[EM] Five Slots and Cranor
fsimmons at pcc.edu
Wed Apr 25 20:42:55 PDT 2001
The second after I hit "Return" I knew I shouldn't have suggested just
going with the computer's strategies.
But I think I'm getting close to a simple explanation and simple algorithm
that accomplishes the same thing as Cranor's method without all of the
iterations and messy probability (based on perfect CR information),
something that the average voter could understand with a little effort.
In any case, if Cranor's method were used in public elections, there
should be a little check box on the ballot that asks if you want your
ballot Cranor optimized or not. If you check yes, then your ballot is
supplemented with the Cranor optimized ballot. The original is used for
expression, while the optimized is used for instrumentality. Otherwise
(with the option declined), the original serves both purposes.
I like the distinction (and associated terminology) of expression and
instrumentality, and the recognition that both may contribute to the
voter's true optimum strategy in ways that Cranor's method (presumably
optimizing expected instrumental utility) may not handle to the
satisfaction of the voter.
In other words, it may just as impossible to aggregate the aesthetic
"utility of expression" with the utilitarian (pragmatic) "utility of
instrumentality" as it is to add apples to PC's.
Joe has done us a great service by suggesting some valuable conventions of
terminology. It appears that every science has to start with taxonomy.
Only when we have a clear and logical way of communicating what we mean
can we hope to progress beyond discussions that boil down to arguments
P.S. See a few inserted comments below.
On Wed, 25 Apr 2001, Joe Weinstein wrote:
> 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.)
> PROLOGUE #1. EXPRESSIVITY.
> 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.
This is exactly the conclusion that I have come to. Expressivity is the
number one concern of IRV supporters. And Expressivity without "spoilage"
is a close second. They know that IRV beats Approval in expressivity, and
they believe that IRV beats Approval in spoilage avoidance. They can live
with non-monotonicity and the other defects of IRV if they are not offered
a method which is truly and obviously superior in these first two
> 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.
> PROLOGUE #2. STRATEGY.
> 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.
Note, however, that Mike has recently expressed his opinion that some kind
of CR has the best hope of beating IRV, based on similar reasoning.
> 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.
> PROLOGUE #3. CAN WE COMBINE INSTRUMENTALITY AND EXPRESSIVITY? It's easy to
> 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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