Ranked ballots only? (was Re: Attachment CRITTBL1)

[Steve Eppley]

Bruce A wrote:
> BACKGROUND PAPER 
> SOME RELATIONSHIPS AMONG VOTING METHODS AND THE MAJORITY,
> CONDORCET, AND MONOTONICITY CRITERIA
[snip]
> A. INTRODUCTION
> Each voter casts one ballot by ranking (1st, 2nd, 3rd, etc.) as
> many of the candidates as the voter wishes, with ties allowed, and
> with any unranked candidates on a voter's ballot being considered
> as tied for last by that voter.
[snip]

You begin as many do, by limiting the voters to ranked ballots (or
at most ranked+approval ballots) without explaining why more voter
expression (candidate ratings) isn't allowed.  Granted, this is
beyond the scope of this paper, but how about including a reference
to an explanation? 

You've advocated Regular Champion, I believe, which is a ranked
ballot method.  Why do you believe that rated ballot methods are
inferior?  (I hope no one infers from my question that I believe
rated ballot methods are superior... it's just a question and not 
a statement!) 

* *

Here's an example of a rated ballot method which might be reasonably 
good (ignoring the complexity for the voters and the ballot recording 
devices):

1. Each voter is permitted to rate all the candidates on a main
scale of -100 to +100.  In addition, each voter may rate pairs of
candidates on as many supplementary scales of -100 to +100 as s/he
desires.  Pairing info on supplementary scales overrides pairing
info on the main scale.  Candidates unrated on the main scale by a
voter are treated as if the voter rated them -100 on the main scale.

Example ballot:
   N =  +80,  C =  -50,  D = -90         <----- main scale
   N = +100,  D = -100                   <----- supplementary scale
   N = +100,  C = -100                   <----- supplementary scale
   C = +100,  D = -100                   <----- supplementary scale

2. The ballots are tallied pairwise: If a voter rates candidate A
higher than B, then the difference is added to A's count in the 
A vs B pairing.  If a voter rates candidate B higher than A, then 
the difference is added to B's count in the A vs B pairing.  

The example ballot above would tally as +200 for N over D, +200 for
N over C, and +200 for C over D.  All the info in the main scale has
been overridden by the supplementary scales--unless there are unrated
candidates also running, in which case the voter would be wise to
either at least change the N=+80 to +100 in the main scale or, better
still, append more supplementary scales.

3. Candidate A beats B pairwise if A's count in the A vs B pairing
is greater than B's.  Etc.

Presumably this family of methods would produce results similar to
pairwise ranking methods, since most voters would probably learn to
"extreme-vote" using either +100 or -100 on the supplementary scales.
(Extreme-voting is equivalent to casting independent full-strength
votes in pairwise ranking methods.)  The supplementary scales allow
the voter to get rid of the lesser-of-evils dilemma, assuming the
tie-breaker above (part of the "Etc.") is Condorcet(0).

A possible advantage of pairwise rating over pairwise ranking is 
the "mandate" info contained in the main scale.  Voters have fewer
incentives to misrepresent their main scale preferences since the
supplementary preferences, if any, will be tallied instead.  They 
may have an incentive to misrepresent the intangible mandate, 
however.

Note: My description of this method should not be interpreted as 
advocacy of this method.

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