An American election season seems like a bad time to sing the praises of human rationality. Candidates make promises that will never be kept yet voters somehow accept; thoughtful arguments hold no sway, while sound bites carry the day. What a comedown from the Enlightenment ideals, the faith in rationality, that inspired the founding of the republic. And it is even worse than you might think. Some things you think should be possible to figure out rationally if only you exerted yourself aren't. If you actually succeeded in living a life of reason—never voting without weighing each candidate's record carefully, never buying an appliance without consulting Consumer Reports, never begging the question, never erecting straw men, never falling into any of the other traps that flesh is heir to—you still would find yourself doing things that made no sense, not because you had failed but because reason itself is a saw blade missing a few teeth.

Throughout the 20th century scientists and mathematicians have had to accept that some things will always remain beyond the grasp of reason. In the 1930s Kurt Gödel famously showed that even in the rational universe of mathematics, for every paradox that deep thinking slaps down, new ones pop up. Economists and political theorists found similar limitations to rational rules for organizing society, and historians of science punctured the belief that scientific disputes are resolved purely by facts. The ultimate limits on reason come from quantum physics, which says that some things just happen and you can never know why.

Yet events have taken a strange turn in the past decade. The very theory of quantum physics that seemed to box in human knowledge also proves to liberate us. It expands our knowledge not just of the physical world but also of ourselves. By enriching the rules of rational thought, it gets us out of dead ends where reason leads us. Taken in the broader framework quantum physics provides, human behavior may not be as irrational as the evening news makes it seem.

The Weight of Reason

Few lived and breathed the Enlightenment dream more than the Marquis de Condorcet, one of the leading mathematicians of the late 18th century. Emboldened by the success of Newtonian physics, a few simple rules that explained the fall of apples and the orbits of planets, he sought to create a science of society to match. Reason, he thought, could make the world a better place. He and other Enlightenment thinkers campaigned for a progressive political agenda: the abolition of slavery, equal rights for women, universal public education. A friend of Thomas Jefferson, Benjamin Franklin and Thomas Paine, Condorcet became an early leader of the French Revolution. “The moment will come when the sun will shine only on a planet of free men, knowing only reason as their master … learning how to recognize and smother beneath the weight of reason the first signs of superstition and tyranny, should they ever dare to reappear,” he wrote in 1794.

Then came the fall. The revolution took its dark turn. Condorcet was arrested, died in prison the next day and was buried in a communal grave that was later lost. The Enlightenment gave way to Romanticism. For many leading thinkers, the excesses of the revolution discredited the entire progressive agenda.

As if to heighten the tragedy, Condorcet had come to question the Enlightenment idea of the will of the people. He showed that democratic voting systems lead to paradoxes: people's choices can add up in mutually contradictory and unresolvable ways. Mathematician and political essayist Piergiorgio Odifreddi of the University of Turin in Italy gives an example: In the 1976 U.S. presidential election, Gerald Ford secured the Republican nomination after a close race with Ronald Reagan, and Jimmy Carter beat Ford in the general election, but polls suggested Reagan would have beaten Carter (as indeed he did in 1980). The electorate's preferences were intransitive: preferring Carter to Ford and Ford to Reagan did not mean preferring Carter to Reagan. Carter won only because the primaries came first. “Who was elected is determined only by the order in which you do the two elections, not by the electorate,” Odifreddi says. In committees and legislatures, presiding officers can exploit this order dependence, or noncommutativity, to steer a vote their way.

In 1950 Kenneth Arrow, then a graduate student at Columbia University, showed that there is only one sure way to avoid paradox: dictatorship. The order of the elections no longer matters when one voter has decisive power. This sobering discovery helped win Arrow the 1972 Nobel Prize in Economics. “It's an analogue of Gödel's theorem,” Odifreddi says. “It proves there are limitations to the general idea we have of democracy.” Gödel himself may have formulated a version of Arrow's theorem even earlier; similar ideas appear in an argument he gave for the existence of God.

If democracies usually avoid Condorcet's paradoxes, it is because voters lie on an ideological spectrum, giving their views some coherence and mutual consistency [see “The Fairest Vote of All,” by Partha Dasgupta and Eric Maskin; Scientific American, March 2004]. Ironically, although Western culture valorizes independent, nonideological thinking, such thinking can actually cause a voting system to seize up. In politically unsettled times, Odifreddi says, the spectrum gets tangled, and democracy becomes not just somewhat but completely dysfunctional.

The same year that Arrow proved his theorem, mathematicians Merrill Flood and Melvin Dresher discovered another conflict between individual and collective decisions: the Prisoner's Dilemma. The police catch two thieves and offer each a reward for snitching on the other. If both stay mum, both get off scot-free; if both snitch, both get the book thrown at them. Given these incentives to snitch, both do—but then both lose [see box on next two pages]. This dilemma is a model for the limitations of laissez-faire economics. It punctures the neoclassical economic wisdom that individuals acting in their own rational self-interest collectively produce the best outcome.

A related letdown is the “liberal paradox” that economist Amartya Sen of Harvard University articulated in 1970. Much as Arrow cast doubt on democracy and Flood on market economics, Sen blew a hole in the notion of individual rights. The most basic right is that an individual should have veto power over decisions that affect only him or her. Sen's original example was censorship: the decision to read or not read a book affects only that person and therefore should fall under his or her control. Majority rule has always been in tension with individual rights: a majority can impose its will on a minority. What is stranger is that even unanimous rule violates rights—in other words, an individual's rights can be threatened by decisions the individual implicitly supports.

In a not so hypothetical variant on Sen's example, consider two voters, Blue and Red, passing judgment on a government welfare program. Blue prefers that both of them receive the benefits; failing that, he would like Red to get them, being the needier of the two. Red prefers that neither get the benefits; failing that, he should be the one to get them—to save Blue from the corrupting influences of public assistance. Because they are deadlocked, they have to settle for their second choices. Thus, the program is foisted on Red and denied to Blue, so neither controls decisions that affect only them. All these paradoxes suggest that some disputes in our society go on and on not because people are being inconsistent or unreasonable but because the mechanisms of rational decision making, intended to reconcile diverse points of view, can instead heighten conflict.

Paradox Lost

In the 1950s and 1960s mathematicians explored various ways to escape the Prisoner's Dilemma. One method was the use of conditional strategies. Instead of choosing between staying mum or snitching, each suspect could tell the interrogators, say, “If my partner stays mum, then I will, too.” With the right set of if-then statements, the individuals can avoid jail time. Crucially, neither will gain by switching strategies, so a rational calculation of self-interest leads them to cooperate [see “Escape from Paradox,” by Anatol Rapoport; Scientific American, July 1967]. What is best for the individual is best for the group. Yet the scheme does have a fatal flaw: the partners have to agree to stick to conditional strategies and to not change their mind at the last minute and snitch. They need a foolproof way to keep each other in line.

Quantum physics provides one. In 1998 physicists Jens Eisert and Martin Wilkens, both then at the University of Potsdam in Germany, and Maciej Lewenstein, then at the University of Hannover in Germany, suggested that a pair of entangled particles can serve as a binding contract [see “Schrödinger's Games,” by Graham P. Collins; Scientific American, January 2000]. Through these particles, the partners can coordinate their decisions without knowing in advance what those decisions are—information they could have used to flout the contract. In 2001 Jiangfeng Du of the University of Science and Technology of China in Hefei and his colleagues demonstrated the scheme in the laboratory. They entangled two hydrogen nuclei and beamed radio pulses at them to execute the stages of the game.

Italian mathematical physicist Gavriel Segre suggests that a similar trick could prevent voting deadlock without having to install a dictator. He says he became interested in the subject in the summer of 2008, when he read an interview of his compatriot Odifreddi in the newspaper La Stampa. Citing Arrow's theorem, Odifreddi asserted that representative democracy was obsolescent. “I didn't agree with this fact, and I began to think of a way to overcome the Arrow theorem,” Segre says.

Segre argues that quantum physics enriches the possibilities of voting. Like Schrödinger's cat, a citizen can be of two minds, voting both yes and no—a so-called superposition. When aggregated, votes can either add up or negate one another. They can become entangled with one another, representing a kind of pact among citizens to vote in a coordinated way, like the binding contract in the quantum Prisoner's Dilemma. In this case, unlike the classical one Arrow considered, the will of the people can be perfectly consistent.

Unfortunately, Segre's proof is very abstract, and several experts on voting theory consulted for this article doubt whether it is correct, let alone whether it could be written into a 21st-century constitution. Yet physicist Artur Ekert of the University of Oxford and the Center for Quantum Technologies in Singapore says that Segre may be on to something. Because quantum physics is probabilistic, a quantum voting system may avoid inconsistencies without an absolute dictator—just a ruler whose say-so carries the day on average and can be overruled from time to time. “We will have a dictator but a much weaker one,” Ekert says.

Critique of Pure (Classical) Reason

Quantum physics does not erase the original paradoxes or provide a practical system for decision making unless public officials are willing to let people carry entangled particles into the voting booth or the police interrogation room. The real significance of these findings is that quantum physics provides a model for human behavior in which apparent irrationality makes total sense.

In real life, people cooperate much more often than they would if they were driven purely by a rational assessment of their self-interest. When psychologists ask volunteers to play the Prisoner's Dilemma, the players sometimes stay mum despite the strong incentive to snitch. If Alice believes Bob will snitch, she will definitely snitch. If she believes Bob will stay mum, she will probably still snitch but might stay mum. “Might” is typically just 20 percent of the time, but it shines a glimmer of hope into a mean-spirited game.

What is downright weird, though, is that if she is not sure what Bob will do, Alice becomes more likely to stay mum. No purely rational creature would do that. According to classical logic, if she thinks there is a 50–50 chance of Bob staying mum, she should take the average of her two tendencies and stay mum 10 percent of the time. Yet in psychology tests, volunteers under these circumstances stay mum 40 percent of the time.

In quantum logic, the average of zero and 20 can indeed be 40. Alice's propensities—definitely snitch if Bob snitches; probably snitch if he stays mum—partly cancel each other out if she has to juggle both eventualities in her head, so she goes with her other choice and stays mum. “These two individually good reasons interfere with each other and so make it less likely that the person will defect,” says psychologist Emmanuel Pothos of City University London.

In 2009 Pothos and psychologist Jerome Busemeyer of Indiana University Bloomington devised a quantum model that reproduces the result of the psychology experiments. The underlying reason it works is that most people do not have fixed preferences. Our feelings are ambivalent and conditional on what people around us think. “We are very contextual creatures,” Busemeyer says. “So there is no attitude sitting there waiting to be measured.” A quantum superposition captures those mixed feelings. It does not mean our brains are literally quantum computers, as some physicists have speculated. Rather quantum physics is a useful metaphor for the fluidity of human thought.

In a way, this emerging subject of quantum cognition takes quantum physics back to its roots. In the early 20th century Niels Bohr and the other creators of the theory drew on ideas from psychology, such as the work of William James. Quantum theory came of age in a period when rationalism, which had swung in and out of intellectual fashion since the Enlightenment, held little appeal. World War I did not lend itself to optimism about the human capacity for self-betterment, and a theory that placed bounds on human knowledge appealed to Bohr and his colleagues. Yet intellectual history goes in cycles. By renewing optimism about human knowledge and behavior, perhaps today's quantum physics will help inspire a new Enlightenment and reinvigorate our hollow politics.