Consensus, Condorcet(0), and Condorcet(1/2)

[Hugh R. Tobin]

At 08:53 AM 7/28/96 -0700, Steve Eppley wrote:
>Hugh T wrote:
>>Steve E wrote:
>>>Which of the following is the greater violation of democratic 
>>>principle in a 2-candidate race:
>>>  1. Electing candidate A even though A lost to B (46 to 54).
>>>  2. Electing candidate A even though A lost to B (34 to 46, 
>>>       with 20 who have no preference between them).
>-snip-
>
>>But in the tiebreak we are comparing the results of at least three
>>pairwise races.
>-snip-
>
>Sure, I know that.  But there's an important connection.  What is
>the "largest votes against" tie-break measuring?  What's the meaning 
>of each pairwise race?
>
>The C>A=B voter is already counted as a vote against A in the AC
>pairing and as a vote against B in the BC pairing.  You seem to
>be saying that this voter should also be counted in the AB pairing
>because s/he'd benefit if we do that.  I don't think that's a
>sufficient reason, and I think it would muck up the meaning of 
>what's being measured.  
>

 I had thought it was agreed that a voter ranking candidates equally should
at least
have the option to cast half-votes each way, and the question was whether
there should
be multiple choices with explanations of their potential consequences on the
ballot (and,
if so, what should be the default), or a fixed rule designed to capture the
intent of sincere 
voters' rankings.  If half-votes are not even allowed, then voters who are
sincerely
indifferent as between lower-ranked candidates (and who do not have a
strategy based
on expectations of which will beat the other) must engage in vote-pairing or
random 
selection in order to give full effect to their votes for their first
choices.  As a candidate, I would
encourage my supporters to rank all candidates below me randomly if they
have no preference
among them or are completely ignorant about the others, so that I will have
the best chance to 
win a pairwise tie.  Is it desirable to encourage voting such false
preferences?   (One could
argue it provides an incentive to become informed and make choices --
obviously those who 
favor systems that throw out all truncated ballots think so -- but at least
in those systems the 
importance of complete rankings is easily understood by the voters, which is
not the case in 
Condorcet-0 -- it subtly robs the truncating voter of a portion of his total
voting power, in a small
number of cases,  to elect his first place candidate).

I submit that if we want the pairwise races to reflect sincere preferences,
so that an apparent
Condorcet winner really is the candidate who would win against each other
one, then we should try
to minimize incentives for voting insincere preferences.  My half-vote
proposal does
this far better than the alternative of always counting equal rankings as zero.

The other point that I intended to raise, by providing an example showing
all votes rather than
responding to the question as you posed it, was that your comparison omits
information that 
is relevant to the aggregate unhappiness of the voters with various
outcomes.  That only 46% 
voted against a candidate in her only loss is more impressive if the reason
is that a large number 
of voters ranked her equally with another at the top of their ballots (or at
least above all other members of the Smith set), than it is  if a large
number ranked her equally with another at the bottom of their ballots.
In the former case it could be that electing either A or B would maximize
the political utility of the voters
who ranked C last, so 46% really reflects the total "unhappiness" from the
election of A.   In the latter case it seems  that 46% understates aggregate
unhappiness.  In that case I do not see that we should measure
aggregate unhappiness  as being less than it would be if the "C" voters who
ranked A and B
equally had instead split equally between them. 

Consider this example:

A=B>C  20
A>C>B  12
B>A>C  20
C>B>A  26
C>A>B  22

A beats C 52-48
B beats A 46-34
C beats B 60-40

Isn't there a better case for electing A over C here, than in my earlier
example where  the
lower "turnout" between A and B reflected abstention by voters who all
preferred C to both of them?

(snip)

>>From an older message:
>
>>Consider a slight modification of this scenario: Dole's strategists
>>get a minority of his supporters, 18 per cent of the total, to
>>order-reverse (alternatively, they really prefer Nader), the rest
>>sincerely vote Dole, Clinton.
>>
>>28 Dole, Clinton
>>18 Dole, Nader
>>20 Clinton
>>34 Nader, Clinton 
>
>With Condorcet(0) the Dole reversers would be burned at the stake if
>they elected Nader instead of Clinton, so reversal isn't a plausible
>scenario in my opinion.
>
Whether it is plausible with these specific names is beside the point.  As I
argued elsewhere, an attempt at reversal that barely fails is not implausible
in some circumstances.  Likely it will be those Dole voters who see the least
difference between Clinton and Nader who will be willing to take the chance of
reversal, so strategy shades into sincere preference -- in practice we would not
really know how many were reversing, and how many sincerely were so disgusted
with Clinton that they would even prefer Nader.  

>The alternative--that 18 D>N>C voters really do prefer Nader--is more
>plausible.  A question we shouldn't ignore about the alternative
>scenario is: who *ought* to win with those sincere preferences?  
>Why not Nader?  If the win is instead accorded to Clinton, 48 voters 
>will be happier and 52 will be unhappier.  If the win is accorded to
>Dole, 46 voters will be happier and 54 will be unhappier. 
>

If Nader wins because the Clinton voters could have elected half-votes but
ignorantly voted only for Clinton in the belief that a second ranking would be
used only to decide between Dole and Nader (whom they find equally
unacceptable),
then I count this as a failure of an unduly complex  system.  If Nader wins
because 
the Clinton voters did not even have the option to cast half-votes, then I
have to ask, 
should Nader really prevail in the case where he is ranked equally with Dole
at the
bottom of all Clinton voters' ballots, when had the Clinton voters all voted
a second
choice, and two-thirds of them had actually preferred Nader to Dole, Nader
would 
have lost?  And should the Clinton voters be coerced into voting false
preferences in 
order to maximize the chance to elect their candidate?

-- Hugh Tobin

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