y/n strategic instability.

Hugh R. Tobin htobin at ccom.net
Sat Nov 16 00:20:48 PST 1996

The following comment on an earlier exchange seems to have been lost in
the ether.  Though Mike Ossipoff has since been more critical of a "y/n"
overlay to Condorcet, I attempt again to post it, lest it be thought
that others on the list might accept such an alteration.

Mike Ossipoff wrote:
> Demorep said:
> [snip]
> If your point is that it would be good to add a y/n vote &
> disqualify anyone who gets "n" from a majority, then no one's
> arguing with you.

I would argue against adulterating Smith//Condorcet with a
disapproval/disqualification element.  If I understand the idea
correctly, it would mean that the Condorcet winner (or winner of the
Condorcet tie-breaker), A, would be disqualified if a majority of the
total number of voters who expressed a preference between any two
candidates voted "n" to A (Or may one even go to the polls just to vote
"n" or "y" to one or more candidates even without voting in any pairwise
contest?  If not, then I think the "y" votes are meaningless.). If the
candidate who otherwise would win were disqualified, it is not entirely
clear to me what this would mean: for example, would all losses to that
candidate in pairwise races be disregarded to select a new winner, or in
case of a circular tie would the second least-beaten member of the Smith
set be elected?  (Note that unless it is made very easy, or even the
default option, for the voter to disapprove "all of the below", very
minor candidates likely would be nondisqualified even though probably
less acceptable to the majority, were their views known, than those
expressly disapproved, which might include all the major candidates --
this would present difficulties for any rule that attempted to pick a
winner from nondisqualified candidates outside the Smith set rather than
call a new election.)  

If adding disapproval means that B may be elected although a majority of
those voting in the race A vs. B prefer A, and although no other
candidate beats A, this clearly contradicts the basic democratic
principle underlying Condorcet. 
Moreover, the argument for disapproval naively assumes that a voter will
choose "y" or "n" based on a sincere comparison of a candidate to some
standard, without regard to the effect of this choice on the outcome of
the election.  Voters know that choices are meaningful only relative to
the alternatives, and with the guidance of political campaigns (and as
has been noted on this list) they will make choices on the ballot in
light of the effect of those choices under the system in use. Voters
would vote "n" to all but one candidate not because those other than
their favorite were unacceptable in some absolute sense, but because of
the consequences of their disapprovals under the system: e.g., their
favorite could win even though another candidate might be Condorcet
winner (or circular tie winner), or at least their first choice would
get another chance soon (see quoted text below).  If their candidate
were expected to be Condorcet (or tiebreak) winner, then (depending on
the rules) they might disapprove all others as a defensive measure, so
as to get a new election rather than losing outright to disapprovals by
supporters of other candidates.   
For example, if I were a "wing" candidate in a 3-way race fearing a loss
to a Condorcet winner in the middle, and if the other wing candidate
were clearly the least acceptable to the middle, wouldn't I tell my
followers that both others must be deemed unacceptable?  If both other
candidates can be disqualified by "n" votes, but I get few enough "n"
votes from the middle, then don't I win as the only non-disqualified
candidate?  (If the rule is that disqualifying the Condorcet winner
always triggers a new election, perhaps I also have to engineer, or hope
for, a circular tie, but thanks to disapproval I need not win the usual
tiebreak).  The middle may defensively give me "n" votes, but then
everyone is disqualified and I still can get a new election instead of
four years of middle.  Assuming the rules would allow me to win as the
only nondisqualified candidate, then possibly the other wing will
approve the middle candidate in order to prevent this, but this leaves
me no worse off for having urged my followers to disapprove the middle
-- and illustrates that the y/n decision can be affected in both
directions by relative preferences.

Regardless of any organized strategy, as a voter backing a major
candidate I would be inclined to rate all other candidates as
"unacceptable" if that could either help elect my first choice or
prevent another candidate from winning outright.  Unless there is an
apparent risk that X, one's third or lower choice, will be one's highest
choice remaining undisqualified, in circumstances where one's higher
than X (but not first) choice could have won if not disqualified, there
is nothing to be gained by refraining from disapproving everyone except
one's first choice.  

>But, as has been repeatedly pointed out to you, there wouldn't
>be an election anything like the one you describe, where everyone
>is majority-rejected.

As indicated above, offensive and defensive "n" votes easily could cause
this result in a three-way race.  All it requires is that voters prefer
to risk having a new election than to acquiesce in victory by their
respective second-ranked candidates, even if they strongly prefer their
second-ranked candidates over the third candidate.   

Even if we assume little or no strategic thought by voters, by adding a
feature that allows a nondisqualified candidate to defeat the candidate
who would win under Condorcet, we would favor candidates whose backers
are most doctrinaire, i.e. they regard all others as "unacceptable".
Thus, adding the disapproval feature would not ensure election of more
"acceptable" candidates, though it would add further potential for
strategic voting, could unneccessarily violate majority rule principles,
and could result in unstable and short-lived regimes. I would think
Condorcet would rests uneasily in his grave if such a dramatic change to
his system could pass without objection on this list.

My votes for Smith//Condorcet and Condorcet are for those systems
without any adulterations except as I have expressly stated on my

> As I said, though, just on the chance that that happened, when
> using the added y/n vote, it would be better to merely limit
> the winner's term or hold another election very soon, rather
> than to just not have a President. Otherwise, one of the
> gentlemen in your example would surely take over.
> Mike
> --

-- Hugh Tobin

More information about the Election-Methods mailing list