In 1785, a French mathematician named Marie Jean Antoine Nicolas de Caritat (known as Marquis de Condorcet) used statistics to champion democracy.

Democracies are based on the collective decisions of large groups of people. But citizens aren’t experts on every topic, and so they may be prone to errors in the choices they make. And yet, Condorcet argued, it’s possible for a group of error-prone decision-makers to be surprisingly good at picking the best choice.

Condorcet’s logic was simple. Assume you have a group of people each independently making a choice about a question. Assume that they have a chance of making the wrong choice–but that their choices are better than random. If the decision they’re trying to make is either thumbs up or thumbs down, for example, their chance of picking the right answer only needs to be greater than 50 percent. The odds that a majority of them will pick the right answer is greater than the odds that any one of them will pick it on their own. What’s more, Condorcet argued that the group’s performance gets even better as its size goes up.

Condorcet’s argument is the foundation of what’s now commonly called the “wisdom of crowds.” Individuals who have imperfect understanding of a situation can band together to become good at collective decision-making.

There are some famous stories that illustrate the wisdom of crowds. Just over a century ago, Sir Francis Galton asked 787 people to guess the weight of an ox. None of them got the right answer, but, pooled together, their collective guess was almost perfect. In his book, The Wisdom of the Crowds, James Surowiecki writes about the game show “Who Wants to Be a Millionaire?” Contestants could get help answering questions either from an individual friend whom they considered an expert, or from a poll of the audience. The majority of the audience picked the right answer 91 percent of the time, while individual friends only did so 65 percent of the time.

Many scientists have used Condorcet’s idea (known as the jury theorem) as a launching pad for exploring collective decision-making. They’ve expanded the basic theory to include more features of crowds–such as the way information can move through them. They’ve tested out versions of the jury theorem on real groups of humans and animals. And their research has shown that crowds really can be wise. People can indeed make better decisions in groups than on their own. And while animals may not be able to pick presidents, they can also make good decisions in groups. It may be hard for an individual fish to recognize a predator in a murky ocean and escape in time. But a school of fish can pool its uncertain information to avoid enemies.

In fact, animals can make some remarkably sound choices among remarkably complicated options. In this feature I wrote for Smithsonian, I described the decisions that honeybee swarms make. Thomas Seeley, a Cornell biologist, has shown that a swarm of honeybees can choose among several possible locations to build a new hive. And they’re able to choose the best spot in terms of size, temperature, and other factors.

But now a leading expert on crowd decisions is starting to question some of the basic rules of the wisdom of crowds. In a new study, Iain Couzin of Princeton and his graduate student Albert Kao argue that, in most case, small groups are wiser than big ones.

This result came as a surprise to Couzin. For over a decade he’s been studying collective decision-making, combining mathematical models with sophisticated experiments on fish, insects, and other animals. (For more on Couzin’s work, check out fellow Phenom Ed Yong’s 2013 Wired feature2013 Wired feature2013 Wired feature and my 2007 profile in the New York Times.)

To develop their models for how animal swarms make decisions, Couzin and his colleagues have made certain assumptions. That’s how science always works–rather than try to replicate every facet of reality, you assume that some of them are irrelevant to the phenomenon you want to understand. But in recent years, Couzin and Kao started to question two of the most basic assumptions about collective decision-making.

The first assumption goes all the way back to Condorcet. It’s the idea that all the votes cast by a group are truly independent of one another. Each voter, in other words, makes a decision based on his or her own imperfect information about the subject. To do so, each voter has to gather information on a question on his or her own. In these conditions, the casting of each vote is like rolling a separate set of dice.

That might well be true in some cases, but Couzin and Kao could imagine many cases where it wouldn’t be. If people all gather information about a presidential candidate from different news sources, their votes will be based on independent sources of information. But if they all get their information only by watching the same show on MSNBC, their information isn’t independent. Instead, it’s what scientists describe as correlated.

A similar situation holds true for animals. If two fish are swimming on opposite sides of a school, they may have two entirely different fields of view of their surroundings. The information that one fish gets on one side is uncorrelated with the information that the other fish gets. And that means that the decisions they make based on cues in their environment are also uncorrelated. Their uncorrelated information gives them a collective wisdom that a single fish, with its limited amount of information, can’t gather.

By contrast, two fish swimming side by side see almost entirely the same scene. Their information is correlated. And that means their decisions are correlated, too. If one fish gets misled by a mirage, the other one is likely to be misled as well.

Couzin also became concerned by how wisdom-of-the-crowd experiments are set up. Scientists typically present a group of animals (or people) with a single cue they can use to make a decision. They might offer a school of fish a visual cue and see if they decide it’s a predator they have to escape.

But in the natural world, animals are swamped with information from lots of sources. Individuals on the lookout for predators may use not only their eyes, but also their ears and their noses.

This feature of real decision-making may have huge effects on how crowds perform. It’s not simply that each fish is keeping track of more than one cue. It’s also the fact that some cues may be very reliable and others may be unreliable. Some cues may be correlated, and others uncorrelated. And animals may learn to pay more attention to some cues and disregard others.

Couzin and Kao wondered how these factors could affect the wisdom of crowds. They put together a series of mathematical models that included correlation and several cues. In one model, for example, a group of animals had to choose between two options–think of two places to find food. But the cues for each choice were not equally reliable, nor were they equally correlated.

The scientists found that in these models, a group was more likely to choose the superior option than an individual. Even in these more realistic conditions, the wisdom of crowds survives.

Couzin and Kao expected that the bigger the group got, the wiser it would become. But they were surprised to find something very different. Small groups did better than individuals. But bigger groups did not do better than small groups. In fact, they did worse. A group of 5 to 20 individuals made better decisions than an infinitely large crowd.

The problem with big groups is this: a faction of the group will follow correlated cues–in other words, the cues that look the same to many individuals. If a correlated cue is misleading, it may cause the whole faction to cast the wrong vote. Couzin and Kao found that this faction can drown out the diversity of information coming from the uncorrelated cue. And this problem only gets worse as the group gets bigger.

Small groups, Kao and Couzin found, can escape this trap. That’s because probability works differently in small groups as opposed to large ones. It’s not unheard of, for example, to roll the same number a few times in a row. But it’s really weird to do so a thousand times in a row. Likewise, in a small decision-making group, a lot of individuals may end up using uncorrelated cues–the ones that give wisdom to crowds.

Couzin and Kao’s analysis, which has just been published in the Proceedings of the Royal Society, doesn’t prove that the wisdom of big crowds is a fatally flawed idea. But it does serve as a warning that even simple factors can have a big impact on how groups make decisions. And it may help to explain how real animals form groups.

When scientists first came to appreciate how groups can make decisions, a question naturally arose: why don’t all animals live in gigantic groups? Some researchers argued that big groups had drawbacks that balanced the advantage they offered in making good decisions.

But Couzin and Kao wonder if such drawbacks don’t, in fact, exist. Perhaps animals live in smaller groups because smaller groups are better at making decisions.

Even the animals that do live in big groups may not actually be solving problems en masse. Only a small fraction of the group may actually be casting votes, while the rest follow their lead.

Couzin and Kao’s work also raises some questions about how we humans make decisions. If people are basing their decisions on the same information, they may be more prone to bad decisions in big groups. All things being equal, smaller groups might do better. And big groups might improve their choices if people avoided relying on the same sources of information.