Condorcet ballot options

Hugh R. Tobin htobin at
Sun Nov 17 15:33:54 PST 1996

donald at wrote:
> Dear Condoret people,
> I have a very good suggestion on how to improve the pairing in Condorcet
> elections.
> I suggest that we put the pairs on the ballot instead of constructing the
> pairs after the election. For example - the ballot could look something
> like the following for four canaditates:
>        |   A[]   |   A[]   |   A[]   |   B[]   |   B[]   |   C[]   |
>        |   B[]   |   C[]   |   D[]   |   C[]   |   D[]   |   D[]   |
>        |  Vote   |  Vote   |  Vote   |  Vote   |  Vote   |  Vote   |
>        | for one | for one | for one | for one | for one | for one |
> The first advantage of doing the pairs on the ballot is that we do not have
> to deal with the many combinations of Vote-Sums. A four candidate election
> would have as many as sixty-four combinations - two hundred for a five
> candidate race. But, by putting the pairs on the ballot the pairing results
> are given directly without dealing with any combinations of Vote-Sums.
> The second advantage is that this way is more honest because the voters
> would be actually comparing the candidates one to one instead of merely
> indicating second choices.
> Third: If the people vote for the pairs directly maybe we will have fewer
> circular ties. Some of you have blamed the voters for circular ties, I do
> not know if this is true, but this way the voters may show more
> responsibility. We may be able to get the ties down below fifty percent.
> Donald,

The above message may well have been intended as a joke, as the method
proposed would be extremely burdensome for the voter in a many-candidate
race, and would offer no administrative benefit.  Translating rankings
into pairwise tallies is a trivial matter for modern computers. 
Requiring voters to vote individually in each race would make Condorcet
appear unnecessarily complicated, and could lead to anomalous results
where mainstream voters don't bother to vote against fringe candidates
(unless one adds a default option -- the voter is deemed to have voted
for A over C if he or she voted for A over anyone and C over nobody). 
Yet there is the germ of an issue here worth discussing.  What options
should the voter have on the ballot?  Should the only option be to rank
the candidates from the top, with equal rankings allowed at any level
and with all unranked candidates considered equally last?  In the latter
part of this message I suggest it may be important that voters be
allowed to rank from the bottom, in lieu of or in addition to ranking
from the top. 

Allowing the voter choose between ranking candidates and voting in each
pairwise race separately would permit individuals with non-transitive
preferences to express all of them.  But while non-transitive
preferences in the aggregate result naturally from the multiple
dimensions of the political universe (different issues motivating
different voters; there is no question of "blaming" them), an individual
who votes A over B, B over C and C over A would seem to be irrational or
confused.  Perhaps an individual who consciously votes to implement the
preferences of others as well as his own (e.g., two family members who
may be ineligible to vote), could rationally vote in a non-transitive
manner.  Conceivably, a voter trying strategically to affect results in
a circular tie would want the option to vote non-transitively in some
circumstances, e.g. to vote for Z against X in the pairwise race in
which he expects X to suffer the worst loss (if any), in order that his
favorite Y may be least-beaten, while preferring X over some other
candidates that he prefers over Z.  Accommodating such cases seems
insufficient justification to complicate the ballot with the optional
individual pairwise votes, and with the necessary explanation to the
voter of the options; however, if it would defuse an objection that the
Condorcet system is culturally biased in that it imposes the rationality
of Aristotle and Descartes on voters, I would not object to allowing a
voter to write in a pairwise vote that overrides the order stated in his
or her ballot ranking.  

There is no reason to expect that allowing voters to vote in each race
would reduce circular ties.  This would be true only if individual
non-transitive preferences of some voters would tend to offset, rather
than amplify, the effect of aggregate non-transitive preferences among
those voters (the vast majority, one hopes) who would vote the same way,
at least as to significant candidates, under either system. 

I think there is something to be said for a different option that allows
a voter more easily to vote in certain pairwise races without voting a
ranking that includes all the candidates in those races.  For example,
suppose there are 20 candidates, and the voter knows nothing about most
of them but believes X must be worse than all others.  The voter can
vote A, B, then 17 equal rankings, then X (or leave X off).  But this
may be cumbersome enough that the voter will not bother (he will simply
vote A,B) or he may negligently fail to rank one or more of the 17. 
(Ossipoff has argued that ballots frequently will be "truncated.") 
Psychologically a voter may feel that he should evaluate the other
candidates and decide that they really are equal before ranking them
that way, even though he would be willing to vote X last with the same
effect.  Moreover, the voter might want to prefer even any unknown
write-in candidate over X.  One could give the voter the option to rank
his ballot from the bottom, leaving the middle (and even the top, if the
voter so chose) unfilled.  This would not be a substantive change in
Condorcet (except perhaps for the implied insertion of "any write-in
candidate" in the ranking of the voter who chooses to vote from the
bottom); it is merely a shorthand method of voting.  But if we let X=
Hitler with a plurality, and if we posit that the rest of the political
spectrum is fractured among a large number of candidates whose
supporters may fail to recognize the importance of casting a complete
ranking, then it could be important to allow the voter easily to vote
"anyone but X" or "A over everyone, and everyone over X".

If this option has already been discussed to death I apologize. I think
this is somewhat different from what has been called the "None of the
Below" or "NOTB" option, as that is described in the SW report as
representing a threshold of approval or disapproval.  What I suggest is
purely a means of casting votes in pairwise races. 

How would the ballot form implement voting from both top and bottom,
without getting too confusing?  On a paper form one could vote from the
top by putting "1, 2, 3 ..." by the names of the candidates and from the
bottom with "Z, Y, X...".  (But perhaps a ballot with nothing but an "X"
by one candidate should be counted as if it were a "1".)  With a
computer interface the voter could be given the choice of (a) inserting
such numbers and letters, with the system then generating a ranked list
for him to confirm, or (b) dragging names with a mouse into a list where
the top is within a graphic of the government office and the bottom in a
wastebasket, in each case with a prompt to confirm that the voter really
means to leave the unranked candidates equally ranked in the the middle,
not at the bottom.  A computer could be very helpful to show graphically
the effects of one's rankings. For example, if the voter has ranked from
top and bottom the names -- and photos or icons, if desired -- of
unranked candidates could jump into position at an equal level in
between the top-ranked and bottom-ranked candidates, before the voter
confirms the ballot.  The computer would allow rankings to be changed
easily before making the ballot final.  Still, I can see some problems
for voters who are illiterate and/or uncomfortable with computers.  If
there are others who think this option has any merit they may have
better ideas.  Perhaps the paper ballot should remain an option until
computer literacy is universal.

-- Hugh Tobin

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