If you’re looking for an unrepresentative group of Americans, the House of Representatives isn’t a bad place to start. Its members are disproportionately old and white. More than 80 percent of them are men. They spend around four hours per day on the phone, asking people for money. Unlike most other telemarketers, they have a median net worth of almost $900,000. More than a third of them hold law degrees.

Last Tuesday, not much changed. Once again, the American people went to the polls and elected a group of people who, in aggregate, only vaguely resemble the American people.

The problem isn’t new. A representative assembly, John Adams wrote in 1776, “should be in miniature an exact portrait of the people at large.” (By “people,” of course, he meant “white men”). But by the 1780s, when Anti-Federalists challenged the young Constitution, a big part of their concern was that “representation as provided for in the Constitution would be skewed in favor of the most prosperous and prominent classes,” writes the political scholar Bernard Manin.

Good observation, Anti-Federalists. And here we are.

If we want a more representative Congress, there’s a relatively simple solution. It sounds strange, but it has a long history, and, just as a thought experiment, it can tell us a lot about certain tensions inherent in representative government. It’s called sortition.

Here’s how sortition works: for any given election, you take the names of every eligible citizen, and you put those names in a very, very big hat. (Note: you don’t have to use a hat, and there are many variations on this method). Then you draw a certain number of names out of the pool. Those are your legislators. It’s democracy by lottery.

For the House of Representatives, for example, we could pull 435 names out of a giant lottery of all American citizens 25 and older, and, voilà: legislators!

You may feel that this is an incredibly stupid idea, but keep two things in mind. First, sortition was the main system for choosing political officials in ancient Athens. As you’ll recall from civics class, Athens was the template, muse, and foundational bedrock for the American Republic. And, second, we already use sortition to select an important deliberative body, the trial jury. Those jury summonses that you get in the mail? Blame the Athenians.

The Athenians considered sortition to be an especially democratic way of choosing certain decision-makers. They took their political lotteries so seriously that they used a special machine, called a kleroterion, to make the process harder to corrupt.

Today, there are people who talk about using sortition more widely in our society. They aren’t just populist rabble-rousers. They include a Dublin academic, a left-leaning Yale professor often cited as a possible Supreme Court nominee, and an online activist who has given a talk to the Texas Constitutional Militia. They don’t necessarily think that we should pick Congress from a giant hat. But they suggest that, when we talk about democracy, we should at least talk about lotteries, too.

Sortition rests on two rather unique properties of random sampling. The first of these—which I’ve written about more extensively elsewhere—is that chance is essentially incorruptible, at least until someone rigs your lottery machine. No matter how much money the Koch brothers or Tom Steyer spend, they cannot convince a lottery to choose one person over another. What could be more impartial than chance?

And, second, as your random sample gets larger, you tend to get closer and closer to a sample that mirrors, in almost every respect, the qualities of the entire population. More than any other system, random sampling gives you “an exact portrait of the people at large.” It’s the Law of Large Numbers. (This doesn’t work, of course, for small samples, and you’d be hard-pressed to find someone who wants to elect a president by lot).

Sure, you could end up with a Congress that consists solely of libertarian veterinarians, or elderly communists, or whatever. But the probability is vanishingly small that you’d end up with anything other than a Congress that, in aggregate, is a kind of America-in-miniature.

If you think of representative democracy as a way to elevate the best citizens into positions of power, then random sampling won’t seem appealing. (Our current electoral system might not feel appealing, either). But if you think of representative democracy as a way to give all citizens equal access to power, or as a way to channel the ineffable will of the people, then it’s hard to find a more efficient system than a lottery.

As it stands, our system chooses very weird people—specifically, the kind of people who think that being in Congress sounds fun. “It is impossible by elections to choose normal people,” argues Yoram Gat, an Israeli software engineer with a PhD in statistics. Gat is one of the founders of Equality-by-lot, a popular sortition blog. “Normal people are kind of anonymous,” Gat told The Daily Beast. “In a large society, there is just no way, no theoretical way, to choose, to elect, normal people.”

Really, sortition strikes at the tension at the heart of elective representative democracy. Legislators are supposed to represent us. At some level, this means that they’re supposed to be like us. But the very process of election tends to favor unusual, extraordinary people—what Bernard Manin calls “the principle of distinction.” So we end up with professional politicians, type-A go-getters, and electoral dynasties. When they campaign, these contenders try to seem as normal as possible, and as extraordinary as possible, all at the same time. It’s an awkward balancing act. They often just sound like robots.

What would have happened, last Tuesday, if we had allowed sortition to determine the make up the 114^th House of Representatives? The group would be almost evenly split between men and women, for one thing. It would be less wealthy, less educated, and less white than the gang that will show up in Washington in January. Its members would not be beholden to any special interest groups, at all, for their selection. For better or for worse, only a few of them would be lawyers. A whole lot more of them would be under the age of 40.

There are problems, here, of course—particularly regarding accountability—and it seems unlikely that we’ll be choosing Congress by lottery anytime soon. Still, there are other places where, like trial juries, sortition make sense. Two Canadian provinces have experimented with using random citizen panels to set election regulations. And randomly selected panels are well suited to political questions that we might otherwise addresses through a big referendum. (Referenda tend to be expensive, rife with misinformation, and favorable to extreme positions).

But the real value of sortition, maybe, is to remind us that our democracy is an ongoing balancing act between finding a Congress that represents the best among us, and a Congress that’s representative of, well, us.