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Why first-past-the-post voting is fundamentally flawed
http://www.newscientist.com/article.ns?id=mg19826511.600&print=true
12 April 2008
Phil McKenna

ONE person one vote is the mantra of democracy. And as Americans
prepare to elect a new president this year, they'll be weighing up
who to cast their precious vote for. Yet giving each citizen just
one vote may not serve democracy's best interests. It can all too
easily throw up a winner who in a straight fight with the runner-up
would not be the majority's choice - surely a negation of
democracy.

How can this happen? It's to do with the way voters are allowed to
express their preferences, and how those choices are turned into a
winner. Most elections in the US, the UK, Canada, India and many
other countries use what is technically called a plurality voting
system (better known as first-past-the-post) for single-winner
elections. Every voter chooses one candidate from those standing,
and the candidate with the most votes wins.

It's beautifully simple. But it can also be strongly influenced by
fringe candidates with relatively little support. By taking votes
that would otherwise go to one of the leading candidates, these
"spoilers" can tip the outcome in favour of that candidate's main
rival. In five of the last 45 US presidential elections, plurality
voting has handed the White House to the second most popular
candidate, according to William Poundstone, author of Gaming the
Vote: Why elections aren't fair. "It's really the worst system. Its
only virtue is that it is the simplest way of voting, which is why
we put up with it," he says.

Voting reform initiatives in the US usually focus on problems with
voting machines and on the electoral college used in a presidential
election - an antiquated system that gives more weight to voters
from some states than from others. Yet arguably the larger problem
with elections in America and elsewhere is plurality voting itself.
Is there a fairer alternative?

Researchers and politicians have long known of plurality's
weaknesses, but until recently most believed the alternatives
weren't any better. In 1950, economist Kenneth Arrow, then a PhD
student at Columbia University in New York, seemed to prove once
and for all that it was impossible to have a method of voting that
was entirely fair (Journal of Political Economy, vol 58, p 328).

First, Arrow assumed that all voters would vote honestly rather
than try to manipulate the system. Then he identified five criteria
that he felt a good voting system should meet. Three of them seem
obvious: every election should result in a decisive winner; if a
candidate is the unanimous favourite, he or she should win; all
candidates should be treated equally.

A fourth criterion stipulates that all voters should count equally
and be anonymous, in order to guarantee freedom of expression and
ensure that it is not only the wishes of a dictator or minority
elite that count. Finally, Arrow's fifth criterion states that if
you look at any three candidates, the way the system reflects
voters' preferences for candidate A or B should be independent of
their views about candidate C. That is, liking candidate C
shouldn't force voters to desert either A or B.

Plurality voting fails to meet the last criterion. One recent
demonstration of this failure happened in the 2000 US presidential
election. It is now widely accepted that the Green Party candidate
Ralph Nader took votes that would otherwise have counted towards Al
Gore. A voting system that met Arrow's fifth criterion would have
ensured that the winner in the race between Al Gore and George W.
Bush would not depend on whether Nader was standing too (see
Diagram).

Arrow applied his test to all the proposed voting systems that
allowed voters to rank candidates in order of preference. He found
that no voting scheme could meet all his criteria. The conclusion,
which came to be known as Arrow's impossibility theorem, spawned a
new field of study called social choice theory and earned Arrow the
Nobel prize in economics in 1972. "It really caused decades of
despair. It asserted that no voting system is going to be fair,"
says Poundstone.

But could Arrow have overlooked better options? Warren Smith, a
former mathematics professor at Temple University in Philidelphia,
and co-founder of www.rangevoting.org, claims to have circumvented
Arrow's theorem with a controversial voting system called range
voting, which the theorem doesn't cover. According to Smith, range
voting consistently yields the most satisfying result for the
greatest number of voters.

Chances are you are already familiar with range voting. It is used
to rate videos on YouTube, or score entrants on Hot or Not, where
users subject photos of themselves to public scrutiny. In an
election, each voter would score candidates on a scale of 0 to 9,
say, or mark them with an X for "no opinion". Unlike plurality
voting, where you have only one vote, range voting allows you to
express a view about as many candidates as you like. And if you
feel equally about two or more candidates, you can give them the
same score. When all votes are cast, the candidate with the highest
mean score wins. A variant of the system was used in Venice in the
Middle Ages to elect the city's leaders. Over the years it fell
into obscurity, but in 2000 Smith renamed it and began promoting it
again as a fairer alternative to plurality voting.

Range voting satisfies each of Arrow's five requirements, something
no other voting system has been able to accomplish. "It's better
than plurality in every way except possibly simplicity," Smith
says. "It allows voters to express more preference about the
candidates, eliminates the problem of vote splitting, and tends to
elect winners that are more representative of the majority will."

Smith bases these claims on a series of computer simulations in
which he tested 31 voting systems to determine which yielded the
least disagreeable result for the greatest number of voters. To
gauge this he measured "Bayesian regret", a parameter that attempts
to quantify how unhappy groups of people are following a poor
outcome. The better the voting system, the less Bayesian regret it
causes. He claims the improvement in expected human happiness when
switching from plurality to range voting would be about the same as
the impact of introducing democracy in a dictatorship.

Smith isn't the first to use Bayesian regret to compare voting
systems, but in previous models no one system consistently came out
on top. Smith says this is because they didn't include range
voting, but his study is controversial because it has not been
accepted for publication in a peer-reviewed journal. Smith claims
this is because reviewers have an irrational aversion to range
voting.

Others say his methods are unclear. "One would have to study the
computer program to know whether the comparison is valid," says
Eric Maskin at the Institute for Advanced Study in Princeton, New
Jersey, who won the 2007 Nobel prize in economics for work he did
on the rules that govern voting systems. Critics also point out
that the system requires voters to assign values to candidates,
something Arrow ruled out on the grounds that the values assigned
have no real meaning.

Claude Hillinger, an economist at Ludwig Maximilian University in
Munich, Germany, who has devised a similar value-based method that
he calls evaluative voting, says Arrow's exclusion is groundless.
"Systems that give a range of values have more meaning than ranking
systems because you have the freedom to assign any number to any
candidate that you wish."

More than half a century after publishing his landmark theorem,
Arrow, now 86 and professor emeritus at Stanford University,
maintains that voting systems based on scores rather than rankings
don't measure up. "I don't think [range voting] is a true voting
system," he says. Before publishing his theorem, Arrow and his
colleagues considered value-based systems but dismissed them. "We
felt there was no meaning to compare values between people," says
Arrow. Maskin, a former student of Arrow's, agrees. "If I say that
I prefer Clinton to Obama, the statement has meaning - I would put
Clinton in office rather than Obama. But what does it mean to
assign Clinton 7 points and Obama 4?"

Ripe for manipulation

Not only are the numbers meaningless, Maskin says, but such
attempts to quantify preference give voters a strong incentive to
exaggerate. "Say I slightly prefer Clinton over Obama, but I am
concerned that Obama is surging ahead, I have every incentive to
overstate my liking of Clinton and my dislike of Obama," Maskin
says. No system is entirely safe from such manipulation, but Maskin
says range voting is particularly prone to strategic voting because
voters can safely inflate and deflate scores without compromising
their support for their preferred candidate.

Political campaigner turned voting reform advocate Rob Richie is
also dismissive of range voting. "I think what Smith and the other
range voting supporters haven't grasped is campaign psychology,"
says Richie, who is executive director of voting reform advocacy
group FairVote. "It's one thing to use range voting on Hot or Not
or for other internet voting when you don't have a big stake in the
outcome. But when you really care who wins, you are really trying
to help your side."

In other words, the big problem Richie foresees is that candidates
would have a strong incentive to persuade their supporters to vote
strategically. "Strategic voters will beat non-strategic voters,
and when that occurs there is a real problem with our democracy,"
Richie says. Smith says these effects would cancel out between the
different candidates because a similar share of each candidate's
constituency would vote strategically.

If the one voting system that apparently satisfies Arrow's criteria
for single-winner elections is destined to be confounded by
political manoevrings, what's the alternative? Many electoral
reformers argue that instead of getting hung up on devising a
perfect voting system, we should adopt the system that works most
of the time. So which among the dozens of alternatives would that
be?

For Maskin, the answer is the Condorcet method, named after
18th-century French mathematician the Marquis de Condorcet. Voters
rank each candidate in order of preference. They can give two or
more candidates the same rank, or not rank a candidate at all. This
makes for a rather complex set of possible outcomes that requires
computers to calculate the winner in all but the smallest
elections. In essence it works like this: for every possible
combination of two candidates, the computer scans through all the
rankings and counts how many times each candidate is ranked higher
than their adversary. The overall winner is the candidate who wins
the most of these one-on-one comparisons. Crucially, this means
that the Condorcet winner in an election need not necessarily be
the candidate with the majority of first-choice rankings.
Proponents of Condorcet say it is the fairest method because it
elects the candidate that the greatest number of people find the
least disagreeable. The downside is it can elect a candidate that
no one wanted as their first choice.

Condorcet has yet to be used in any government elections, but there
is another ranking system that has made that grade. Known variously
as instant run-off voting (IRV), preferential voting and the
alternative vote, it uses the same ranking system as Condorcet, but
the count is different. First candidates are ranked according to
how many first choices they received, as in plurality. If no
candidate has an overall majority, the candidate with the least
number of first-choice votes is eliminated and their votes are
reallocated according to the second choices on the eliminated
candidate's ballots.

IRV's strength is that it places great value on voters' first
preferences. "IRV will never elect a candidate who doesn't have
substantial first-choice support," says Richie, whose organisation
FairVote promotes the system.

Richie points to the method's proven track record in Australia,
where it has been used since 1918 to elect the country's House of
Representatives. According to Ben Reilly, director of the Centre
for Democratic Institutions at the Australian National University
in Canberra, preferential voting was brought in to replace
plurality and prevent fringe candidates from spoiling the election.

Another major advantage of IRV is that it allows smaller parties to
campaign for election and present their views without the risk of
splitting the votes of larger parties. "The smaller parties have a
really strong interest in running candidates even where they can't
win the election, because they can have a strong influence on
policy," Reilly says.

IRV is not without its faults. "It's not quite as vulnerable as
plurality," Maskin says, "but it doesn't rule out spoilers or the
chance that a candidate without a majority might win." Stranger
yet, when things get really close in an instant run-off vote,
selecting your favourite candidate could in theory do more harm
than good. "If you increase your vote for somebody in IRV it can
make them lose," says Smith.

For example, suppose there is a tight three-way race in which
candidate A leads but doesn't have an overall majority, while
candidates B and C are vying for second, with B voters preferring A
as their second choice and C voters preferring B as their second
choice. If candidate A courts and wins too many of the C voters,
then candidate C will be eliminated first and his or her votes will
give candidate B the overall victory.

"The problem I have with these little paradoxes is that they break
down in the real world," says Steven Hill, director of the
Political Reform Program with the New America Foundation, a
political advocacy group that supports IRV - and there is indeed no
record of the scenario described above ever having happened in
practice. "In reality, you would have to have members of the Green
Party voting for the Republican candidate," says Hill.

Of all the alternatives to plurality voting, IRV is the only one
that has gained a toehold in government elections. For example, San
Francisco, California, and Takoma Park, Maryland, use it in
municipal elections. And presidential hopefuls John McCain and
Barack Obama have both supported efforts to adopt the system in
state-wide elections.

As campaigners try ever sneakier ways to manipulate the plurality
system, so the need for change is growing more pronounced. Having
seen how Ralph Nader split the liberal vote in the 2000 US
election, Republicans helped fund his 2004 campaign in the hope
that he might undermine the Democrats again. The practice has now
become commonplace in American politics.

But change is in the air. After casting a half-century-long shadow
of despair over the field of voting theory, even Arrow seems to be
softening his stance. "Most systems are not going to work badly all
of the time," he admits. "All I proved is that all can work badly
at times."

Could plurality voting have had its day? Perhaps it's time to give
every man and woman more than one vote.

Focus on America - Delve into the science and technology questions
facing the USA in our special report.

Weblinks

Test different voting systems
http://www.amstat.org/mathandvoting/index.cfm?fuseaction=submit
Comparing IRV with Plurality
http://www.instantrunoff.fairvote.org/how/gates/votesequence.html