Lions, bears, and tigers the interplay between individual and group decision-making, oh my!

A. A fable

Once upon a time, there lived a community of animals in a forest. The animals generally lived in harmony, until one day, when everything changed.

One of the rabbits had just returned from a short trip, and she arrived with news. “Everybody listen up!” said the rabbit. “I just discovered something that will change all of our lives. This could seriously be the best thing that’ll ever happen to us.” The animals were intrigued.

“So here’s the deal,” said the rabbit. “I just went over to the human camp and I saw them making a big pile of wood. First I thought, ‘No big deal, this is just humans doing weird human things.’ But then they pulled out this…” The rabbit presented a matchbox that the humans had left behind. “…and they struck one of the sticks against the box. The next thing I know, I saw a huge, orange glow arise out of nowhere.  They call this orange glow ‘fire’.”

“And!” continued the rabbit. “The fire can be used to do all sorts of cool things. The humans use it to make food hot, and believe me, hot food tastes really good. I know because they fed me some.”

The animals were getting excited now.  “What else can it do?” asked another rabbit. “Well,” the first rabbit said, “since it’s hot, you can just sit next to it in the winter to warm yourselves up. No more cold winters, guys! It’s also really bright, so you can actually use it at nighttime to see in the dark. I could go on and on here, but it’s really just best if I show you.”

One of the squirrels was a bit concerned. “Wait,” the squirrel said. “If the fire is really hot, could this be dangerous? I know when the sun is really hot I start to hurt all over. I’m not so sure I like the idea of basically making a second sun right in our backyard. Do we even have a plan for how to get rid of it if we don’t like it?”

“That’s silly,” the rabbit shot back.  “Fire is great and you’ll definitely change your mind when I show it to you.”

The squirrel was upset that the rabbit thought his concern was silly. The other squirrels were upset as well, and started arguing with the rabbit. The other rabbits joined in, and soon it became an all-out debate of rabbits versus squirrels.

Hence started the Rabbit-Squirrel Wars of 2250.1

The debate shifted from the reasonable to the ridiculous. The rabbits’ arguments evolved into: Fire scares away demons, if you hate fire then you’re an element-ist, and squirrels have low IQ’s and their opinions should be disregarded. The squirrels’ arguments included: Fire has been scientifically proven to give you cancer,2 making fire is like idol worship and will upset the Sun God, and everybody knows all rabbits are liars anyway.

A line had been drawn in the dirt. Nothing could convince any of the rabbits or squirrels to change their minds. They were locked into their respective positions.

Then there were the bears. The bears watched the rabbit-squirrel debates. They understood which arguments were good, and which arguments were bad. They realized there were good arguments both to start fire and to refrain from doing so. But they didn’t really know how to weigh these good arguments against each other.  So they figured they would remain mostly neutral, at least until they could receive some guidance from some wise authority.

The lion was wise.3 After the lion heard all the arguments from the rabbits and the squirrels, she went back to her den. A few hours later, she came back out and said to her bear friend, “I’ve thought about the fire debate long and hard, and I’ve come to support the idea of starting a fire. I’ve looked into the human literature on fire, and I’ve found a number of studies supporting the benefits of fire, and not as many studies concerned about safety. I’ve done a rough calculation of the potential benefits minus the potential costs, and it seems like the benefits outweigh the costs by a factor of two when converting all measures to quality-adjusted life-years. I’d say that starting a fire is likely the way to go with a 80% confidence interval. You can check my analysis if you’d like.”

The bear nodded, understanding enough to follow, but being lazy, didn’t bother to check the analysis or do his own. The lion is wise, he thought, so I trust her analysis. I’ll support fire.

The bear went to tell his bear friends that the lion supports fire. The bear’s friends all understood that the lion was wise, so they all decided to support fire as well. They went to tell their friends, and those friends went to tell their friends, and so on and so forth until the entire community of bears decided to support fire. Many of the later converts didn’t even hear of the lion’s analysis; they just saw that the rest of the bear community was coming around to support fire, and the bear community was generally smart, so they would support fire, too.

Finally, one day, the lion gathered the entire forest community to take a vote. “In incredibly complex debates like these that divide communities,” stated the lion, “we have to go by majority opinion. All in favor of fire, say aye!” The rabbits and bears all said “Aye!” in unison. “All opposed, say nay!” Only the squirrels said “Nay!”

It was clear; the squirrels were outnumbered, and the pro-fire crowd had won out. The lion, trusting in the results of a direct democratic vote, took the matchbook, and, with all the animals in nervous anticipation, set fire4 to a tree…

…and soon after, the forest was no more.

B. Mo’ bears, mo’ problems

I think one of the failure modes of society is to have too many rabbits and squirrels5; that is to say, there is a real danger to having too many people who have become one with their beliefs, and who cannot even imagine changing their minds in response to opposing argument. This is something I touch upon here. But this is clearly not the problem in the story above. If it were all up to the rabbits and squirrels, the vote would have come out to a tie, and there would have been no forest fire.

I don’t think the lion’s the problem, either. She was well-intentioned, her analysis was pretty thorough, and she even put the question out to a democratic vote. Perhaps in hindsight she got the analysis wrong, but it doesn’t feel right to put any blame on her when she was just one individual making her own analysis in a transparent, honest fashion.

No, I think the problem here is that there were too many bears.


“I’m very disappointed by my fellow bears.”

Having bears in your society seems like a good thing a priori. Isn’t it good to have people in your society who listen to expert opinion, and who are willing to change their minds toward the societal consensus?

To an extent, yes. But problems can arise when a lot of people start thinking this way.

To see why, let’s first take a look at what happens in situations with few or no bears; namely, in prediction markets. Prediction markets are simple: They are betting markets where traders can buy and sell contracts that cash in for $1 if a particular outcome occurs. For example, a contract may read “The Green Bay Packers will win the 2016-2017 Super Bowl,” and it may cost $0.20. If you think that this outcome is at least 20% likely to occur, then you’ll buy the contract; if you don’t, then you’ll wait until the price falls. Every time somebody buys or sells a contract, the market price self-adjusts to reflect the new balance between supply and demand. As a result, the market price of a contract represents the consensus of all traders at any point in time on the probability of the event occurring, just as the price of a stock represents the market consensus on the future value of a company.

Prediction markets are perhaps most well-known for being applied to election forecasting. While you might think that polling already serves as a reliable way to predict the winners of elections, given that pollsters ask respondents directly who they’ll be voting for, there is good reason to believe that prediction markets are more accurate. In a study comparing the predictions of one of the oldest prediction markets, the Iowa Electronic Markets, to 964 polls taken over the course of five presidential elections from 1988 to 2004, the authors find that the IEM predictions were closer to the actual outcome 74% of the time.

The accuracy of prediction markets in election forecasting has sparked interest for implementation in other domains as well.  Many large companies either have used or now use prediction markets (Google. Hewlett-Packard. Eli Lilly. General Electric. MotorolaBest Buy.) to forecast metrics such as expected demand for a product, product launch dates, or clinical trial enrollment rates. US intelligence agencies have also been interested in implementing prediction markets to forecast future political events around the globe, albeit with some pushback.

What makes prediction markets so accurate? As the theory goes, when a group of individuals is involved in making a prediction, each individual brings both useful information and error. Useful information brings an individual closer to the truth, while error pulls him or her away from the truth. With a diverse group of individuals that’s making independent judgments about the probability of an outcome, the errors tend to be random and cancel out, leaving only useful information. The group as a whole accumulates more useful information than any single individual has, and so tends to make more accurate predictions than even the most well-informed individuals in that group. The general phenomenon described here is known as the “wisdom of crowds,” and applies not only to prediction markets but to any decision-making body made up of independently-acting individuals.

Let’s return to the bears. Contrary to the individuals that make up a wise crowd, who make independent judgments, the bears made their judgments of the benefits and risks of fire in a completely dependent fashion; each bear either listened to the lion or to the consensus of the bear community, without making an independent analysis. For the bears, error is not random; the errors are all systematically pointing in the same direction as the lion’s. Rather than the errors canceling out, the bear community amplified the lion’s error by a number-of-bears-fold. And unfortunately for the forest community, the lion just happened to be wrong on this one.6

As smart as any individual lion is, a wise crowd is generally smarter.

C. Should I be a lion or a bear?

Say it was your job to look after forest communities in general. Seeing what happened with the fire debates in the first forest, you head to the next forest over and start an education program targeted to bears. You try teaching the adult bears about the wisdom of crowds, and you tell them that it is virtuous to make your own judgments and do your own research. To the bear cubs, you say that lions are awesome and well-respected, and don’t you want to be just like a lion when you grow up? At the end of your education program, you think you did as good of a job as you could, but you notice that the bears aren’t really changing their behavior. The bears that took your course are still just replicating the lion’s opinion, because, well, the lion is wise. What’s going on here?

Above all else, bears are lazy. They don’t want to make independent judgments, because doing so takes time and energy. And as someone who thinks like a bear much of the time, I sympathize with that sentiment.

Because despite everything I said about the wisdom of crowds, and the dangers of making dependent decisions, part of me thinks being a bear is OK sometimes. If I needed to do independent research every time I wanted to have a belief about a complex matter, then I wouldn’t have much time for much else. It’s just so much easier to look up what the experts say about the matter, assume those beliefs, and then call it a day.

(I mean, why would I do my own research into the pros and cons of marijuana legalization when this already exists?)

If my goals include both having true beliefs and saving time, then being a bear is a great way to advance both those goals at once. Unfortunately, being a bear means I’m not contributing to the wisdom of crowds, and in fact am contributing to more highly correlated errors in the crowd. So there’s a tension here between what would be best and easiest for me, and what would be best for the group.

This sets up a dilemma: In forming beliefs, do I do my own independent research, taking up a lot of my time and energy but also building up robustness in the crowd consensus? Or do I just look up the relevant experts and believe what they say?

On any given topic, do I contribute to the marketplace of ideas, knowing that by doing so I’m making it less likely to hold true beliefs myself? Or do I take from the marketplace, knowing that every time I do so I weaken it just a little bit?

Put concisely: Per issue, do I be a lion, or do I be a bear?

There’s probably no general answer here, and it’s going to depend on how important the topic is to me, how much time it would take me to research the topic, and how much the topic in question is amenable to being completely understood by a small group of experts. Other than that, I don’t really have any guidance on this, and I don’t know where I would go to look it up. So…if you’re a lion when it comes to when-to-be-a-lion-and-when-to-be-a-bear, I’m listening.

(P.S. I was going to end the post here, but I just discovered something relevant and interesting that didn’t really fit anywhere else, so I’m just putting it here. So you know those prediction markets I told you about earlier? A couple months ago, the markets received some flak for “failing” to predict Brexit; they had put the probability at about 25% even just the day before. Now, it is a bit sketchy saying that any one probabilistic estimate is “wrong,” since even events with a 25% probability occur, well, one out of every four times. But anyway, what I find interesting is the retrospective analysis that occurred as a result.  In attempting to explain the market “failure,” some have stated that prediction markets have become too stable as of late, not updating to new information as much as they once used to, and becoming more inaccurate as a result. They speculate that this is due, ironically, to the increased reputation that prediction markets have received. Now, as the theory goes, rather than traders in the market acting on their own private information and making independent judgments, traders have more and more started to take the prediction market prices themselves as reflecting the “true” probabilities. So even when a new poll comes out that contradicts the current market prices, traders will discount the poll, because the market must be right. Putting things in zoological terms, the prediction market itself has become a lion, and the traders are turning into bears.  This gives new meaning to the phrase “bear market.”)

The Conclusion Box: Providing information to-go.

A. Rabbits and squirrels fight.  Bears listen to lion.  Lion says fire, so fire.

B. The problem in the previous story is that the bears were all making dependent decisions, correlating their errors with one another.  In contrast, a crowd of individuals making independent judgments typically makes a more well-informed decision as an aggregate than any single individual could; this is exemplified by the accuracy of prediction markets.

C. Unfortunately, the lesson here isn’t just as simple as “be a lion instead of a bear,” because being a lion incurs a lot of cost on our time and energy.  You’ll probably have to pick and choose on which topics to be a lion, and on which to remain a bear.


1This is set way in the future, after we genetically engineer all forest animals to speak English, because reasons.

2Citation: Squirrel, S. Sq. J. Fire Sci. 2250, 1, 1–2.

3I don’t know what kind of stable forest community includes rabbits, squirrels, bears, and lions, but this is my story, so I’ll do what I want.

4Um, I guess we’ve genetically engineered them to have opposable thumbs, too.

5This quote is not to be taken out of context.

6For more on this kind of dependent decision-making, see information cascades.


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