Roughly 2,500 years ago, the citizens of Athens developed a concept of democracy that's still hailed by the modern world. It was not, however, a democracy in which every citizen had a vote. Aristotle argued that such a practice would lead to an oligarchy, where powerful individuals would unduly influence the masses. Instead the Athenians relied on a simple machine to randomly select citizens for office. It's an idea whose time has come again.

Two separate research initiatives—one from a pioneering cryptographer and a second from a team based at Stanford University—have proposed a return to this purer, Athenian-style democracy. Rather than expect everyone to vote, both proposals argue, we should randomly select an anonymous subset of electors from among registered voters. Their votes would then be extrapolated to the wider population. Think of it as voting via statistically valid sample. With a population of 313 million, the US would need about 100,000 voters to deliver a reliable margin of error.

Such proposals can inspire horror. But the fact is, one man, one vote is broken. In the last presidential race, nearly 40 percent of the voting-eligible population didn't cast a ballot. And that was a good year, with the highest turnout since 1964. If we select fewer people to vote, we can get a better representation of what the country wants.

At the same time that turnout is low, the issues put to voters are increasingly complex. States ask voters to decide on issues ranging from drug laws to arcane budget rules. In 2010 California voters were asked to decide on 14 such propositions, in addition to choosing candidates for local, state, and federal office. Few people have enough time to make thoughtful decisions, so these important questions are decided based on snap judgments and 30-second TV ads. James Fishkin, director of the Center for Deliberative Democracy at Stanford, argues that our system isn't living up to its democratic potential: "There is so little time for deliberation that some people make leadership choices based on whether they like a candidate's hairstyle."

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Fishkin has charted a new course by organizing small-group deliberations as part of legally binding decision processes in 18 countries, including Greece and even China. A randomly selected group of ideally 200 to 300 citizens spends one or two days listening to experts on both sides debate the merits of an initiative or a candidate. Then the group votes and the results are enacted.

The concept shouldn't be so shocking. Every time we take a drug that's been through clinical trials, we tacitly accept that the experience of a small group is applicable to the overall population. And we rely on randomly selected citizens to serve on juries, where they make life-and-death decisions. Jurors are given the time they need to analyze the issues. Why wouldn't we want the same thing for important local and national issues?

Cryptographer and voting-technology expert David Chaum has developed his own elegant model—which he calls a "random-sample election"—that prioritizes the anonymity of the voter. A randomly selected voter receives a ballot in the mail and is directed to an election-commission website that features candidate debates and activist statements. This would allow voters time to deliberate in their home, without being identified publicly.

Chaum's model enables voters to verify online that the choices on their paper ballot are registered correctly. In 2009 and 2011, as a proof of concept, an optical-scan technology he helped create was used successfully to conduct full-participation municipal elections in Takoma Park, Maryland, a town of 16,715. Given the added significance of each vote in a small-group election, Chaum's verification system would add a valuable degree of accountability to the balloting process.

Small-group elections also offer an end run around the problem of campaign finance reform. TV ads are a blunt weapon to influence a small, random selection of people. Door-to-door canvassing, multistate campaign operations, and annoying phone banks would likely disappear, removing the necessity for politicians to raise millions. Previous attempts at finance reform have failed. Small-group elections solve the problem at its root.

They also address a more fundamental issue: Our democracy isn't functioning as well as it should. A vast swath of our population is underrepresented. For those who do vote, their choices are heavily influenced by reductive ads often financed by wealthy individuals or corporations with vested interests. Small-group elections could save taxpayers hundreds of millions of dollars a year. And since they are easier to run, they could be held more often, giving citizens a greater voice in government. If we aspire to be a country governed by the people, we should return to the foundations of our democracy: Let a random subset of the citizenry make reasoned decisions that best express the national will.

Contributing editor Joshua Davis (jd@joshuadavis.net) votes in every San Francisco election.