policy : Putting democracy to the test

PHILIP BALL

How does a voter in a democratic system determine his or her choice of candidate? While politicians fret about whether to focus on health care, the environment, crime or a good TV profile, a group of Brazilian physicists claim in the July issue of Physical Review E that it all comes down to the same basic process in the end. The work reveals no magic formula for would-be power-mongers, however -- it says simply that voters’ choices seem to be a product of several sub-decisions.

Sounds trivial? Don’t be too hasty, for the statistics of voting are a subtler matter than you might imagine. R. N. Costa Filho and colleagues from the Federal University of Ceará in Brazil have analysed the voting patterns in the October 1998 elections in Brazil, where voting is compulsory and a proportional election system is used. The electorate totalled over one hundred million, selecting a president, senators and congressmen from thousands of candidates.

The physicists analysed the fraction of the vote that each of the various candidates secured: how many got five percent, how many got ten per cent, and so forth. When the number of votes cast is divided up between the candidates in this way, there is a mathematically precise way of expressing the fact that relatively few candidates get large fractions of the votes, and that a larger number of candidates get fewer votes. The researchers discovered that the mathematical law buried within the voting statistics was strikingly familiar: it was an exact inverse relationship.

This kind of relationship is seen for many widely different natural phenomena, such as the relationship between earthquake frequency and magnitude (more powerful earthquakes are less frequent), or between the size and frequency of certain kinds of landslide or volcanic outburst.

Some scientists believe that this type of so-called ‘scaling law’ is one of the fundamental attributes of nature’s machinations; but it is by no means obvious that it should apply to elections. Costa Filho and colleagues found that the same scaling law applied whether they looked at just the voting statistics of São Paulo (with around 23 million voters) or those of the country as a whole, suggesting that the law is unlikely to be sensitive to regional issues. What causes this particular relationship to arise?

The inverse law applied only over a limited range in the data -- there were deviations for the candidates who secured the greatest or smallest fractions of the vote. The researchers argue that this sort of behaviour is expected for a process whose outcome depends on the outcomes of several independent sub-processes, each of which has a definite probability. Thus, you might say, a voter considers a number of deciding factors, such as the candidate’s position on this or that issue, and makes a final choice based on her feelings about each of the issues in turn. This would be different from a choice made for interdependent reasons -- such that, for example, a candidate’s questionable business dealings influence the voters’ views about his stance on public health.

Of course, it is extremely hard in practice to break down anyone’s decision-making process in this way. But perhaps the most appealing aspect of the work is that it shows that election systems do seem to have some internal logic that can be quantified. One could therefore investigate whether other countries, perhaps with different voting systems, show the same scaling behaviour -- and if not, one might speculate about why not, and what that implies for the democratic process.

© Macmillan Magazines Ltd 1999 - NATURE NEWS SERVICE