快猫短视频

YOU probably think you base decisions such as who to vote for, or which brand of coffee to buy, on a rational weighing up of the facts. Well, maybe, but try this simple experiment, first performed four decades ago and reproduced many times since. Stand on a busy street corner and look up at the sky. The crowd will part around you, indifferent to whatever it is you may be looking at. Now enlist the help of a friend to stand beside you and also look skyward. Soon, others will stop and gaze up as well. A similar thing would happen if you and your friend boarded an empty elevator and faced the rear wall. As more passengers boarded many would face the back wall too.

These well-known illustrations of peer pressure seem like amusing ticks, of little relevance to any important decisions. But physicists have begun to show how this fundamental human 鈥渇orce鈥� can determine how opinions spread in a population. Their work suggests that the swings in public opinion or the distribution of votes in an election have as much to do with people鈥檚 tendency to be influenced by their neighbours as the details of a candidate鈥檚 policies.

Jozef Sznajd and his wife Katarzyna Sznajd-Weron, both physicists at the Polish Academy of Sciences in Warsaw, were the first researchers to investigate the physics of peer pressure. Since then, many others have followed what is now known as the Sznajd model. This is based on the idea that, in certain aspects at least, human society is not so different from a bar magnet.

The basic tool the physicists apply is known as the Ising model, which was developed in the 1920s to understand how iron and similar materials become magnetised. In the equations of the Ising model, clumps of iron atoms are represented as little 鈥渟pins鈥�, regularly spaced on the corners of a lattice. At high temperatures, the axis of each spin is as likely to point one way as another, as they鈥檙e all jiggled into disarray by thermal vibrations.

In this state, a piece of iron has no overall magnetisation. But because the clumps feel the influence of their nearest neighbours, it鈥檚 actually more comfortable for them if the axis of their spins all point in the same direction. So as the temperature, and therefore thermal vibration, is reduced, one by one the spins flip to point in the same direction as their nearest neighbours (see Diagram). At a critical temperature they will all have flipped so that all the spins end up pointing in the same direction. This is the most comfortable 鈥� or, in physics terms, lowest energy 鈥� state, and is what gives a piece of iron its magnetism.

The Ising model is a standard tool for physicists studying the behaviour of magnets, but the Sznajds decided it might also be able to model other systems composed of small, shifting units 鈥� human society, for example. So they substituted animal magnetism for electromagnetism in the Ising model. And when they did, out popped a surprisingly accurate model of human behaviour.

They first considered a rather simple situation. Individuals are arranged along a line and can vote for one of two parties. Each initially (and randomly) prefers either party A or party B. If your two neighbours both prefer A then you will also come to prefer A 鈥� if you don鈥檛 already, that is. A similar thing happens with B, of course. And that鈥檚 all there is to it.

In this model the eventual result is dull: it鈥檚 always unanimity or a stalemate. But the evolution of the model 鈥� how overall public opinion changes over time 鈥� tells a much more interesting story.

Take a simple question, of the kind pollsters ask every day: do you think the future will be good? When Sznajd ran a computer simulation of this, it showed that opinions fluctuate wildly in time, as you might expect. But the opinion an individual holds at a certain time can be correlated with the opinion they have a short time later. The researchers found that the probability that an individual would change their mind after a certain length of time had elapsed followed a power law: the probability of changing their mind after time t is t^鈭�1.5.

Power laws occur in many natural phenomena, from sand dunes to earthquakes, and indicate the existence of 鈥渟elf-organised criticality鈥�. In other words, the system repeatedly moves into a state where things are finely balanced and a small disturbance in one part of the system can trigger massive changes across its entirety. Indeed, the Sznajds found that, in certain critical situations, one person changing their opinion could cause an 鈥渁valanche鈥� of opinion changes, just as one extra grain of sand can cause a critically loaded sand dune to collapse.

To check the accuracy of his model, Sznajd found some data that tracked the fluctuations in optimism among the people in the Polish study. Pollsters asked a group of people the vague question, 鈥淎re things getting better?鈥� and their data reproduced the same fluctuations and correlations computed by the Sznajd model. It seemed that the ebb and flow of feelings on the matter didn鈥檛 follow external events as much as it did gossiped opinion.

Simple solution

When Dietrich Stauffer, professor of theoretical physics at Cologne University, came across Sznajd鈥檚 findings he was hooked by the simplicity of the idea. 鈥淚 liked it immediately, and was angry that I did not invent this model myself years earlier.鈥� Channelling his anger, Stauffer quickly took up Sznajd鈥檚 model and began to play.

First, he wanted to make the model more realistic. So he allowed the individuals to rest on a two-dimensional lattice. In this arrangement, if an individual鈥檚 four nearest neighbours share an opinion, the individual will be converted to that opinion.

Stauffer also tried some other models. He let his population move randomly around the lattice, sharing opinions and exerting influence, as people do at a cocktail party, say. To make it even more realistic, he also tried a model designed to mimic the evolution of actual networks of friends and relations (快猫短视频, 13 April, p 24). This connects people together in a manner that faithfully reproduces what we know of the characteristics of real social networks.

Finally, convinced that the Sznajd model could be an effective mirror of human influence, Stauffer and his colleagues A. T. Bernardes and J. Kertesz looked for a real-world test. The best option, they found, was in elections.

They analysed the distribution of the number of votes different candidates obtained in Brazilian council elections 鈥� that is, say, six candidates get 14,000 votes, 12 get 10,000 and so on 鈥� and worked out the number N(v) of candidates getting v votes each. Plot a logarithmic graph of N(v) against v and you get a curve whose slope gives you an 鈥渆xponent鈥� 鈥� a way to characterise the democratic process. In the Brazilian elections that Stauffer鈥檚 team looked at, the exponent was about 鈭�1.

The team then used their Sznajd model to run a simulation of people influencing their neighbours鈥� vote on square and cubic lattices, and using a complex social network. All three methods reproduced the observed distribution of votes in the Brazilian election with uncanny accuracy. And all gave slopes close to 鈭�1 (see Diagram).

That was no fluke, Stauffer believes. He has also tried to model the process using what he once thought was the best model of democracy that physics had to offer. In this attempt, he assumed that the distribution of votes must be caused by 鈥渃lustering鈥�. Metallic atoms in solutions gather together to form clusters, whose size depends on the characteristics of the 鈥渟eed鈥� particle which initiates the process. Stauffer thought people would cluster around candidates in groups whose size depended on the attractiveness of their ideas. But when he modelled the election with the physics used to describe the clustering process, the result failed to match the real election data. The number of clusters of a given size gave a characteristic exponent of about 2.

Now this might be disappointing to advocates of the democratic process, who would like to think that it鈥檚 all about people being drawn to the candidates and their ideals. It seems that is just plain wrong. According to Stauffer and his colleagues, we鈥檙e at the mercy of peer pressure. It鈥檚 social factors that strongly influence the outcome of an election. At the start of the election period, each candidate has their own group of voters. Some weeks go by, people argue with their friends, and a vote is taken. The results indicate that people are heavily influenced more by those arguments than by what the candidates do or say.

And if you accept that peer pressure has a lot to say about the democratic process, Stauffer has a further warning for would-be politicians. When the opinion polls come in halfway through your campaign, don鈥檛 think that being in second place is OK. It鈥檚 a disaster 鈥� even if a second-place final result would be good enough.

Stauffer obtained this insight when he ran a system whose population can hold one of four possible opinions covering the spectrum of beliefs from one extreme to another 鈥� call them A, B, C and D. People holding similar opinions can influence one another, so a block of four people who believe B would influence their neighbours to believe B if they currently believe A or C, but would not affect someone believing D. Start with a random distribution of opinions and let it run. Almost everyone, unsurprisingly, usually settles on the same opinion. Sometimes a second opinion survives, but the others are eliminated.

But the opinions that are eliminated are almost never the ones you鈥檇 expect. Put your confidence in the halfway opinion poll rankings and you could be shocked. Stauffer ran 10,000 simulations of this evolution of four opinions. Whoever was second at half-time ended up coming third in 92 per cent of the simulations. 鈥淭o be first or third is good,鈥� Stauffer says. 鈥淪econd place is dangerous.鈥� The opinions that won were always moderate 鈥� either B or C 鈥� but the second place went to an extreme: A or D. When the electorate talk and influence one another, you鈥檇 better watch out if you鈥檙e looking like a comfortable runner-up.

This lesson seems consistent with the events of the French presidential elections held in April. The far-right candidate, Jean-Marie Le Pen, came from behind to oust the socialist Lionel Jospin in the first round of voting, much to everyone鈥檚 shock. People were so outraged by the idea of an extreme right-wing candidate having a chance at the presidency that spontaneous protests broke out on city streets.

But Stauffer鈥檚 result seems to indicate that a large group of people were initially close enough to the right-wing vote to be influenced by their more extreme neighbours. Add in the fact that this vote came almost exclusively from one block of the country, and the role of local influence seems obvious.

Stauffer says he would expect similar laws to be at work in elections worldwide. Physicists have observed that vastly different systems, from boiling water to ferromagnets and traffic jams, all exhibit the same behaviour. This universality, he suspects, is at work in human systems as well. Details, such as how much television they watch, should have only a minor effect on the final outcome. Peer pressure is a human phenomenon, he believes, and won鈥檛 change from country to country.

Far more important would be the form of the election 鈥� whether it is for candidates or parties, for example. 鈥淚n a vote dominated by parties instead of candidates, we just have a handful of parties and thus a handful of results,鈥� he says. The effects of peer pressure might still be there, but there鈥檚 simply not enough data for an ironclad statistical analysis.

More recently, Stauffer and his collaborators have begun to include such phenomena as 鈥渇rustration鈥�. This occurs in complex materials like glasses and certain metal alloys. When the spins inside the material can鈥檛 find an arrangement that suits them all, the spins are said to be frustrated. The result is many different possibilities for the final arrangements of spins, but none of them is the perfect, low-energy solution. It鈥檚 an area of study that is helping physicists get a handle on the processes behind protein folding in biological systems 鈥� especially when the folding goes wrong.

And, Stauffer believes, exactly the same kind of frustration arises when people receive conflicting advice. By studying the physics of frustration, he and his colleagues have found that neighbours reach a consensus more easily when they get together in informal, small groups than when they meet only in large, scheduled committee meetings. This result could have some bearing on corporate decision-making, and perhaps throw some cold water on the currently popular 鈥渢own hall鈥� meetings in American politics.

Indeed, Stauffer believes his results could provide many useful pointers to social scientists looking for explanations and predictions of the way groups of people, from neighbourhood watch committees to national political parties, might reach consensus.

Of course, that鈥檚 not to say that Stauffer鈥檚 simple simulations hold all the answers. They can鈥檛 predict an election result, even if they can expose the type of process behind it. After all, the shifts and swings in opinions must surely be far more complicated than the flips of an atom in a magnet 鈥� or is that just what the politicians would have us believe?

The new physics of peer pressure says there鈥檚 only one way to be sure that our future elections are not determined by the opinions of our neighbours. We need to abolish the right to free speech: it鈥檚 undermining democracy.