Condorcet vs Approval

[Joe Weinstein]

[The following message was composed and sent Fri 2 March 2001 approx 6 PM 
Pacific Standard Time.  Hours later my Hotmail postmaster indicated - 
without giving any reason - that delivery of this message to eskimo.com 
would be delayed by 48 hours, i.e. to Sun 4 March 2001 approx 6 PM.  Maybe 
this copy will be delivered earlier. - Joe]


On Fri. 2 March (or Sat. 3 March in Sydney) Craig Layton wrote:

"Joe wrote (in relation to Forest's Condorcet//Approval compromise):..."

My query:  Joe who?  Not I.

As a matter of fact I have no enthusiasm for Condorcet - or for any other 
pairwise comparison methodology which simply looks at qualitative 
preferences but ignores their strengths (i.e., preference is taken as one of 
just three alternatives:  positive, negative or zero, and it doesn't matter 
how strong a positive or how strong a negative).

To be sure, one can do - and get lots of professional credit for - some 
arcane math by investigating various qualitative pairwise comparison schemes 
and issues.  Witness Arrow; and Don Saari, who did truly ingeniously show 
that in one sense Borda is by far the least paradox-prone of all scoring 
methods applied to qualitative preference.

For me, Condorcet (as most methods treated here in the EM-list) has much the 
same problems noted specifically for Irv about six weeks ago. Namely, the 
method gratuitously (indeed, from my viewpoint, stupidly) disregards 
preference info given or readily retrievable from the voter.  For its part, 
at each stage, Irv disregards all voter preferences other than between 
(currently) top and lower places.  For its part Condorcet ignores different 
strengths of preference.  All preferences are classed as either positive 
(never mind with what strength), zero, or negative (again, never mind 
strength).

For me, Condorcet breaks down at the very beginning, in the simplest case, a 
2-candidate contest between A and B, where Condorcet Winner A beats B over a 
majority of the voters by very shallow preference, but B beats A over the 
remaining voters by heavy preference.  E.G.,  suppose (on a grade scale of 
100) the voters grade the candidates as follows:

    55% of voters:  A(80) B(75)
    45% of voters:  A(40) B(80)

To me it is clear that the deserving winner is B, the candidate with a 
higher grade average (which some people equate exactly, and I roughly, to 
higher 'social utility').  Of course, one might argue (in my view, 
correctly) that - for purposes of true social utility - a grade of 40 is 
surely worth more than just exactly half of a grade of 80, etc.  However, 
even if grades were in some way convex-transformed to reflect this view, 
before being averaged, B would still be the clear winner.

In order to 'justify' Condorcet (or another qualitative-only preference or 
ranking method), its partisans could insist that the election method allow 
only qualitative preferences to be expressed on the ballot.  Their one 
credible material excuse would be that the computers requisite for more 
quantitative input and tabulation would be too expensive or slow or 
unreliable.  Nowadays (and prospectively) this excuse is utterly mistaken.  
However, if one sincerely believed it, one should be more consistent and 
demand use of Approval (i.e. just pass-fail grading of each candidate): 
compared with Approval, such methods as Condorcet (not to mention Irv) are 
far more complex and demanding computationally.

High-res grading provides a direct way to express quantitative preference 
strengths, and (through grade averaging) provides readily tabulated and 
consistent scoring of candidates.  By comparison, methods like Condorcet or 
Irv both disregard voter information (on preference strengths) and are 
computationally more intensive.
High-res grading makes so much sense that an Irvie cultist to whom I 
explained it could think of only one rejoinder: it's too 'corny'.

Yes, direct grading of candidates is 'corny', and makes a far less 
interesting research-game topic than complex info-discarding pairwise 
comparison setups like Condorcet or Borda.  Similarly, today's money-based 
price-based economy is far too 'corny'.  Economic life and research could be 
a lot more interesting if we ditched money and went to a system of pairwise 
product barters.  Yes, and we could ditch Kepler's elliptical planetary 
orbits in favor of Ptolemy's more interesting and far less corny system of 
epicycles.

I leave to a forthcoming posting a full discussion of the issue of Hi-res vs 
Low-res grading, = Approval.  (But hint: the old argument - that hi-res 
'strategy' boils down to that of Approval' - is less than decisive, because  
- as some of Approval's staunchest supporters here have lately noted - the 
utility of a vote embraces not only the direct outcome but also the ability 
to send a message, so the above 'strategy' is not all there is to true 
strategy: in fact, it's only a small part.) At least Approval, like 
higher-res, is part of the family of unconstrained grading methods.  
Considering criteria which I also plan to post and discuss soon, any one of 
these methods is superior to the bother of Condorcet(let alone Borda, Irv, 
etc.).

THANKS FOR YOUR HEED

Joe Weinstein
Long Beach CA USA

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