Let's rename Smith-Condorcet

Hugh Tobin htobin at redstone.net
Mon Jan 13 01:51:52 PST 1997


"Instant Majority" seems to imply that the winner will have a
majority.  The question is, a majority of what?  Only if we mean "a
majority in at least one pairwise race (excluding equal rankings from
the denominator)" can we say that Smith//Condorcet guarantees that the
winner will have a "majority".  (One might even quibble that tied
pairwise races could elect a candidate who does not have a majority in
any race.) In S//C there may well be no pairwise race in which the
Condorcet
winner or tiebreak winner has a majority of the total of all voters who
have
ranked any candidate in the election. On the other hand, a loser in S//C
may well have a such a majority in one or more races.

     When I earlier suggested that the use of "majority" in the
statement of the so-called "Majority Rule" criterion was ambiguous, it
was courteously explained to me that it clearly meant a majority of the
total voters casting ballots, and it was pointed out that the more basic
criterion requiring election of the Condorcet winner, if any, was not
about majority rule.  To call S//C "IM" seems inconsistent with the
notion that "majority" clearly relates to the total of all voters
casting ballots, because the Smith//Condorcet algorithm never asks
whether a candidate has a majority in that sense.  I understand that
one of the effects of using the [EM] version of the algorithm is to
avoid electing a candidate who has a "full majority" against him or her
in a
pairwise race, even in case of a circular tie, unless each other
candidate in the Smith set has a larger majority against him or her, and
that it is argued that therefore S//C is more consistent with majority
rule than systems which do not have this effect.  However, the
relationship between this feature and the term "Instant Majority" is too
attenuated to enable supporters of S//C to defend that name against the
charge that either the name is misleading or the system is ineffective
to deliver what it promises.  IRO supporters will pose examples and say,
"where is your Instant Majority?"

To many, "Instant Majority" may imply a vote-transfer method by which
candidates' totals are increased through elimination of other
candidates, until someone has a majority.  The use of "instant" connotes
an iterative process that is being compressed.  Thus, it is more
descriptive of inferior systems that do have these features.  It also
suggests that the output of the algorithms used in these systems, such
as IRO, is something necessary or desirable.

The proposed name does not imply use of pairwise counts, much less the
[EM] tiebreaker.  It may be asking too much of a pithy name to cover the
latter, but if we are to improve on use of proper names, it seems we
should choose a name that implies that the beats-each winner, if any,
will be elected.

I would suggest avoiding "Instant"; it smacks of commercial hype --
"instant winner" is what you are not after you scratch some sweepstakes
promotion card, and there is a risk that puritanical types will
associate the method with instant gratification, to be contrasted with
primaries or runoffs where one must earn victory.

Incidentally, the abbreviation "IM" means "International Master" to
chessplayers (this is the category below Grandmaster -- very good, but
not the best).

I was loathe to suggest my feeble attempts at a catchy acronym, but am
emboldened by Rob Lanphier's efforts.  
"Undefeated or Lowest Total Reached by Adversary" could be "ULTRA" -- I
know this is not quite technically accurate. 
"Beats All or Least Loss by Opponent's Total" could be "BALLOT".
I am sure others can do better.
Good night.

-- Hugh Tobin



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