[EM] Five Slots and Cranor

Joe Weinstein jweins123 at hotmail.com
Wed Apr 25 19:14:04 PDT 2001

Forest et al,

In any EM-ointment there's always a gadfly. This time it's me.

(Note to NEWER list members.  For your reference in following these 
comments, below in a special Background section you will find a basic 
taxonomy and terminology for 1-winner election methods.  This material is 
admittedly slanted to some of my own preferences and suggestions.)

I have argued in earlier postings that there is a simple rock-bottom reason 
why even problematic methods such as IRV appeal to many reform advocates 
over Approval: namely, these methods use higher res, and therefore allow 
greater expressivity.  For instance, with any method using res>1, a Green 
voter could mark the ballot so as to express Nader>Gore>Bush.  Such 
expressivity is feasible with current computer technology, and would be very 
useful for encouraging participation and satisfaction in large-scale public 
elections - even though Approval (res=1) will usually do nicely for 
small-scale or collegial elections.

There are two major obvious reasons to bother voting: (1) expression - to 
express one's preferences, so as to 'send a message' to politicians so as to 
affect future politics; and (2)instrumentality - to have an effect on the 
direct outcome, the choice of winner.

Many discussions - here in EM-list postings as elsewhere - presume wrongly 
that voters care only about instrumentality and therefore that optimal voter 
'strategy' concerns only instrumentality and not also effective expression.

For instance, compared with Approval, higher-res CR methods are more 
expressive, but are often decried as being subject to 'strategic collapse': 
for optimal strategy, a CR vote uses just the same extreme grades (0 or 1) 
as does Approval.  The claim is correct for a strictly instrumental 
strategy, but is wrong for some expressive strategy, for instance for a 
voter whose interest is to send the message 'A>B>C', expressing a comparison 
of three candidates.

see from the above example that optimal extreme-grading (0 or 1) strategies 
for instrumentality will interfere with strategies for some expressivity - 
UNLESS the method used at least partly decouples the two functions.

An obvious procedure would be to conduct 'PARALLEL BALLOTING':  each 
candidate may be awarded both an instrumental grade (notably, using res=1 as 
for Approval) and an expressive grade (notably, using a high res value, e.g. 
res=100).  Taken over all ballots, the instrumental grades will yield a 
candidate's instrumental score, and the expressive grades will yield a 
candidate's expressive score; and - although both scores will be reported - 
the winner is found from just the instrumental scores.

It appears that Demorep's ACMA method provides for a parallel balloting 
procedure in which, however, both ballots have both instrumental and 
expressive functions.  (I hope to have a more cogent comment in a later 

For simplicity and likely more consistency, one may try instead to HYBRIDIZE 
the parallel ballots into a SINGLE BALLOT.

In its essence, that's what Forest Simmons' 5-SLOT method does.  It has 
instrumental res=1, amounting to Approval. Expressively, it uses res=4, 
namely scholastic grading, where letter grades A,B,C,D,F correspond to 
numerical grades 1.0, 0.75, 0.50, 0.25, 0.00.  Each expressive grade is 
given instrumental meaning:  a grade of A,B or C is an instrumental 
'approve' (=1.0), and a grade of D or F is an instrumental 'disapprove' 

COMMENTS ON 5-SLOT.  I suggest that 5-SLOT be kept simple - with no special 
meaning (and therefore no stimulus) to compound markings such as AB (let 
alone CF, etc.).  To minimize spoiled ballots, just credit each candidate 
with the highest mark made (with F as default if none is made at all).

COMMENTS ON CRANOR.  As noted above, an optimal CR strategy for concerns 
which are at least partly expressive, not instrumental, may well fail to 
reduce to Approval voting.  Would Cranor's strategy operate credibly for 
such a strategy?  (I have no idea: for me 'Cranor' is simply the label for a 
black box whose claimed properties, let alone actual properties, remain 

Anyhow, suppose the voting authorities badger me, the voter, with a clever 
suggestion, e.g. Cranor's.  Sufficiently detailed rationale for this 
particular suggestion will likely be too complex for me, let alone a typical 
voter, to comprehend.  On the other hand, a suggestion without such 
rationale would be quite patronizing.

Even worse would be balloting which presumes my automatic endorsement of the 
suggestion.  It's bad enough to be told that 'Computer knows better than you 
do how best to get what you want'.  It's even worse to be told that 'because 
Computer knows better than you do what to do, therefore Computer will 
automatically act for you'.

Joe Weinstein
Bixby Knolls
Long Beach CA 90807 USA

BACKGROUND (FOR NEWER LIST MEMBERS ONLY)  An attempt at consistent 1-winner 
EM Terminology and Taxonomy.

Each of the usual 1-winner EM may be viewed as a scheme in which, on her (or 
his) ballot, each voter marks each candidate with a grade between 0 (=worst 
possible, full failure, full disapproval) and 1 (=best possible, full pass, 
full approval), inclusive.

The marked grades may be explicit, or they may be implicit, a coding for 
'ranks'.  For instance, with 5 strictly ranked candidates, ranks 1-5 code 
into grades 1, 3/4, 1/2, 1/4, 0.

For a given number N of candidates, each usual method allows a given 'res' 
('resolution'), = number of nonzero grades.  For instance, a strict ranking 
method has res = N-1.  Other than ranking methods, most methods have a fixed 
res, independent of N.

Methods with fixed res=1 include Approval and the prevalent Lone-Mark 
method. With these methods, each candidate receives either 0 (fail, 
unmarked) or 1 (pass, marked). (Lone-Mark is often termed 'Plurality' - a 
total misnomer; properly speaking the term 'plurality' means just that the 
candidate with the highest vote score wins: which occurs for EVERY 1-winner 

The big difference between Lone-Mark and Approval is that the former is 
'constrained' but the latter is 'unconstrained' or 'free-choice'.  In a 
constrained method, one cannot validly mark each candidate independently of 
how one marks (with allowed grades) the other candidates.  Thus, on a valid 
Lone-Mark ballot at most one candidate can be marked: all other candidates 
must be unmarked.

Lone-Mark is the case for res=1 and S=1 of Cumulative voting, where the sum 
of grades over all N candidates is constrained to be at most some fixed sum 
S less than N.

Approval is the case for res=1 of unconstrained fixed-res grading, alias CR 
('cardinal ratings').  Specific attractive values >1 for res are res=100 
(centile or exam grading), res=10 (Olympic grading) and res=4 (scholastic 

All the above discussion concerns how a voter may MARK her ballot.  Methods 
differ also in respect of how marks on the various ballots are combined to 
give overall SCORES to candidates.

The usual scoring approach is averaging (or summation): each candidate's 
score is just the overall average grade (or, equivalently, the overall sum 
of grades) received on the individual ballots. Such average scoring is used 
by Lone-Mark, Approval, Cumulative and CR methods, and (alone among usual 
ranking methods) the Borda method.

The most important alternative scoring approach is Condorcet scoring: a 
class of scoring methods which feature pairwise comparison of pairs of 

The currently heavily propagandized and promoted ranking method IRV 
('instant runoff voting') uses yet another scoring procedure.  As this 
list's postings frequently note, IRV has many problems. For instance: (1)IRV 
will elect an otherwise unpopular candidate over a candidate A who happens 
to be even fewer people's first choice but everybody's high second choice; 
(2) IRV need not faithful to voter intent (in tech lingo, IRV is not 
monotone): increasing the support for candidate A may turn A's victory into 
defeat(!); and (3) IRV scoring may be very complex and expensive: 
computations cannot be done by simple aggregation over precincts but have to 
iterate repeatedly from nationwide results.

----Original Message Follows----
From: Forest Simmons <fsimmons at pcc.edu>
Reply-To: election-methods-list at eskimo.com
To: election-methods-list at eskimo.com
Subject: [EM] Five Slots and Cranor
Date: Wed, 25 Apr 2001 11:56:13 -0700 (PDT)

Yes, I keep coming back to the five slot method too...
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