Quantum in the North; Random in the South

A couple of interesting workshops happening this week both studying information, not the usual classical notions of information but quantum and random information.

At Banff in the Canadian Rockies we have the BIRS Workshop on Quantum Computation and Information Theory. This workshop will examine the properties of quantum information and tie it together with people working on quantum algorithms and complexity.

Meanwhile in Córdoba, Argentina on the edge of the Sierra Chica mountain is the Conference on Logic, Computability and Randomness 2004. Much of this conference focuses on random sets, not from a probability distribution but single sets that "look" random. Rater surprisingly, whether we define random sets by passing statistical tests, foiling betting strategies or using Kolmogorov complexity, these notions often lead to equivalent definitions of random.

While circumstances keep me in Chicago I say to the participants of both meetings: Enjoy the mountains and save some theorems for me.

NSF News

Arden Bement, who has been serving as the acting director of the National Science Foundation since Rita Colwell stepped down in February, has been nominated for the permanent director position.

The US Senate continues to work on the appropriation bills to set funding levels for next years US fiscal year that starts October 1. The CRA has a summary of the various bills affecting research funding in computer science (see also this note from AIP). Most worrisome (as I've mentioned before) is the funding for the VA-HUD bill that covers the NSF. The House committee would cut the budget by 2%. The CRA has an Advocacy Alert, still time to contact your senators.

Email's Curse of Success

Computer Scientists have communicated via email since the mid-1980's. Back then email worked quite well: You would send a message and usually get a quick response. We avoided telephone tag, trying to reach each other by phone when we needed to talk to each other quickly. Research ideas spread quickly; the world became smaller. Even within a department communication became paperless as one can get a message out to everyone far quicker electronically.

So what went wrong? We still use email today as the primary source of communication among computer scientists. But send a message today and I've learned to wait on average a couple of days to expect a response, if I get one at all.

Spam is the obvious culprit. Spam does clog our inboxes and even worse many of us don't carefully go through our spam folders and some legitimate mail gets unread. Spam has also made some computer scientists reluctant to share their email addresses online. But spam is not the only issue.

Email has become the communication of choice in the rest of the world as well. Besides messages from other scientists, I get email about my daughter's soccer team, announcements of upcoming concerts, warnings from the local police departments, a morning summary of the New York Times, financial information, utility bills and much more. All legitimate and usually useful email but it takes longer to work through it and slows down the time to respond to other scientists. Not to mention the many other web distractions such as news and weblogs (So stop reading this blog and respond to my emails. You know who you are.)

I can't rely on older technologies; since computer scientists expect email they check even less often their phone messages and postal mail. I can't rely on newer technology; computer scientists are surprisingly slow in adapting to new tools (like mail attachments) and it'll be years before instant messaging becomes common in the scientific community.

Oddly enough in our highly connected society it becomes harder and harder to get someones attention. So what am I doing? Slowly collecting the cell phone numbers of other computer scientists. Want mine? Send me an email.

Is the AP Test to Blame for Shifting CS Enrollments?

It is no secret that undergraduate enrollments in computer science have been dropping over the past five years. Students follow the money and, with the perception of a weaker job market in computer-oriented careers, less students are willing to study computer science.

Why does computer science follow the job market so closely? We don't see such swings in physics or history but such swings are common in engineering disciplines. Are undergraduate viewing computer science more as engineering than science? And why?

One theory I recently heard puts the blame on the Advanced Placement (AP) Computer Science Exam given to high school students. The reasoning goes as follows: The AP exam has a strong emphasis on the Java programming language and so high school teachers, teaching to the exam, focus most of their course on syntax and coding of Java. This gives the impression to students that computer science = programming.

I don't agree with this assessment. I looked at some sample CS AP tests. The tests, particularly the AB exam, requires some knowledge of data structures and simple algorithms. Nothing deep but enough that students should realize that computer science is more than just programming.

There was a surge of interest in computer science when I started college in the early 1980's (with the advent of personal computers) before an AP test in Computer Science even existed. Also I've heard of declines in enrollments outside the US where they don't use the AP tests.

But in the end we shouldn't be that worried about shifting enrollments. Advances in computer technology have helped drive computer science from a virtually non-existent discipline forty years ago to one that many universities now consider one of their most important departments. Better to have enrollments that swing up and down with the state of the computer industry than one that stagnates at the low end.

Favorite Theorems: List Decoding

August Edition

In coding theory, one typically maps a string to a code such that with some small amount of error in the code one can still recover the original string. What if the amount of error is too much to give a unique decoding? In the 1950s Peter Elias suggested the idea of list decoding, coming up with a short list of possibilities one of which is correct.

Madhu Sudan showed that list decoding can be achieved in scenarios where one cannot do unique decoding.

Decoding of Reed-Solomon Codes Beyond the Error-Correction Bound by Madhu Sudan

In this paper Sudan gives a polynomial-time list-decoding algorithm that can deal with errors in the code beyond what regular codes can handle. Later Guruswami and Sudan give a polynomial-time algorithm that handles what is believed to be the best possible amount of error.

List-decodable codes have had applications to many areas including pseudo-random generators, extractors, hard-core predicates, probabilistically-checkable proofs and a neat result by Sivakumar on the implications of SAT being membership-comparable.

We've seen many other important papers in coding theory from computer scientists over the last decade. Besides the work on list decoding I should also mention Spielman's breakthrough result showing linear time encodable and decodable codes building on the initial work of using expander graphs for codes developed by Sipser and Spielman.

For much more on coding see the surveys by Sudan on List Decoding and Guruswami on Error-correcting codes and Expander Graphs.

Which Affiliation?

Dieter van Melkebeek and I had a mild disagreement over an issue in writing a paper and he suggested I discuss it on my weblog. So here goes.

We're working on a journal version of a paper where we did the research back when we were both in New Jersey (Dieter is now on the Wisconsin faculty). Dieter listed our current institutions on the paper. I think that we should list our institutional affiliation when we performed the research, or more precisely the place paying the salary at that time. I don't feel that strongly about the issue so I am letting Dieter have his way, especially since he did the vast majority of the writing. I did ask that we have footnotes explaining our affiliations at the time of the research. (As a side note, footnotes should also contain other support information such as grants, where one was physically located when the research was done if different and contact information, though these days one needs only know how to spell my name correctly when using Google).

So I'll open this up to my readers. Which affiliation should one use? Or are we just arguing over an issue that nobody really cares about?

Just Because I'm a Scientist Doesn't Mean I Know Anything

My six-year old daughter playing with her friend on the computer ran into some problems. So she found me in the house and said, "Daddy, I know you are a computer scientist so you know everything about computers and we need you to fix our game."

I've learned to expect this attitude from adults. Often when I talk to a non-academic about being a computer scientist I get responses like, "Should I get Windows or a Mac?", "I was thinking of setting up a wireless network." or "What do you think of that Google IPO?". Of course this is on top of them thinking I have a cushy academic job teaching three hours a week with summers off.

For my daughter I just went ahead and fixed her problem. I know when she becomes a teenager she'll run circles around me on the computer and will say "When I was a kid I thought you knew everything about computers. What do you computer scientists do anyway?" Then we can talk.

The Electoral College

As everyone knows from the 2000 election, the United States does not use a majority rule to choose the president, rather they use a more complicated system known as the Electoral College. With some calls for the abolishment of the Electoral College, let's take a look at the College from a computer science point of view and see the rather clever device our founding fathers have created.

In short the Electoral College works as follows: 538 electors are allocated to states as the sum of the senators (2 for each state) and representatives (proportional to population). In most states, each voter picks a single candidate and the candidate that wins the most votes receives all of the electoral votes for that state. The candidate winning the majority of the electoral votes becomes president. More details here.

In computer science terms (assuming two candidates), we have a weighted majority of majorites or a depth-2 neural net. It has some properties that you would want:

• Monotonicity: If a candidate wins the election and more people vote for him, he will still win.
• Fairness: Barring a tie, if all the votes were switched the other candidate would win.

The College does lack symmetry, a permutation of the voters could lead to a different result. Only the simple majority function has symmetry, monotonicity and fairness. But symmetry is not necessary for an election scheme.

The United States is just that, a collection of fifty states each with their own laws, cultures and economies, united under some common principles. A simple majority would have the large populations centers overwhelm the rest of the country in choosing our leader. A majority of majorities would give some states far more power than their size would dictate. So a compromise was formed, a weighted majority of majorities to give small states some but not too much influence. The fact that this process does not always agree with majority is not a bug but a feature that preserves the balance between small and big states, rural and urban America. It also keeps balance between states of the same size, an lopsided vote in California would not overwhelm a closer vote in New York.

Some things I would change in the Electoral College: Electors should be required to vote for the candidate they represent; for each state we should have a ranked voting method instead of plurality takes all; the tie-breaking rules should be changed, now they give too much power to the small states.

The winner of the World Series in baseball is not the team that scores the most runs but the team that wins the most games, a majority of majorities and most people feel it gives a better indication of the better team. Why shouldn't elections deserve a system at least as sophisticated?

Is Encryption Doomed?

Considerable Slashdot discussion about a Technology Review article Is Encryption Doomed? subtitled Our entire information society rests on a fragile foundation that mathematicians are racing to dismantle.

That fragile foundation is the P versus NP question. Much of current cryptography is based on the NP problem Factoring which would have an efficient algorithm if P were equal to NP. If P = NP than no other method of public-key cryptography would be possible either. However, as I have argued before, the loss in public-key crypto would be greatly offset by the gain in efficiency of nearly every other aspect of our lives. Encryption's doom would be society's gain.

Factoring is not believed to be NP-complete and we could have the worst of all possible worlds with no cryptography and no new algorithms for problems we care about, one of five possibilities explored by Russell Impagliazzo.

Racing to dismantle is a bit of an overstatement. First of all we have nothing to worry about. As Juris Hartmanis once said, "We all know that P ≠ NP, we just don't know how to prove it." Remember too that all mathematics is based on unprovable assumptions about consistencies of logical theories. Doesn't seem to seriously bother anyone.

The article quotes Adleman as saying "From my perspective, we are no nearer to solving the problem now that we were when bell-bottom pants were cool." Adleman is an optimist; we do not even currently have a good approach to showing P ≠ NP. We are much further away from solving the problem than ever before.

Theory in the Coca-Cola Capital of Iowa

  

Today I gave the talk at the Atlantic Theory Seminar, not Atlantic as in ocean but Atlantic, Iowa (population 7,257). Located halfway between the theory groups of Iowa State and Nebraska, the Cass County branch of the Iowa Western Community College hosts a theory seminar every couple of months. Pretty impressive that these theory groups, faculty, postdocs and students, drive two hours each just to join for a seminar and talk theory with each other. Quite an enjoyable day in rural America.

Sorry about the quality of the picture above. We didn't have a digital camera so I took the picture with my cell phone.

Computationally Simple One-Way Functions

An upcoming FOCS paper is drawing a lot of interest at TTI and Chicago, Cryptography in NC⁰ by Benny Applebaum, Yuval Ishai and Eyal Kushilevitz.

Don't let "NC⁰" scare you, it simply means that every output bit depends on a constant number of input bits. In this paper the authors show that under reasonable assumptions one can have one-way functions and pseudo-random generators where each output bit depends on only four input bits. Quite surprising that such simple functions can be so hard to invert.

Their proof uses a clever but not overly complicated reduction using randomized polynomials from a larger class (⊕L/poly) to NC⁰ and so if one-way function and PRGs exist in the larger class than slightly weaker versions exist in NC⁰ respectively. The larger class contains many functions conjectured to be one-way or a PRG, including those based on factoring.

I remember Mike Sipser mentioning in a complexity class I took back in the mid-80's that "We don't even know how to show there are no one-way functions in NC⁰." Now we know why.

What happened to the future?

Disney World has two areas originally designed to give a glimpse of "the future", Tommorowland in Magic Kingdom and Future World at EPCOT, which itself once stood for Experimental Prototype Community of Tomorrow. These areas give somewhat a nostalgic view of the future from the time of my childhood but not of the future from today.

Not only has society's view of the future changed but even the view about the future has changed. We live in an era of massive changes in technology particularly in access to communication and information. In the "Spaceship Earth" ride that shows the history and future of communications, the future shows two kids seeing and playing games with each other through video monitors, a task easily accomplished today with webcam-equipped networked PCs. But the ride missed many aspects of computers and the web. Who would have thought when I was a kid that I would now be writing this post on a commuter train that soon will be read around the world.

On the other hand we also dreamed of flying cars and space planes but the technology of transportation has not significantly changed since I was born and I don't expect major changes in the next forty years. So the future has come but not quite as we expected.

Technology has made the world a more homogeneous place. When at the Norway pavilion at EPCOT, an American visitor asked a Disney worker from Norway about what the country was like to visit. "The towns are like mid-size American cities" was the reply. I guess it is a small world after all.

ε and the Olympics

Back from Disney World and ready to tackle the new academic year. Thanks to Adam Klivans for his guest posts. Interesting to see that COLT glorifies the open problems. In complexity we prefer to see them closed.

Varsha Dani emailed a note about an article describing an Amazon tribe with no concept of numbers. I guess they don't send anyone to the olympics where numbers seem king.

Watching gymnastics I am always amazed how winning seems to depend on sticking the landing. After a rather complicated and lenghty routine why should whether your feet move at the end be the difference between Gold and Bronze? The answer lies in the ε; the best gymnasts can uniformly hit the major elements of their routines but consistently sticking the landing is much more difficult and that what makes or breaks the result.

We see the ε issue in many scenarios, most notably the 2000 US presidential election where confusing ballots in one county created a huge controversy. The budget of the NEC Research Institute is miniscule compared to the revenue of NEC corporate. A couple of years ago NEC eeked out a profit about the same size of the cost of the Institute and all of a sudden the NEC Research Institute looked very expensive to NEC. In another example, consider the relatively large power a small party can have in a coalition in a parlimentary system.

The best way to avoid the ε problem is by decisive victories. Solidly beat your opponent in an election or have enough parlimentary seats so you don't need small partners. Make enough of a profit so that a cheap research lab stays that way. One only gets the ε problem when one has a statistical tie and then the small things take on great importance.

In gymnastics one would want a system where a greatly superior gymnast can score high enough that a small jump on the landing won't make a difference. But the current system doesn't allow that; with a top score of 10 the world's best gymnasts all get well over nine, making it impossible to put enough of a gap between a the best and the rest.

"Conclusions and Open Problems" (by Adam Klivans)

Unless Lance has been involved in some unfortunate roller coster accident, this is most likely my last post. It remains to be seen whether I will be allowed to keep my posting privileges here on the board (place your bets on "No"). What I've taken away from this experience, more than anything else, is that posting every day is a tremendous time sink. Lance, kudos to you for the almost daily missive.

At the end of most technical talks is the obligatory "Conclusions and Open Problems" slide, usually the least thought out moment of the presentation, which consists of a brief summary of the talk and a list of the most obvious (difficult) open problems. For the last few years, COLT has glorified the open problems section and allocates about an hour of time for a presentation of open problems. The open problems themselves must be submitted months beforehand and are refereed (how rigorously is anyone's guess); accepted problems appear in the proceedings. A list of this year's open problems can be found on the COLT 2004 program schedule -- the session was held on Friday evening.

Are there any other computer science conferences where open problems are refereed and given their own slot in the program? It always seems to work out well at COLT, and while I am aware of open problems being presented at rump sessions at various conferences, I don't know of other venues which require advance submission of problems.

With that, gentle reader, I return you to Lance's wise embrace. If I ever get to guest blog again, I will reveal what's hidden in Lance's "Private" directory here on fortnow.com. Some "lost" theorems apparently-- here's an aborted post entitled "Soon I will be famous: a simple proof that NP = coNP" -- and here's another unfinished note with some not so nice things to say about Algorithms. And what's this? A love letter to Jessica Simpson? Oh if only we had more time.

Constant Depth Circuits, Fourier Transform, and Learnability (by Adam Klivans)

First, thanks to Jeff Erickson for the lone comment on my previous post. For a second I was worried that I would have to post about Quantum Learning to bait Scott Aaronson into commenting. Fortunately, we're past that. I also realize now that being in Chicago I'm just a two hour drive away from you Jeff at UIUC. Maybe you, Ernie, and I should get some 3-D hotcakes at the local Waffle House-- on me.

Many top notch researchers come to visit the Toyota Technological Insitute here in Chicago. This fall alone Lenore Blum, Bruno Codenotti, Prahladh Harsha, and Jaikumar Radhakrishnan will be in residence along with TTI's regular faculty.

Yishay Mansour visited in August for about two weeks, and I had the chance to ask him about his work along with N. Linial and N. Nisan which pioneered the use of discrete Fourier analysis in computational learning theory. The paper Constant Depth Circuits, Fourier Transform, and Learnability gives a quasi-polynomial time learning algorithm for constant depth circuits with respect to the uniform distribution. More importantly, it pointed out a connection between the Fourier concentration of a Boolean function and its learnability.

If f is a Boolean function, we could imagine writing f as a multilinear polynomial in n variables mapping {-1,1}^n to {-1,1}. Every Boolean function can be written as such a polynomial whose total degree is at most n. Each coefficient of this polynomial measures the correlation of f with that monomial. These are the Fourier coefficients of f. Linial, Mansour, and Nisan showed that if the sum of the squares of the coefficients of monomials of degree d and larger is small, then there is an n^{O(d)} time algorithm for learning f with respect to the uniform distribution-- roughly speaking it is sufficient to estimate the coefficients of only the low degree monomials and output this polynomial.

What does any of this have to do with constant depth circuits? They also proved that for any circuit of depth d, the sum of the squares of the coefficients on the terms of degree (log n)^d and higher decays rapidly. From the above paragraph this gives us a quasi-polynomial time algorithm. For a rough intuition as to why this is true, consider one implication of Hastad's Switching Lemma, namely that parity cannot even be approximated by constant depth circuits. Thus every coefficient of a sufficiently large monomial (each monomial is a parity function) must be small.

As it turns out, according to Yishay, the work stemmed from an effort to prove circuit lower bounds, rather than a plan to develop new learning algorithms. The authors were inspired by Kahn, Kalai, and Linial's work on the influence of variables on Boolean functions and thought that discrete Fourier analysis might be the right tool for studying circuits. They happened to be correct-- in an unexpected way.

Banff Revisited (by Adam Klivans)

Hey, you're back! And I'm really starting to feel comfortable at this posting gig. Thanks for all of the comments I got about my previous post-- all zero of them.

A few weeks ago Lance reported on the events from a complexity workshop he was attending at the Banff International Research Station, an institute similar to the International Space Station except that it's in Canada rather than outer space.

What Lance didn't mention was that at the exact same time, some important computer science conferences were taking place just down the street at the Banff Park Lodge. I was participating in the 17th annual Conference on Learning Theory (COLT) which was co-located with the International Conference on Machine Learning (ICML) and the Conference on Uncertainty in Artificial Intelligence (UAI).

Back when COLT stood for Computational Learning Theory (circa 1988-2002), the conference was known for focusing on the computational complexity of machine learning. Nowadays the conference still operates from a theoretical perspective, but, as the Conference on Learning Theory, the program covers everything from game theory and economics to kernel methods in addition to traditional PAC style results.

A PAC style result that appeared in COLT 2004 which may be of interest to the readers of this web log is Polynomial-Time Prediction Strategy with Almost Optimal Mistake Probability by Nader Bshouty. His paper solves a problem in the online learning setting. In this setting, an unknown function f is chosen from some fixed concept class and at time t a learner is presented with an input x chosen according to some distribution D.

The goal of the learner is to run in time polynomial in log t (and all of the other relevant parameters) and predict the value of f(x) with mistake probability O(1/t) (Haussler, Littlestone, and Warmuth proved that this mistake probability is optimal). Bshouty shows that if the concept class is PAC learnable, then there exists an online learning algorithm which runs in time polynomial in log t and achieves mistake probability O(log t/ t). His algorithm has an exponential improvement in running time as previous solutions ran in time polynomial in t. The algorithm works by iteratively creating a branching program based on hypotheses considered at previous time steps. A boosting-type procedure dictates which branch to take for any new input.

In the spirit of being controversial (Lance asked me to be controversial), I could discuss the pros and cons of the change from Computational Learning Theory to Conference on Learning Theory (as a concrete example of differences in the community, about half the participants at the COLT business meeting wanted to see COLT co-located with STOC in 2006-- University of Washington folks make your move-- and the others wanted to co-locate with ICML). I'll leave that, however, for my faithful readers to debate. I will point out that it's hard to argue with the increase in attendance at COLT over the last few years.

Favorite Theorems: The Harmonic Sieve (by Adam Klivans)

What does Lance Fortnow do after getting a paper accepted to FOCS? He goes to Disneyworld for a week, of course. While Lance blasts pasts celestial satellites on Space Mountain, I will humbly try to replace the irreplaceable.

Considering the topic of yesterday's post, if there were a list of favorite theorems in computational learning theory, a field which makes only brief appearances here on the weblog despite its many connections to computational complexity, Jeff Jackson's algorithm for learning DNF formulas would certainly be on it.

A DNF formula is a Boolean formula written as an OR of ANDs (e.g. x_1 and x_2 OR x_3 and x_5). The size of a DNF formula is equal to the number of terms or ANDs. The problem of PAC learning an unknown polynomial-size (in n, the number of variables) DNF formula with respect to an arbitrary distribution remains one of the most notorious open problems in the field (for background on PAC learning see this post or Kearns and Vazirani's excellent book An Introduction to Computational Learning Theory).

In fact, even if we restrict the underlying distribution on examples to be the uniform distribution, the fastest algorithm for learning DNF formulas runs in quasi-polynomial time (a result due to K. Verbeurgt-- the main idea being that only terms of logarithimic length have a chance at being satisfied, so longer terms can be ignored).

If, however, we allow the learner to make queries to the unknown DNF formula, i.e. if the learner can choose any input x and ask for the value of the DNF formula evaluated on x, then the learner can succeed in polynomial-time.

The solution, due to Jeff Jackson in 1994, shows how to learn polynomial-size DNF formulas with respect to the uniform distribution in polynomial-time (again assuming the learner has query access to the unknown DNF). His algorithm, which he has called the Harmonic Sieve due to its use of Fourier analysis, builds on work due to Blum, Furst, Jackson, Kearns, Mansour, and Rudich (``Weakly Learning DNF and Characterizing Statistical Query Learning Using Fourier Analysis'') which showed that for any DNF formula with s terms, there exists a parity function which agrees with the DNF formula on roughly a 1/2 +1/s fraction of inputs.

The next step of the algorithm involves a novel application of Boosting algorithms (see this post for more on Boosting) for combining these parity functions to obtain an accurate hypothesis. The output of the Harmonic Sieve is not a DNF formula but a threshold of parity functions.

The Harmonic Sieve is one of the rare examples in computational learning theory of a polynomial-time algorithm for an expressive concept class. It is natural to ask whether the queries are essential for the algorithm. Unfortunately it seems like the answer is yes-- we do not know how to learn decision trees or even juntas (both strictly weaker concept classes than DNF formulas) in polynomial-time with respect to the uniform distribution unless the learner has query access to the unknown function. Removing the dependence on queries would be a real breakthrough.

By the way, the interface on blogger.com is worse than I ever could have imagined. Apologies in advance for formatting errors.

Favorite Theorems: Parallel Repetition

July Edition

Consider a simple Arthur-Merlin game: Arthur probabilistically chooses a string r sends it to Merlin who responds with y and then Arthur runs some algorithm A(r,y) to decide whether to accept. Merlin's goal is to achieve the highest acceptance probability possible p for Arthur. Suppose we run the game twice in parallel, Arthur sends r₁ and r₂ and Merlin sends y₁ and y₂ and Arthur accepts if A(r₁,y₁) AND A(r₂,y₂). The highest possible acceptance probability will be p².

Now consider the MIP model with two Merlins M₁ and M₂ who cannot communicate with each other. Arthur sends u and v to M₁ and M₂ respectively who respond with y and z. Arthur accepts based on some function A(u,v,y,z). Once again M₁ and M₂ try to achieve the highest possible acceptance probability p. Now we run the game twice in parallel, Arthur sending u₁ and u₂ to M₁ and v₁ and v₂ to M₂ receiving y₁ and y₂ from M₁ and z₁ and z₂ from M₂ and accepting if A(u₁,v₁,y₁,z₁) AND A(u₂,v₂,y₂,z₂).

One might assume that the best the provers can achieve is p² (an assumption in fact made in an early paper co-authored by a certain weblog author) but in some circumstances the provers can do better. However Ran Raz shows that if p is less than 1, one can get an exponential decrease in p with a polynomial number of parallel rounds in

A Parallel Repetition Theorem by Ran Raz

This paper settles one of the more perplexing aspects of multiple prover proof systems with a highly complicated proof. The result also plays a critical role in reducing the number of queries in probabilistically checkable proof systems which led to some optimal approximation bounds.

As a side note I am off on vacation tomorrow and Adam Klivans will guest blog in my absence. Enjoy.

Wisdom of Crowds

Keeping with this week's theme of prediction, I just finished reading The Wisdom of Crowds written by New Yorker writer James Surowiecki. The book makes the case that large groups can make great decisions, often better than any individual in a group, if three conditions occur:

1. diversity of the members of the group,
2. independent opinions of the group members, and
3. a method for aggregation of the opinions.

Surowiecki's very readable book gives many examples where group decisions do quite well (sports betting, Google's search techniques based on other's web pages, Linux) and where group decisions fail (stock market bubbles, committee meetings, strong CEOs).

Chapter 8 is devoted to science and how many widely spread scientists developing and criticizing various theories lead to explosive growth in our understanding. He also notes that this ideal world has its flaws as unknown researchers have a harder time selling their work than more established scientists.

I don't agree with all the conclusions drawn by Surowiecki but he does lay out what we need to do and not do to benefit from the pooled knowledge of a group. We can also draw lessons in computer science as computation and information gets more distributed that we need to integrate to find the best solutions we can.

Fun with Information Markets

Just over a year ago the Department of Defense cancelled their program on using markets to predict future world events, an overreaction that stopped funding a potentially powerful prediction tool. Robin Hanson has a comprehensive web page giving a history and plenty of links.

Information markets live in limited academic-based markets like the Iowa Electronic Market and offshore sites like Tradesports. For example the current price on Tradesports for Bush winning the election is 51.5 which translates to a 0.515 probability that Bush will win indicating a very close contest.

For each state, Tradesports has a security on whether Bush will win that state. They also have some bundles of states. The price for Florida is 50.1, Ohio 55.4 and Bush winning both Florida and Ohio is 47.1. This gives a surprising correlation between Florida and Ohio. If you believe the theory there is a very high 0.94 probability that Bush wins Ohio given that he wins Florida and with a 0.89 probability these two very different swing states will go the same way.

Tradesports gives David Vitter a 59 percent chance of becoming a senator from Louisiana. David Vitter is the brother of CS theorist and former SIGACT chair Jeff Vitter.