Scott Aaronson is a skeptic, to say the least. He made an amazing public bet to demonstrate his confidence. He pledged that if Deolalikar wins the $1 million prize, Aaronson will top it off with $200,000 of own money. Even more amazing: Aaronson made the bet without even reading the proof. [Update: I should have said "without reading the proof in detail": see comments] (Perhaps more amazing still: a PC World journalist characterized Aaronson’s stance as “noncommittal” without a drip of sarcasm.) [Hat tip to Dan Reeves.]

As Aaronson explains:

The point is this: I really, really doubt that Deolalikar’s proof will stand. And while I haven’t studied his long, interesting paper and pinpointed the irreparable flaw… I have a way of stating my prediction that no reasonable person could hold against me: I’ve literally bet my house on it.

Aaronson is effectively offering infinite odds [Update: actually more like 2000/1 odds: see comments] that the question “P=NP?” will not be resolved in the near future. Kevin McCurley and Ron Fagin made a different (conditional) bet: Fagin offered 5/1 odds (at much lower stakes) that if the question is resolved in 2010, the answer will be P≠NP. Bill Gasarch says that he, like Aaronson, would bet that the proof is wrong… if only he were a betting man. Richard Lipton recounts a discussion about the odds of P=NP with Ken Steiglitz.

But beyond a few one-off bets and declarations, where is the central market where I can bet on P=NP? I don’t even necessarily want in on the action, I just want the odds. (Really!)

My first thought was the Foresight Exchange. It does list one related contract — Good 3SAT Algorithm by 2020 — which should presumably go to zero if Deolalikar’s proof is correct. It hasn’t budged much, consistent with skepticism (or with apathy). My second thought was the PopSci Predictions Exchange (PPX), though sadly it has retired. InklingMarkets has a poll about whether P=NP will be resolved before the other Clay Institute prize questions, but not about how it will be resolved or the odds of it happening. (The poll is one of several markets sponsored by the Woodrow Wilson Center’s Science and Technology Innovation Program — hat tip to Vince Conitzer.) I don’t see anything at longbets, and anyway longbets doesn’t provide odds despite it’s name.

In 1990 Robin Hanson provocatively asked: Could gambling save science?. That question and his thoughtful answers inspired a number of people, including me, to study prediction markets. Indeed, the Foresight Exchange was built largely in his image. P=NP seems one of the most natural claims for any scitech prediction market.

All these years later, when I really need my fix, I can’t seem to get it!

If it wasn’t clear in my original post, I found Aaronson’s bet incredibly useful and I am thrilled he did it. I believe he should be commended: his bet was exactly what more scientists should do. Scientists should express their opinion, and betting is a clear, credible, and quantitative way to express it. It would be as shame if some of the negative reactions caused him or others not to make similar bets in the future.

I just wish there were a central place to make bets on scientific claims and follow the odds in the vision of Robin Hanson, rather than every scientist having to declare their bet on their own individual blogs.

This month I’ve had five times more traffic than in any other month since I began blogging in Oct 2006, even during woblomo.

Why? I paid Paul Graham a compliment that struck a minor viral nerve, spreading through twitter, facebook, and blogs and sending over six thousand people my way on July 16 alone according to quantcast. Of course most have since dispersed.

Power on the web flows backward through referrals to the sites that people begin their day with, the sources of traffic. Referrals from social media, unpredictable and bursty though they may be, are inexorably on the rise. As they grow, power will shift away from search engines, today’s referral kings. Who knows, this may embolden publishers to take previously unthinkable steps like voluntary delisting, further eroding the value of search. This has all been said before, perhaps best by Mark Cuban starting in 2008. It would be a blow to openness and hurt users, but would spark a fascinating battle.

Another meta note: I installed a new WordPress theme: Suffusion. It’s fantastic: endlessly configurable, bug free, fast, and well designed. I happened upon it by accident when WP 3.0 broke my old theme and I couldn’t be happier. Apparently written by a teenager, I donated to his beer, er, coffee fund.

In the eyes of a casino, a sharp is indistinguishable from a cheat. More than boring, this seems fundamentally unfair and unsustainable, inviting disguise. It also turns off a wealthy, influential, and game-loving segment of the population.

What I want: A casino by geeks for geeks that celebrates innovation, encourages cleverness, welcomes gadgets and wifi, and fosters hacking, outwit, and outplay.

At least one casino has seen the light. The M Casino in Las Vegas is parterning with Cantor Fitzgerald to support in-game sports betting with few rules and caps, inviting sharps to, more or less, “bring it on”.

…gamblers can bet on the game even during play, accepting ever-changing point-spreads and odds. They can invest money on a Knicks foul shot going through the hoop or a Dodger getting to first base — contending with ever-evolving odds.

More critically, bettors can create hedges while jumping in and out of positions. But instead of buying into the fast-breaking moves of Microsoft, they’re betting on the Mariners’ impending fortunes.

This form of wagering is new to Las Vegas but old-hat in other markets.

…unlike in most other casinos, laptop computers are welcome.

…”The M wants [sharp bettors] to be there,” believes [professional sports-bettor Steve] Fezzik. “They want your information, and that’s a progressive attitude.”

Kudos to M for taking a chance on a more interesting future and to Cantor for making it happen.

What Cantor is debuting may not be a whole lot more than betfair indoors, but it’s a long overdue start. Here’s to hoping we see even more innovation, including smarter and more expressive markets.

Dan and I built a second prototype in PHP. It was even uglier but about twice as fast and somewhat useable on a small scale (at least by user willing/able to formulate their own propositions in PHP). Yet it still wasn’t good enough to serve thousands of users accustomed to simplicity and speed.

The final live version of Predictalot was not only pleasing to the eye — thanks to Sudar, Navneet, and Tom — but pleasingly fast, due almost entirely to the heroic efforts of Mridul M who wrote a mini PHP parser inside of java and baked in a number of datbase and caching optimizations.

It seems that high-level programming languages haven’t climbed high enough. To field a fairly constrained web app that looks good and works well, we benefit greatly from having at least three specialists, for the app front end, the app back end, and the platform back end (apache, security, etc.).

Here’s a challenge to the programming language community: anything I can whip up in Mathematica I should be able to run at web scale. Math majors should be able to create Predictalot. Dan and I can mock up the basic idea of Predictalot but it still takes tremendous talent, time, and effort to turn it into a professional looking and well behaved system.

The core market math of Predictalot — a combinatorial version of Hanson’s LMSR market maker — involves summing thousands of e^x terms. Here we are in the second decade of the new millenium and in order for a sum of exponentials to execute quickly and without numeric overflow, we had to work out a transformation to conduct all our summations in log space. In other words, programming still requires me to think about how my machine represents my number. That shouldn’t qualify as “high level” thinking in 2010.

I realize I may be naively asking too much. Solving the challenge fully is AI-complete. Still, while we’re making impressive strides in artificial intelligence, programming feels much the same today as it did twenty years ago. It still requires learning specialized tricks, arcane domain knowledge, and optimizations honed only over years of experience, and the most computationally intensive applications still require that extra compilation step (i.e., it’s still often necessary to use C or Java over PHP, Perl, Python, or Ruby).

Some developments hardly seem like progress. Straightforward HTML markup like border=2 has given way to unweildy CSS like style=”border:2px solid black”. In some ways the need for specialized domain knowledge has gone up, not down.

Visual programming is an oft-tried, though so far largely unsuccessful way to lower the barrier to programming. Pipes was a great effort, but YQL proved more useful and popular. Google just announced new visual developer tools for Android in an attempt to bring mobile app creation to the masses. Content management systems are getting better and broader every day, allowing more and more complex websites to be built with less time touching source code.

I look forward to the day that computational thinking can suffice to create the majority of computational objects. I suspect that day is still fifteen to twenty years away.

Here’s an illustration why. Abe Othman recently alerted me to intrade’s market on where basketball free agent LeBron James will sign, at the time a featured market. Take a look at this screenshot taken 2010/07/07:

The market says there’s between a 42 and 70% chance James will sign with Cleveland, between a 5 and 40% chance he’ll sign with Chicago, etc.

In other words, it doesn’t say much. The spreads between the best bid and ask prices are wide and so its predictions are not terribly useful. We can occasionally tighten these ranges by being smarter about handling multiple outcomes, but in the end low liquidity takes the prediction out of markets.

Even if someone does have information, they may not be able trade on it so may simply go away. (Actually, the problem goes beyond apathy. Placing a limit order is a risk — whoever accepts it will have a time advantage — and reveals information. If there is little chance the order will be accepted, the costs may outweigh any potential gain.)

Enter automated market makers. An automated market maker always stands ready to buy and sell every outcome at some price, adjusting along the way to bound its risk. The market maker injects liquidity, reducing the bid-ask spread and pinpointing the market’s prediction to a single number, say 61%, or at least a tight range, say 60-63%. From an information acquisition point of view, precision is important. For traders, the ability to trade any contract at any time is satisfying and self-reinforcing.

For combinatorial prediction markets like Predictalot with trillions or more outcomes, I simply can’t imagine them working at all without a market maker.

Abe Othman, Dan Reeves, Tuomas Sandholm, and I published a paper in EC 2010 on a new automated market maker algorithm. It’s a variation on Robin Hanson‘s popular market maker called the logarithmic market scoring rule (LMSR) market maker.

Almost anyone who implements LMSR, especially for play money, wonders how to set the liquidity parameter b. I’ve been asked this at least a dozen times. The answer is I don’t know. It’s more art than science. If b is too large, prices will hardly move. If b is too small, prices will bounce around wildly. Moreover, no matter what b is set to, prices will be exactly as responsive to the first dollar as the million and first dollar, counter to intuition.

Our market maker automatically adjusts its level of liquidity depending on trading volume. Prices start off very responsive and, as volume increases, liquidity grows, obviating the need to somehow guess the “right” level before trading even starts.

A side effect is that predictions take the form of ranges, like 60-63%, rather than exact point estimates. We prove that this is a necessary trade off. Any market maker that is path independent and sensitive to liquidity must give up on providing point estimates. In a way, our market maker works more like real bookies who maintain a vig or spread for every outcome.

The market maker algorithm is theoretically elegant and seems more pratical than LMSR in many ways. However I’ve learned many times than nothing can replace implementing and testing a theory with real traders. Final word awaits such a trial. Stay tuned.

I agree, but if computer science is not the “T”, then what is it? It’s funny. Computer science seems to span all the letters of STEM. It’s part science, part technology, part engineering, and part math. (Ironically, even though it’s called computer science, the “S” may be the least defensible.*)

The interdisciplinary nature of computer science can be seen throughout the university system: no one knows quite where CS departments belong. At some universities they are part of engineering schools, at others they belong to schools of arts and sciences, and at still others they have moved from one school to another. That’s not to mention the information schools and business schools with heavy computer science focus. At some universities, computer science is its own school with its own Dean. (This may be the best solution.)

Actually, I’d go one step further and say that computer science also involves a good deal of “A”, or art, as Paul Graham popularized in his wonderful book Hackers and Painters, and as seen most clearly in places like the MIT Media Lab and the NYU Interactive Telecommunications Program.

So where is the C in STEM? Everywhere. Plus A. Computer science = STEAM.**

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* It seems that those fields who feel compelled to append the word “science” to their names (social science, political science, library science) are not particularly scientific.
** Thanks to Lance Fortnow for contributing ideas for this post, including the acronym STEAM.

Then what is Pittsburgh?

A sports town, no doubt, but that doesn’t count.

A hospital town, perhaps. The University of Pittsburgh Medical Center is a sprawling conglomerate of hospitals, doctors, researchers, and medical school, growing organically and through acquisition. Several other private hospitals and networks dot the city.

But with one the the top five computer science departments in the world at Carnegie Mellon University churning out grads at all levels, you might think Pittsburgh would have the seeds of a high-tech ecosystem. Yet there are few major technology companies, startups, or venture capital firms to nurture them locally. (Two exceptions I can think of: Google and CombineNet. Update: Also Intel Labs Pittsburgh.) Instead, CMU students tend to flee for the coasts after graduation.

Could Pittsburgh develop a startup row, a mini Silicon Valley? Pittsburghers have been hoping for and heralding such a transformation for decades. Given the city’s famously steep (SF-worthy) gradients, there’s even a perfect name for it: Silicon Hill.

In selecting Pittsburgh for the G-20 summit, the Obama administration cited Pittsburgh as a post-industrial success story with “renewed industries that are creating the jobs of the future”. But that seems very glass half full as (paraphrasing) one of my Pittsburgh friends noted on Facebook.

Paul Graham wrote a terrific essay (as Paul Graham is wont to do) about how a city might go about buying their own Silicon Valley.* He concludes that it may be possible. “For the price of a football stadium, any town that was decent to live in could make itself one of the biggest startup hubs in the world.” His main conjecture is that the money would fund a large number of good local startups in their infancy but without forcing them to stay — the best startups simply won’t take money that constrains their future options. The funding would have to be rich enough and the environment nice enough that they simply would not want to leave.

Is Graham right and, if so, could Pittsburgh pull it off?

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* See also Graham’s older and longer essay How to be Silicon Valley.

1. Grow as wealthy as possible as quickly as possible, or
2. Maximize expected wealth for a given time period and level of risk

The question is at the heart of a fight between computer scientists and economists chronicled beautifully in the book Fortune’s Formula by Pulitzer Prize nominee William Poundstone. (See also David Pogue’s excellent review.*) From the book’s sprawling cast — Claude Shannon, Rudy Giuliani, Michael Milken, mobsters, and mob-backed companies (including what is now Time Warner!) — emerges an unlikely duel. Our hero, mathematician turned professional gambler and investor Edward Thorp, leads the computer scientists and information theorists preaching and, more importantly, practicing objective #1. Nobel laureate Paul Samuelson (who, sadly, recently passed away) serves as lead villain (and, to an extent, comic foil) among economists promoting objective #2 in often patronizing terms. The debate sank to surprisingly depths of immaturity, hitting bottom when Samuelson published an economist-peer-reviewed article written entirely in one-syllable words, presumably to ensure that his thrashing of objective #1 could be understood by even its nincompoop proponents.

Objective #1 — The Kelly criterion

Objective #1 is the have-your-cake-and-eat-it-too promise of the Kelly criterion, a money management formula first worked out by Bernoulli in 1738 and later rediscovered and improved by Bell Labs scientist John Kelly, proving a direct connection between Shannon-optimal communication and optimal gambling. Objective #1 matches common sense: who wouldn’t want to maximize growth of wealth? Thorp, college professor by day and insanely successful money manager by night, is almost certainly the greatest living example of the Kelly criterion at work. His track record is hard to refute.

Objective #2

Objective #2 refers to standard economic dogma. Low-risk/high-return investments are always preferred to high-risk/low-return investments, but high-risk/high-return and low-risk/low-return are not comparable in general. Deciding between these is a personal choice, a function of the decision maker’s risk attitude. There is no optimal portfolio, only an efficient frontier of many Pareto optimal portfolios that trade off risk for return. The investor must first identify his utility function (how much he values a dollar at every level of wealth) in order to compute the best portfolio among the many valid choices. (In fact, objective #1 is a special case of #2 where utility for money is logarithmic. Deriving rather than choosing the best utility function is anathema to economists.)

Objective #2 is straightforward for making one choice for a fixed time horizon. Generalizing it to continuous investment over time requires intricate forecasting and optimization (which Samuelson published in his 1969 paper “Lifetime portfolio selection by dynamic stochastic programming”, claiming to finally put to rest the Kelly investing “fallacy” — p.210). The Kelly criterion is, astonishingly, a greedy (myopic) rule that at every moment only needs to worry about figuring the current optimal portfolio. It is already, by its definition, formulated for continuous investment over time.

Details and Caveats

There is a subtle and confusing aspect to objective #1 that took me some time and coaching from Sharad and Dan to wrap my head around. Even though Kelly investing maximizes long-term wealth with 100% certainty, it does not maximize expected wealth! The proof of objective #1 is a concentration bound that appeals to the law of large numbers. Wealth is, eventually, an essentially deterministic quantity. If a billion investors played non-Kelly strategies for long enough, then their average wealth might actually be higher than a Kelly investor’s wealth, but only one or two individuals out of the billion would be ahead of Kelly. So, non-Kelly strategies can and will have higher expected wealth than Kelly, but with probability approaching zero. Note that, while Kelly does not maximize expected (average) wealth, it does maximize median wealth (p.216) and the mode of wealth. See Chapter 6 on “Gambling and Data Compression” (especially pages 159-162) in Thomas Cover’s book Elements of Information Theory for a good introduction and concise proof.

Objective #1 does have important caveats, leading to legitimate arguments against pure Kelly investing. First, it’s often too aggressive. Sure, Kelly guarantees you’ll come out ahead, but only if investing for “long enough”, a necessarily vague phrase that could mean, well, infinitely long. (In fact, a pure Kelly investor at any time has a 1 in n chance of losing all but 1/n of their wealth — p.229) The guarantee also only applies if your estimate of expected return per dollar is accurate, a dubious assumption. So, people often practice what is called fractional Kelly, or investing half or less of whatever the Kelly criterion says to invest. This admittedly starts down a slippery slope from objective #1 to objective #2, leaving the mathematical high ground of optimality to account for people’s distaste for risk. And, unlike objective #2, fractional Kelly does so in a non-principled way.

Even as Kelly investing is in some ways too aggressive, it is also too conservative, equating bankruptcy with death. A Kelly strategy will never risk even the most minuscule (measure zero) probability of losing all wealth. First, the very notion that each person’s wealth equals some precise number is inexact at best. People hold wealth in different forms and have access to credit of many types. Gamblers often apply Kelly to an arbitrary “casino budget” even though they’re an ATM machine away from replenishment. People can recover nicely from even multiple bankruptcies (see Donald Trump).

Some Conjectures

Objective #2 captures a fundamental trade off between expected return and variance of return. Objective #1 seems to capture a slightly different trade off, between expected return and probability of loss. Kelly investing walks the fine line between increasing expected return and reducing the long-run probability of falling below any threshold (say, below where you started). There are strategies with higher expected return but they end in ruin with 100% certainty. There are strategies with lower probability of loss but that grow wealth more slowly. In some sense, Kelly gets the highest expected return possible under the most minimal constraint: that the probability of catastrophic loss is not 100%.

It may be that the Kelly criterion can be couched in the language of computational complexity. Let Wt be your wealth at time t. Kelly investing grows expected wealth exponentially, something like E[Wt] = o(x^t) for x>1. It simultaneously shrinks the probability of loss, something like Pr(Wt< T) = o(1/t). (Actually, I have no idea if the decay is linear: just a guess.) I suspect that relaxing the second condition would not lead to much higher expected growth, and perhaps that fractional Kelly offers additional safety without sacrificing too much growth. If formalized, this would be some sort of mixed Bayesian and worst-case argument. The first condition is a standard Bayesian one: maximize expected wealth. The second condition — ensuring that the probability of loss goes to zero — guarantees that even the worst case is not too bad.

Conclusions

Fortune’s Formula is vastly better researched than your typical popsci book: Poundstone extensively cites and quotes academic literature, going so far as to unearth insults and finger pointing buried in the footnotes of papers. Pounstone clearly understands the math and doesn’t shy away from it. Instead, he presents it in a detailed yet refreshingly accessible way, leveraging fantastic illustrations and analogies. For example, the figure and surrounding discussion on pages 197-201 paint an exceedingly clear picture of how objectives #1 and #2 compare and, moreover, how #1 “wins” in the end. There are other gems in the book, like

• Kelly’s quote that “gambling and investing differ only by a minus sign” (p.75)
• Louis Bachelier’s discovery of the efficient market hypothesis in 1900, a development that almost no one noticed until after his death (p.120)
• Poundstone’s assertion that “economists do not generally pay much attention to non-economists” (p.211). The assertion rings true, though to be fair applies to most fields and I know many glaring exceptions.
• The story of the 1998 collapse of Long-Term Capital Management and ensuing bailout is sadly amusing to read today (p.290). The factors are nearly identical to those leading to the econalypse of 2008: leverage + correlation + too big to fail. (Poundstone’s book was published in 2005.) Will we ever learn? (No.)

Fortune’s Formula is a fast, fun, fascinating, and instructive read. I highly recommend it.

__________

* See my bookmarks for other reviews of the book and some related research articles.

The key to understanding this debate is recognizing the difference between anonymity and egalitarianism. A mechanism is anonymous if the outcome does not depend on the identity of the players: two players who bid the same are treated equally. It doesn’t matter what their name, age, or wealth is, what company they represent, or how they plan to use the item — all that matters is what they bid. This is a good property for almost any public marketplace that ensures fair treatment, and one worth fighting for on the Internet. AppleT&T should not block Google Voice just because it’s a threat. In fact, even without legislation, it’s almost impossible to bar anonymous participation on the Internet. Service providers can, if forced to, encrypt their packets and hide their content, origin, and purpose, making them indistinguishable from others.

However no one would argue that everyone in a marketplace should receive identical resources. Players who bid more can and must be distinguished (for example, by winning more items) from players who bid less. So, while it’s wrong to discriminate based on identity, it’s absolutely essential to discriminate based on willingness to pay. That is the difference between an egalitarian lottery (silly) and an anonymous marketplace (good).

Somehow the net neutrality debate has confounded these two issues. I agree that any Internet constitution should include that all packets are equal regardless of their creator or purpose (charging $30 for “unlimited” data and in addition 30 cents per 160-char text message scores 72 on the ticketmasterindex). However, users or services who are willing to pay for it can and should receive higher quality. To do otherwise virtually guarantees wasting resources.

Update 2009/08/27: Mark Cuban (as always) says it well. [Via Tom Murphy]

I agree (nearly) completely. The conference publication system is broken. Computer science papers are by and large not scholarly documents: many are sloppily written in deadline-driven haste with poor literature reviews, often blamed on page limits. Many reviews are rushed or cursory and decisions are safe at best, arbitrary at worst. The conference system encourages balkanization and discourages the emergence of a unified computer science conference.

Journals are better, as long as we move forward and not backward. We need open-access journals with fast turnaround times. Lance’s article itself underscores the point: it’s behind a pay wall, albeit a comparatively inexpensive and lenient one — Lance can distribute the near-final pre-print version on his own web page. That’s good but not good enough.

Kamal and Panos also have some refreshing ideas on this subject. Platforms like Yoav Freund’s machine learning forum represent a natural and intelligent evolution of peer review.