A Vote for Smith//Condorcet

Hugh R. Tobin htobin at ccom.net
Sat Jul 6 23:53:58 PDT 1996

A vote for Smith//Condorcet

As a passive observer of this list for some months, I appreciate being
allowed to vote, and I appreciate the efforts made to facilitate informed=

voting, including Mr. Ossipoff=92s latest list of definitions.

My vote is as follows, reserving the rights to change it before deadline,=

particularly if it is drawn to my attention that any of the conclusions
stated below are materially in error.

First, for Smith//Condorcet (=93SC=94), with a minor modification of the
tiebreak count proposed in paragraph 10, below-- if my voting for this
modified form cannot, under the counting system being used, impair the
prospects of my second place choice over others (if that is not the =

case, disregard this vote).
Second, for SC, as defined by Mr. Ossipoff.
Third, for Smith//Random (which I understand reaches the same result as
SC or Condorcet when there is no circular tie)
Fourth, for Instant Runoff ("IR").
Fifth, for =93plain=94 Condorcet.
Sixth, for Regular-Champion
Next, for Double-complement
Next, for Approval
Last, for all other methods, by which, if it matters, I mean to cast
one-half vote for and against each in each pairwise contest between two =

of those methods.

By way of partial explanation, I have drawn the following conclusions and=

opinions from reflecting upon the stimulating debate in these pages (I
focus mainly on Instant Runoff as an alternative because of the campaign
ad for it that has been posted, and because it is simpler to grasp than
other methods for laypersons who are familiar with actual runoffs):

1.  No democratic system can entirely eliminate strategic voting, or
guarantee to a voter that his best interest lies in sincerely ranking the=

candidates.  It seems Ken Arrow is to be held responsible for this
lamentable state of affairs.

2.  However, in Condorcet a rational voter would insincerely only in
narrowly defined cases: when one could expect to create a circular tie
that one=92s favored candidate, who would not be the Condorcet winner,
would win in the tiebreak (in that case one would still rank one=92s true=

first choice first), or conceivably when one could predict not only a
likely circular tie but also the victory of the worse evil in the
tiebreak (in which case one might vote one=92s second choice first to
enable it to win outright).  In Smith//Random the temptation to strategic=

voting would be least, because success in creating a circular tie would
generate at best a one-third chance of electing one=92s first choice.

3.  In Instant Runoff, under plausible conditions one would often have to=

vote for the =93lesser evil=94 as one=92s first choice, just to elect the=

Condorcet winner, because with sincere voting the worse evil could win
the runoff.  In IR, if you are sure your candidate will win a majority or=

that she will run last, you can safely vote for her as your first choice =

(but see 4 below) -- otherwise, caveat voter.

4.  Under Instant Runoff, in a 3-way race where reliable polling data is
available it may be in the interest of an organized minority of the
supporters of the plurality winner (not occupying the center of the
spectrum) to vote their least favorite candidate (the opposite extreme)
as their first choice, so that the middle candidate (Condorcet winner)
will run last and the second choices of her supporters will be cast in
the runoff round.  This is possible in actual runoff systems as
well, of course.

5. Instant Runoff is still much better than plurality rule: it will pick
the Condorcet winner in some circumstances where plurality would not; and=

even when it does not, it may avoid the Condorcet loser that plurality
would have chosen.  Instant Runoff does address the problem in plurality
where two or more moderate candidates with similar positions divide the =

majority vote and allow a minority extremist to win, though Condorcet, =

SC, or Smith//Random solve it more democratically by using the second =

choices of the extremist=92s supporters to help choose between two =

moderates even if he does not run last in first-place votes.

6.  If one assumes sincere voting is the norm even for IR, then the main
difference in outcomes between SC and IR, for 3-way races where
candidates are spread across a linear political spectrum, seems to be
that SC will more reliably elect a =93middle=94 candidate with the least
first place support.  Whether this result serves the interest of the
majority depends on how one defines that interest and which majority one
refers to.  In a particular election, the two majorities consisting of
the small minority that prefers the middle over either =93wing=94
alternative, plus either of the larger minorities that prefer the
opposite =93wing=94 alternatives, each benefit by excluding the other =93=
alternative.  However, one could argue that the larger majority
consisting of both =93wings=94 may be subject to the rule of a small mino=
that holds the balance of power.  A priori, without knowing how a
particular election will come out, that larger majority might prefer a
system in which the middle voters have to choose one wing or the other,
over a system in which a candidate with a narrow core of support from a
special interest could insert himself between the major parties on the
main issues of the day, and prevail as each wing=92s lesser evil (Condorc=
winner), while extracting benefits for the narrow core constituency as =

the price of compromise.   Therefore -- at least on the assumption that =

sincere voting would be the norm, or that insincere voting in IR will =

only reduce the incidence of different outcomes than SC would produce -- =

it does not seem inherently irrational or undemocratic to prefer IR over =

SC, but it implies a greater desire for decisive outcomes on major =

issues.  This means a willingness to forego compromise and accept the =

risk that the =93greater evil=94 will prevail.  IR may thus imply a great=
er =

reliance upon institutional constraints on the powers of persons being =

elected (IR could be more dangerous, relative to SC, in a state without a=

written constitution or independent judiciary).

7.  Without Smith, in case of a circular tie in Condorcet the victory
could be awarded to someone who loses to all the other candidates; i.e.,
a majority would prefer =93any of the above.=94  It has not been shown th=
adding Smith makes Condorcet any more subject to manipulation, or has any=

other defect, unless I missed something.

8.  Even if individuals=92 preferences are transitive, those of the body
politic as a whole may not be, so in Condorcet circular ties may occur
without strategic voting (I think =93order-reversal cheating=94 is too
pejorative for a strategy within the legal rules).  This means that even
if Smith//Random would effectively eliminate all strategy, the drawing of=

lots would actually occur in some cases, and the apparent legitimacy of
the system might suffer.  The question is whether the value of the
deterrent effect of Smith//Random upon order-reversal strategy outweighs
the appearance of casino democracy and the intuitive unfairness of giving=

a candidate in the Smith set who lost one pairwise contest by a landslide=

the same chance as one who lost one by a bare majority.  On balance I
think not, despite item 9, below.  But if, under SC, a significant number=

of races were to degenerate into order-reversal manipulations or
confusing and deceptive claims about how to elect your candidate by
re-ordering your lower rankings and causing a circular tie, then
Smith//Random could be the remedy.

9.  In Smith//Condorcet (or plain Condorcet), I am not convinced that
opportunities for strategic voting in a 3-way race would be so rare as to=

be a trivial consideration.  Unless I misunderstand, the =93truncation=94=

antidote to order-reversal offered by Mr. Ossipoff is a deterrent that
depends on the credibility of a threat by the Condorcet winner that his
supporters will vote in a manner (refrain from ranking their true second
choice) that cannot help elect their favorite but can help elect their
least favored candidate, just to punish the supporters of their
second-favored candidate.  This threat may lack credibility.  With =

accurate polling and internet communications, it seems to me that a wing =

candidate with a large plurality -- particularly if his political =

positions are closer to middle than are those of the opposite wing, so =

that he may expect most of the middle=92s second-place votes --  might =

plausibly get enough supporters to reverse order and thereby prevail in a=

circular tie.  (If anyone is still interested in this, I=92ll post an =

example or two, and a semi-serious proposal to make the deterrent =

effective).   Even without an organized strategy, it seems that a backer =

of a candidate who does not figure to be the Condorcet winner might =

rationally reverse order among lower rankings, if the polls showed a =

result close to a circular tie that his candidate might win.   But even =

if order-reversal may sometimes succeed, it seems the consequence likely =

would be only the same result as IR would reach with sincere voting.
Indeed, the possibility might ameliorate the potential objection to SC in=

6, above (tyranny of the narrow middle).

10. In Smith//Condorcet, I suggest the tiebreak based on who is
=93least beaten=94 should count equal rankings or non-rankings under
 the following principle:

In each pairwise contest between X and Y, count as 1/2 vote for X and =

1/2 vote for Y an equal ranking of X with Y by a voter, if that voter =

ranked all other members of the Smith set ahead of X and Y.  Otherwise =

count the ranking as 0 votes for each.  (All non-rankings count as equal
last rankings)

It will be objected that this involves counting preferences that were
never voted  --  but I think it gives better effect to the preferences =

that were expressed.  In the tiebreaker we are already using the votes in=

a pairwise contest for a purpose other than that for which they were =

cast.  It is therefore proper to consider what the voters would likely =

have intended if they had known the tally would be used for the secondary=

purpose of a tiebreak involving the loser of that race and at least one =

third candidate.  What a voter would have intended is revealed by her =

ballot, and depends upon the actual effect of counting the half-vote, or =

not -- i.e., is a third candidate who might prevail if it is counted =

ranked by that voter over the two equally ranked candidates?  If she =

ranked all other members of the Smith set ahead of X and Y, clearly the =

answer is =93yes.=94
   Consider the normal case when the voter=92s equal rankings are
at the bottom of her ballot.  It then seems that the =93total votes =

against=94 tiebreak method requires voters to engage in some concerted =

strategic voting to achieve what they would hope and expect to be the =

effect of not choosing between two least favored candidates.  Suppose my =

wife and I have identical preferences among the candidates, and we each =

loathe X and Y equally -- neither is a lesser evil than the other.  We =

would not want either to win a tiebreak over some third candidate because=

we had failed to vote against them in enough pairwise races.  We have no =

idea which would beat the other in the pairwise rankings -- still, it is =

possible that the defeat of one by the other could be that candidate=92s =

worst or only defeat.   Under Mr. Ossipoff=92s Condorcet, I think my wife=

and I need to agree that I will rank Y over X, and she X over Y, so that =

the failure of either of us to express a preference does not result in =

one of them being =93least beaten=94 and winning the tiebreak (possibly o=
ver =

Z, our first choice).  If I have nobody to pair with, I should flip a =

coin.  But of course life is too short to spend thinking about such =

strategies for unlikely contingencies, and most people would not expect =

it to be necessary. Most people would implicitly assume that they give Y =

no greater chance to beat Z  by ranking him equally last with X (or not
ranking either) than by the offsetting spousal pairing arrangement
described above.  (I think Steve Eppley made essentially this point in an=

earlier comment on a Demorep posting when he noted the arbitrary effect
of several thousand voters ranking choices equally, rather than equal
numbers of them ranking those choices in an offsetting manner).   If all
equal rankings were at the bottom of voters=92 ballots, then using the
margin of defeat (with the same effect as counting all equal rankings as
one-half vote for and against each), in lieu of total votes against,
would conform to the voters=92 intent.  But if my wife and I rank X and Y=

equally and rank both over Q, we would not want to engage in vote-pairing=

on X and Y if it would mean Q would win the tiebreak, so the effect of
using margin of defeat would not conform to our intent.  Assuming Z and Q=

are each in the Smith set, we would prefer to have our votes count as 1/2=

for Y against X only for purposes of testing whether Z is less beaten =

than X, and not for determining whether Q is less beaten than X.  =

(Obviously we are indifferent as to whether this 1/2 vote makes Y less =

beaten than X.)  However, I suspect that allowing us to have it both ways=

could cause a circular tie in the tiebreak. Hence my modest proposed =

tweak to the tiebreak count, above.

11.   I confess I do not really understand the theory of Regular-Champion=

-- why it focuses on the number of alternatives beaten, or how (and why)
it is different from choosing among the Smith set based on the highest
number of first-place votes.  Even if that were what it amounted to, I
would be inclined to accept the idea that the possible relevance of
plurality as a tiebreak would be more likely to produce insincere
first-place votes than SC.

I have generally stated the above opinions and conclusions without
elaborate analysis or examples because my intent is to provide some
summary explanation for my vote and to invite correction of any gross
misunderstandings, not to set back the debate several months.  I had
intended to participate earlier but my time available for this intriguing=

and important list has not been sufficient both to absorb all the
valuable material posted by the regulars, and to produce technical
commentary that could withstand their withering scrutiny.  If any
particular item above is considered worth pursuing, I may be prepared to
post more detailed reasoning so that the source of my error can be

 --Hugh Tobin, Seattle

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