weak" choice.  Analysts can rightly infer the voter's preference
order is A>B>C, but additional inferences are shaky, since the B=1
looks at least as much like a full strength vote for A over B as 
an expression that B is "weak." 

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