here is a cynical precept of politics that says
that those who cast the votes decide nothing, but those who count
the votes decide everything.
A third group, though, decides quite a bit, too: those who set
the election rules.
New York City's election rules could be rewritten soon, if the
voters approve Mayor Michael R. Bloomberg's plan to abolish party
primaries in 2009.
The mayor says his push for nonpartisan elections will lead to
fairer elections. But fair can be in the eye of the beholder. While
the pros and cons of the mayor's proposal will be debated in the
coming months, it is worth noting that recent history is riddled
with well-intentioned election reforms that ended up having
Think of the decision to hold the old community school board
elections in the spring, so they would not be overshadowed in
November. Voters forgot they were being held, or did not care, and
turnout had to be measured with electron microscopes.
Then there is New York's system of nominating candidates for
State Supreme Court at judicial conventions, which was supposed to
insulate the bench from politics. The thought now seems risible.
Or take a look at what happened with redistricting, which was
supposed to preserve the one-person-one-vote standard by
periodically redrawing district lines to take population shifts into
account. In practice it regularly becomes an exercise in partisan
gerrymandering, with the political parties redrawing electoral maps
to guarantee themselves safe, uncontested seats. Redistricting, it
has often been observed, turns the age-old principle of having the
electorate choose its leaders on its head.
Some scholars would go so far as to question whether any system
of choosing a winner by way of a vote can truly be fair, at least
when more than two candidates are concerned.
Kenneth J. Arrow, a Stanford University economist, won the Nobel
Prize in economics in 1972, in part for his work in the late 1940's
and early 1950's for developing what came to be known as Arrow's
Impossibility Theorem. It provided proof that there is no way to
arrange an electoral system to perfectly reflect the will of the
people when it comes to choosing a winner from more than two
"It was a little disquieting," Professor Arrow recalled last
week, explaining that he had originally set out to find a good
What's the problem? Depending on how an election is structured,
it is almost bound to have some imperfections from a mathematical
point of view.
In the American system, the candidate who wins the most votes
wins the election, even if he (and it still usually is a he) falls
short of a majority. That sounds fair. But does it accurately
reflect the will of the people, to the extent it can be known?
Consider the last presidential election results from Florida. If
you accept the final, much-disputed tally, it showed that George W.
Bush got slightly more votes than Al Gore, and both men trounced
Ralph Nader. So Mr. Bush won the state, and the presidency. But most
people in Florida voted for someone other than Mr. Bush. And since
most Nader voters would presumably have preferred Mr. Gore to Mr.
Bush, it follows that Mr. Gore would have been a more acceptable
choice to most Floridians than Mr. Bush. But second choices do not
count in the American system.
A number of alternative election systems exist. A runoff election
between the top vote-getters can be held if no candidate gets a
majority of the vote. Such a system, though, can keep members of
minority groups racial, ethnic or ideological from winning, even
when they finish first in the initial count.
In the Democratic mayoral primary in 2001, Fernando Ferrer, who
forged a black-Latino coalition, beat Mark Green. But since neither
man got more than 40 percent of the vote, a runoff election was
held. Mr. Green won the runoff (only to lose the general election),
and some of Mr. Ferrer's supporters complained that the runoff
system was unfair.
Other countries use other voting systems. Many parliamentary
systems use proportional representation an alternative to the
American winner-take-all system in which parties are allocated
seats based on their share of the popular vote. Such an arrangement
gives a voice to smaller parties, giving their representatives a
small number of seats. But critics argue that they create unstable
governments held together by fragile coalitions.
Then there are systems in which voters rank their choices in some
way. One such system of ranking candidates, and choosing the one at
the end with the largest number of points, was championed by
Jean-Charles de Borda, an 18th-century French scientist. And why was
he interested in voting systems?
"He thought the wrong people were being elected to the French
Academy of Sciences," said Donald G. Saari, a professor of economics
and mathematics at the University of California at Irvine who has
written several books about election theory. He said that the Borda
system appears to be the fairest way of voting.
Many groups in the United States now advocate a ranking system
called Instant Runoff Voting. Known by its avuncular-sounding
acronym, IRV, this is a system
in which voters rank their choices. If a candidate wins a majority
of the vote on the first count, that candidate wins. Otherwise, the
losing candidate is eliminated and those votes are accorded to those
voters' second-choice candidate, and so on, until a winner gets a
But changing voting systems can be even tougher than figuring out
a butterfly ballot. For one thing, governing parties like to stick
with the systems that brought them to power. For another, many new
systems sound as if they came out of that New York State Math
Regents exam, the one whose results were discounted because it was
But it is not an academic question. Dan King, a professor of
mathematics at Sarah Lawrence College, offered a hypothetical
example to demonstrate how the choice of election system can
actually determine the outcome of the election.
Imagine nine people trying to figure out which actor was the best
James Bond: Sean Connery, Roger Moore or Pierce Brosnan. (O.K.,
actually Professor King's example said that the nine people were
trying to choose between candidates A, B and C, but this is not math
class.) Four of them like Connery best, followed by Moore, followed
by Brosnan. Three voters like Brosnan, followed by Moore, followed
by Connery. And two voters like Moore the best, followed by Brosnan,
followed by Connery. So who is the best Bond?
In a plurality system, Sean Connery would be the winner: he got
four votes, while Pierce Brosnan got three and Roger Moore got two.
But that's no majority.
But what if a runoff election were held? Roger Moore would be
eliminated, because he got the least number of votes. But the Moore
fans liked Brosnan second best. That would leave four voters
preferring Connery to Brosnan, and five voters preferring Brosnan to
Connery. Pierce Brosnan would be the winner of the 007 runoff.
And in a Borda count giving 1 point to the least favorite, 2
points to the second and 3 points to the favorite Roger Moore
would be the Bond of choice.
"Three procedures, three different winners," Professor King
In the coming weeks Mayor Bloomberg's Charter Revision Commission
will come out with proposals for how a nonpartisan election system
might work: how people will qualify to get on the ballot, whether
runoffs will be held, what the thresholds will be. Some of those
details could be as significant as their primary goal of abolishing
"You can skew the outcome of any election," said Burt Neuborne,
the legal director of the Brennan Center for Social Justice at New
York University School of Law, "depending on how you structure the