How to Survive on a Desert Island

March 7, 2012 Leave a comment

Fish exhibiting swarming behavior. Or, what I imagine Bayes_Bots to look like.

For the last few months, a team and I have been aggressively competing* in the 2nd Social Learning Strategies Tournament. Here’s what it’s all about:

Suppose you find yourself in an unfamiliar environment where you don’t know how to get food, avoid predators, or travel from A to B. Would you invest time working out what to do on your own, or observe other individuals and copy them? If you copy, who would you copy? The first individual you see? The most succesful individual? The most common behaviour? Do you always copy, or do so selectively? If you could refine behaviours, would you invest time in that or let others do it for you? What if you then migrated – would you rely on your existing knowledge, or copy the locals?

The team consisted of a rocket scientist, a mathematician, a genetic engineer, and me.  Fortunately, the other three had enough brainpower to help us put together something interesting to submit.

The deadline for submission was Feb 28, 2012. Our team ended up using Baysian economics to put together a competitor.  If you’re interested, the abstract overview is below.

Bayes_Bots makes decisions based on the expected payoff of the moves in her arsenal: Observe, Innovate, Exploit, and, in the appropriate extension, Refine.  To decide which move to use, Bayes_Bots will look at the distribution of the learned payoffs from Innovate, and Observe.  Bayes_Bots uses Bayesian inference, to learn these distributions: she assumes that the values learned from Innovate and Observe can be modeled by an exponential distribution, and given a distribution on the payoffs associated with each arm, the means of the Observed distributions will follow a Beta distribution, while the payoffs from Observe follow an exponential distribution.  Bayes_Bots will discount older information as less reliable, using Pc as the probability that a given strategy’s payoff changes.

Bayes_Bots will Innovate rarely.  However, she will always Innovate on her first turn; this will help provide new raw information to the collective population of agents.

Observe_who. In the observe_who strategy, Bayes_Bots will not change her strategy.  The assumption is that information is equally valuable from all other agents in the field, regardless of their age, number of times they’ve been observed, etc.

Refine. Bayes_Bots will Refine one of her high-payoff moves at least once, in order to understand what benefit that might have to her overall expected payoffs.  Otherwise, Bayes_Bots will not change her strategy; if other agents refine their strategies, Bayes_Bots will learn the refined payoff.

Localization/Demes. When Bayes_Bots changes to a new deme, she will discard information about the distribution of payoffs from observed strategies.  She will retain information regarding the distribution of payoffs from innovated strategies, as well as the distribution of the means of the observed strategies, as these pieces of information are assumed to be useful across all demes.

If you want to read the full entry, let me know – I’m happy to share out the doc.  It also has our very complex math and equally complex Python code.

*by “aggressively competing” I mean “meet at a coffee shop once a week to pretend we know what we’re talking about and eat chocolate.”

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Separating Facebook users: 4.74 Degrees

January 11, 2012 5 Comments

Remember my less-than-epic, although very entertaining, quest to confirm or deny the famous Six Degrees of Separation experiment, originally conducted by Stanley Milgrim?  My goal was to send out letters, as in the original experiment, and have those recipients do their best to get those letters to a named someone in Boston.  Each link in the chain would write down their name on the letter, and, by the end, we’d have a list of how many people the letter went through to get to that final person.

You might remember that not one letter made it to my contact in Boston.

Many other groups have turned to Facebook to answer the question. Several failed, fake, or ineffective “Six Degrees” Facebook groups have popped up.

However, just a few months ago, the University of Milan partnered with Facebook to report that the average number of acquaintances separating any two people in the world was not six, but 4.74.

The new research used data from 721 million Facebook users, more than one-tenth of the world’s population. Facebook posted the results on their data facebook page.

From the New York Times article:

The experiment took one month. The researchers used a set of algorithms developed at the University of Milan to calculate the average distance between any two people by computing a vast number of sample paths among Facebook users. They found that the average number of links from one arbitrarily selected person to another was 4.74. In the United States, where more than half of people over 13 are on Facebook, it was just 4.37.

That being said, Facebook users are probably a self-selected bunch.  In this case, the people who use Facebook are those who have online access and choose to use Facebook.  They might be better connected individuals than those who do not use Facebook.

Importantly, this study raises questions about definitions like “friend,” “acquaintance,” or “guy you met one time on the bus.”  Which of those actually counts as a connection?

Either way, it’s pretty exciting to know that we’re only a few introductions away from people like Hugh Laurie and David Cameron.*

*If anyone here is Facebook friends with them, let me know.

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Diminishing Marginal Returns to Swans

September 24, 2011 4 Comments

Which is more beautiful?  This:

Many Swans

Or this?

Two Swans

When we lived in Connecticut, a pair of swans took up residency in a pond behind our house.  They were extremely territorial, so we didn’t get too close, but they were beautiful to look at from afar.

One spring, they were joined by what appeared to be their extended family; about thirty additional swans showed up.

Thirty+ swans were not as beautiful as two swans.  Swans had become a commodity, and each one was no longer a unique work of nature’s art.

We had experienced diminishing marginal returns to swans.

From wikipedia:

In economics, diminishing returns (also called diminishing marginal returns) is decrease in the marginal (per-unit) output of a production process as the amount of a single factor of production is increased, while the amounts of all other factors of production stay constant.

Put more simply, we appreciate two swans more than zero swans.  But after some number of swans arrive, we appreciate each swan less than the previous swan.

The graph might look something like this, where “input” is the number of swans, and “output” is how much we appreciate each additional swan:

After the "X," each additional swan is less impressive.

We experience diminishing marginal returns with a lot of things in life.  The first slice of pie is delicious, but the fourth or fifth might not be so enjoyable.  The first 90 minutes Lord of the Rings: Return of the King were incredible, but even the impressive graphics aren’t that great at minute 200.

In most cases, there is a point at which we can have too much of a good thing.

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Your “Choice Muscle” Needs Fuel, Too

August 17, 2011 2 Comments

The New York Times’s John Tierney just published an article about making decisions, called “Do you Suffer from Decision Fatigue?“  It’s one of the best, most in-depth articles I’ve read about the physiology of decision-making.  It’s long, but if you’re into this sort of thing, I really recommend reading it.

(The article is a good followup to my post from a few months ago, which discussed what economists Sheena Iyengar and Tim Harford think about this topic.)

High level summary

  • Making decisions is difficult work, so we get tired of doing it.  At the end of the day after we’ve made many decisions, we either make worse decisions or no decisions at all.
  • We make better decisions when our brains have access to glucose.  This is why we frequently crave sugary foods after a series of tough decisions.  However, having a constant supply of glucose from protein-rich foods ensures better overall decision-making throughout the day.

And who has the best self control?

People with the best self-control are the ones who structure their lives so as to conserve willpower. They don’t schedule endless back-to-back meetings. They avoid temptations like all-you-can-eat buffets, and they establish habits that eliminate the mental effort of making choices. Instead of deciding every morning whether or not to force themselves to exercise, they set up regular appointments to work out with a friend. Instead of counting on willpower to remain robust all day, they conserve it so that it’s available for emergencies and important decisions.

“Even the wisest people won’t make good choices when they’re not rested and their glucose is low,” Baumeister points out. That’s why the truly wise don’t restructure the company at 4 p.m. They don’t make major commitments during the cocktail hour. And if a decision must be made late in the day, they know not to do it on an empty stomach. “The best decision makers,” Baumeister says, “are the ones who know when not to trust themselves.”

The post is available here.

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Choosing between Strawberry, Raspberry, and Blueberry

June 21, 2011 5 Comments

Have you ever been overwhelmed by a restaurant menu with far too many options?  The Cheesecake Factory is notorious for this — they hand out a Bible-sized booklet of different dishes you can choose from.  Most of us feel a little lost examining these menu treatises.  How can we possibly decide on what to eat when there are so many options?

There’s a faction of behavioral economists who think that too much choice is a bad thing; we, as humans, don’t know how to optimize our choices when presented with more than six or seven options. Are they right?

Economist Sheenya Iyengar (I wrote about her here), is a popular proponent of this idea.  Her book, which I’m failing to make my way through right now, details the most popular study backing up the too-much-choice assertion.  It’s frequently cited as proof of the negative consequences of too much choice.

She and psychologist Mark Lepper set up a jam-tasting booth at a grocery store in California.  Sometimes, shoppers were offered six varieties of jam, and at other times, they were offered 24.  Either way, they were then offered a voucher to buy jam at a discount. The results? Shoppers presented with an assortment of 24 jams were 1/10th as likely to buy some than those who were shown only six jams.

A few weeks ago, I had the pleasure of meeting British Economist, and one of my personal heroes, Tim Harford.  He’s written one of my favorite economics, books, called “The Undercover Economist.”  He’s got a new book out now, “Adapt: Why Success Always Starts with Failure,” (This book is the main reason I’ve put Iyengar’s down – I find Harford a much more compelling writer.)

Harford disagrees with the idea that too much choice is debilitating, and wrote about it on his blog.  In a post titled “Given the choice, how much would you like?” he quickly surveys the field of research, including followup studies that have been done, and concludes,

The average of all these studies suggests that offering lots of extra choices seems to make no important difference either way. There seem to be circumstances where choice is counterproductive but, despite looking hard for them, we don’t yet know much about what they are. Overall, says Scheibehenne: “If you did one of these studies tomorrow, the most probable result would be no effect.” Perhaps choice is not as paradoxical as some psychologists have come to believe. One way or another, we seem to be able to cope with it.

My guess is that we have a “choice muscle,” that we can train and teach to deal with larger number of choices.  Like with any other muscle, practice will improve our ability to use it.  If we practice at deciding between a large number of options, we certainly can’t get any worse at it.

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