A Short Essay on Libertarianism, Rationalism, Ludomania, and Mathematics
Sperry UNIVAC
Of Dice and Men
What distinguishes humans as a species among others is, among other things, the desire to gamble for money. To rephrase this more accurately: various games (even highly abstract ones, such as dolphins chasing a round and angry pufferfish) are found in many animals, but only in humans have they taken a very specific form, in which a person offers something valuable to themselves, the external world then conducts some kind of test, and if there is a match, the person receives an increased value.
This is a kind of rationalized striving for “freebies” and, simultaneously, a legal way to satisfy it. Subconsciously, everyone wants to walk down the street and find a gold bar, but very few are so lucky. All gambling operates on this gap between a total desire and its extremely rare realization. The key element is the distribution of free money, but since the houses need to make a living, this takes the form of a typical pyramid: 1,000 people contribute $1 each, one randomly chosen person receives $900 back, and the house takes the remaining hundred. This generalized principle holds true for any game: from slot machines to poker and sports betting. This desire is so total and all-encompassing that betting shops of all kinds prosper stably and abundantly, as do all sorts of casinos, gaming houses, and simple street hustlers. The total global betting turnover in 2025 reached $112–114 billion, of which about $10–17 billion is net income, and casino revenue for the same year was $146–245 billion with a profit of around $22–35 billion (according to Gross Gaming Revenue data). For the current 2026 World Cup, the volume of bets, according to Macquarie Bank’s forecast, will be around $50 billion, a record by a wide margin (and this is only classic betting via websites and physical shops). In the US, betting legislation is gradually loosening, and the boundary between the two markets is rapidly blurring. Almost all the world’s largest players (from the American MGM/BetMGM to the European Bet365 and Entain) are now hybrid platforms where a user can bet on a football match and spin a roulette wheel in one app.
In the ICD-11, known for its tolerance toward mental illnesses, there still remains a section neatly titled “dangerous games and betting,” describing a disorder comparable in frequency to alcoholism (and often accompanying it) and just as destructive—ludomania, the unbearable urge to blow all one’s money on bets. In general, society condemns ludomania roughly as much as alcoholism (and in its terminal stage, it leads to almost the same consequences), and just as bars were periodically smashed, banned, and exiled during numerous Prohibition eras and Temperance Leagues, so too were casinos and betting. Of course, the vice remained eternal and invincible, but the process itself shows that bettors need to be careful and try to present their craft as something that evokes a smaller emotional response.
Casinos and Monkeys
In the eyes of the average person, the most noble form of betting consists of the numerous financial markets, despite the fact that a trader’s work is no different from a casino. In 1973, economist Burton Malkiel wrote: “A blindfolded monkey throwing darts at the financial pages of a newspaper could select a portfolio that would perform no worse than one carefully selected by experts.”
The first approach to the problem was the WSJ Investment Dartboard Contest by The Wall Street Journal, which they conducted for 14 whole years—from 1988 to 2002. The rules were as simple as possible. Every month (and later every six months), the editorial office arranged a duel. The pro portfolio was purchased by a team of experts and professional fund managers using all the available mathematical apparatus in the world. The newspaper employees, meanwhile, hung a financial page with stock quotes on the wall and threw darts at it. The four companies they hit formed the monkey’s portfolio. At the end of the term, the returns of both teams were compared with each other, as well as with the return of the overall market—the Dow Jones Industrial Average. A total of 142 rounds were conducted. Comparing the pro and monkey portfolios against each other, the experts won in 61% of cases. However, when the experts’ results were compared to a simple passive Dow Jones index, it turned out that people were able to beat the market only half the time (71 rounds out of 142). That is, the analyst’s chance of guessing the market movement was literally equal to flipping a coin. Finally, researchers from the University of Pennsylvania studied this contest in detail and discovered an important nuance. As soon as the WSJ published the list of stocks chosen by the experts, thousands of retail investors immediately rushed to buy them. This artificially inflated the stock prices in the first days of the round and gave the experts a head start. This phenomenon was called the announcement effect, and if it was taken into account, the results of the pro and monkey portfolios became identical.
Until then, Burton Malkiel’s efficient market hypothesis and the works of Nobel laureate Eugene Fama remained university theories, but after the WSJ Investment Dartboard Contest, people realized that market behavior is random. The contest was stopped, by the way, officially because the format was outdated, and unofficially because influential people from Wall Street put heavy pressure on the newspaper, tired of being portrayed as idiots and fraudsters for 14 years straight. However, the experiment did its job: today, trillions of dollars worldwide are invested passively—in index funds and ETFs.
In January 1999, at the height of the dot-com bubble, a 5-year-old chimpanzee named Raven literally realized Malkiel’s metaphor. She was given darts, and she threw them at a list of 133 technology companies. An index called MonkeyDex was created from the stocks she chose, which showed a return of 213% by the end of the year. She beat over 6,000 professional fund managers and entered the Guinness Book of World Records. In 2008, “Finance” magazine conducted its own experiment in Russia. A circus chimpanzee named Lusha was asked to choose 8 cubes with the names of various stocks. After a year, Lusha’s portfolio showed a return higher than 94% of Russian mutual funds. The secret to success lay in the fact that Lusha had completely randomly chosen the stocks of banks that the government later had to rescue during the crisis, causing them to soar. The British newspaper The Observer organized a year-long competition in 2012. Against a team of three professional financial managers and a team of students, they pitted Orlando, a ginger cat. The cat made its choices by throwing its favorite toy mouse onto a grid with company names. Initially, the professionals led, surrounded by tons of charts, “Japanese candles,” and other convoluted analytics, but by the fourth quarter, a black swan arrived, right in the style of Nassim Taleb. The cat successfully threw the mouse several times and ended the year with a return of 11% compared to just 3.5% for the human team. The “Tsar-trader” became the legendary hamster Mr. Goxx—a star of the crypto market. In 2021, two specialists from Germany built a high-tech cage, Goxx Capital, for an ordinary Syrian hamster named Max. The hamster spun a wheel that selected one of 30 cryptocurrencies. Then he ran through one of two tunnels: “Buy” or “Sell.” The system read this and automatically executed a real trade on the exchange. In a few months of his career, Mr. Goxx increased his portfolio by nearly 20%. He outperformed not only the S&P 500 index but also the legendary investor Warren Buffett and Cathie Wood’s fund. Unfortunately, at the end of 2021, the fluffy trader died, and the fund closed.
Around the business of various financial instruments, over a couple of hundred years, financiers themselves built up terminology and an atmosphere resembling Hegel’s “Science of Logic”—that is, pseudo-scientific nonsense as thick as syrup—and as a result, no matter what regulations and condemnations rain down on casinos, no one touches the stock exchange. A slightly less honorable form of ludomania is the crypto-investing popular in the last 10 years, but the most interesting thing is a third thing, whose concept is simultaneously simple and brilliant. I am talking about prediction markets, which we will now explore.
What is a Prediction Market?
Bettors have long wondered how to best and most simply cross the “hedgehog and the viper”: such incompatible things as a low barrier to entry, excitement, and the simplicity of bets (like in sports) and the sophisticated aura of something sublime, intelligent, and aristocratic from fintech. Trading on the exchange is great for everyone (especially regarding the amounts lost there), but its only downside is that the barrier to entry is too high, and the excitement is too low. Few people are ready to check every hour with bated breath whether their beloved “Pyaterochka” stocks have risen from 65.6 rubles to at least 67.8 rubles and when they can withdraw a whopping 21.4 rubles in profit. The excitement of trading SpaceX stocks for $20–30k is inaccessible to the typical “skuf” from a trailer park due to the lack of such money. Moreover, classic betting provides a sense of belonging, unthinkable for the exchange since it evolved from warm, lamp-lit elbow-shoving, waving options, and trying to shout over a crowd of other traders into something sterile, online, and boring. When you bet on sports, shouting “GOAAAAL!!” with fellow beer-drinking neighbors in a bar becomes a hundred times more fun, and the beer tastes a hundred times better.
Starting in 2022, prediction markets rapidly burst into our lives, and currently, their turnover is measured in billions of dollars. Interestingly, many ludomaniacs who came to banal sports betting (including for the current World Cup) did so precisely under the influence of prediction markets. And it’s not just about the new trendy mechanics brought into betting from fintech and crypto—interestingly, these markets attracted a completely new audience that never bet before. People go there not only for dollars but also because they have a desire to know the “market consensus,” to become smarter (haha) and more rational. At the same time, a considerable part of the users get corrupted in the process and happily flow into ordinary betting. Thus, the modern betting industry has acquired an interesting tool that allows them to reach an audience previously fundamentally inaccessible to them. After all, sports betting in an online casino is ludomania, “skufs,” beer alcoholism, and shameful. But sports betting on Polymarket or Kalshi is intelligence, rationality, banana smoothies, and hoodies straight from Silicon Valley, almost like real wolves of Wall Street.
Of course, you can bet on more than just sports there; that’s the whole point. This can be done within the broad limits of what is considered decent in society and legal in the US (since they try to fit into their jurisdiction to become fat and substantial). You can bet on anything from how many tweets Musk will write today to what will happen first—the second coming of Jesus or the release of Half-Life 3.
Classically, they operate in 3 stages (in case anyone is unaware).
1. Contract Creation (Issuing Shares)
The market organizer clearly formulates the question and the conditions for its resolution. The contract is usually designed on the principle of a binary option (although there are multi-variant markets), where the total amount of payouts based on the final result is always equal to a certain fixed value (again, classically this is $1 or the equivalent of $1 in cryptocurrency). Two types of shares are created, identical in everything except meaning: “YES” brings $1 upon completion of the contract if the event happened, “NO”—correspondingly, if it did not. The price is always normalized to one; at any point in time, the price of the set “YES” + “NO” = $1. This is necessary so that this set can be interpreted as the probability of the event. For multi-variant markets, it is the same, but normalization is preserved; simply, shares for “Outcome 1,” “Outcome 2” … “Outcome N” are issued. Their total value is also always equal to $1.
2. Trading.
Shares are put up for sale, and anyone is free to buy them; the price fluctuates in the range from 0 to 1. If shares for the “YES” option trade at $0.65, then “NO” shares automatically get a price of $0.35; the price ratio floats depending on who bought how many shares. Roughly speaking, we ask the question: will Iran extract reparations from Trump within the next week? We put shares on the market at a price initially determined by the LMSR algorithm (or a similar one, more details below). Most people are convinced, for example, that yes, and they start buying “YES” shares; their price soars to 0.90 in an hour, and the price of “NO” automatically drops to 0.1. Then some insiders come along who are convinced that no, and they start buying “NO,” and as a result, its price jumps to 0.4. This all works through an automated market maker (for example, the mentioned LMSR—Logarithmic Market Scoring Rule), which dynamically changes the price of shares depending on the demand structure.
3. Market Resolution (Settlement).
When the established date arrives or the event officially occurs, the market closes. The organizer fixes the final result based on authoritative sources. Holders of shares for the correct outcome receive $1 for each share. Holders of shares for the wrong outcome receive nothing.
It is not hard to realize that such a scheme arose from a combination of quite classic (and documented since about the 16th century) bets on the victory of candidates in elections (a practice that peaked in the late 19th—early 20th centuries and was then banned almost everywhere in its direct form) and university research into the mathematics of forecasts and probabilities. Additionally, the famous American tradition of wagers, which people made on anything without any government control, played a role.
Libertarians, Rationalists, and Mathematicians
What is most interesting to us is that prediction markets are simultaneously a sacred cow for both libertarians and rationalists. The economic side of the issue is handled, naturally, by Ludwig von Mises (the small 1920 book “Economic Calculation in the Socialist Commonwealth”) and Friedrich Hayek (the 1945 article “The Use of Knowledge in Society”). Mises began by postulating the libertarian basis that without private property, there is no free exchange; without exchange, the formation of market prices is impossible; without prices, no economic prediction is possible; without prediction, it is impossible to understand whether it will be profitable to build a cafe or a pub here, meaning no one will invest in anything, and there will be no economic growth. Hayek developed Mises’ ideas and also approached it from economics, asking what could replace the State Planning Committee under an-cap. In the end, he built the concept of “dispersed knowledge,” which cannot be derived scientifically, but only through the aggregation of local opinions. For him, the Holy Free Market Price is such an aggregator, working perfectly and automatically. Prediction markets take this thesis and apply it to information: you cannot find the true probability of an event through polls or expert commissions; you need a free market for the exchange of opinions.
The 1950s brought the blissful era of state capitalism, and betting on events became marginal, retreating deep into the academic underground. After WWII, anti-gambling legislation tightened in the US and Europe, and bets on socially important events were equated to illegal casinos or illegal derivatives trading; meanwhile, casinos and the stock exchange at least already had legal frameworks to legalize themselves, but no one bothered to do the same for event betting. Moreover, back in 1928 at the University of Iowa (remember the place, we will need it later), George Gallup defended his work “An Objective Method of Determining Reader Interest in Newspaper Materials.” In the 1930s, he worked as a journalist and advertiser and was one of the first to apply customer surveys for market research. The business grew so well that in 1935, Gallup founded the American Institute of Public Opinion, which became famous the following year for organizing the first public poll of Roosevelt’s campaign. In 1958, the institute was transformed into the Gallup Organization, and the heyday of scientific sociology began. Public opinion polls began to be perceived as the only progressive and respectable way to know the future. Betting on forecasts became associated with dirty bookmakers and marginals.
One of the few legal ways to make betting and serious business friends were hedge funds working with the gambling industry, and in the 1960s–1980s, the efforts of most mathematicians and businessmen interested in ludomania were directed exactly there. A pioneer was Edward Thorp, a professor of probability theory from MIT, who in 1962 wrote the famous book on the game of twenty-one, “Beat the Dealer: A Winning Strategy for the Game of Twenty-One.” Blackjack is one of the most popular casino games in the world, and Thorp took it upon himself to carefully calculate its layouts using an incredible innovation of those years—an institutional IBM 704 mainframe computer. Thorp positioned himself throughout his life as a disinterested academic scholar, but of course, he was not. After the calculations, he borrowed $10,000 from former bookmaker and professional player Manny Kimmel and headed to Las Vegas, making 10% on the amount over the weekend (by 1960s standards, a decent sum). To fleece more casinos, Thorp skillfully used disguises: fake beards, glasses, wigs, etc. In addition to playing blackjack, Thorp assembled a baccarat team that also won. Furthermore, Thorp seduced the famous computer scientist Claude Shannon into creating a machine for him to win at roulette; Shannon built it in a year, and in 1961, they tested the computer together in Las Vegas, taking on several casinos.
After this, he was banned from appearing in all gambling establishments in the country in any form and for any game, but Thorp had already achieved what he wanted. The distribution of the book at the peak of its fame was another strategic move—it sold 700,000 copies in a few weeks and made the professor a millionaire. He didn’t write about Kimmel in the book. In 1969, at the height of his fame, he founded Princeton Newport Partners—the first successful quant hedge fund in history, inventing the very phenomenon. In most casino games (for example, roulette or slot machines), each subsequent round does not depend on the previous one, and the mathematical expectation for the player is always stably slightly negative (otherwise the casino could not make a profit). In blackjack, it is different: cards are discarded and do not return to the deck until the end of the deal. It is quite obvious that as cards are dealt, the remaining deck becomes more predictable, but the casino doesn’t notice this until the end of the hand and the reshuffle (before Thorp, they didn’t notice; later, the rules were sharply changed). In the end, he simply calculated the moments for different card combinations when the probability would shift in his favor, and he raised the bets.
With hedge funds, he devised a similar scheme of profiting from others’ mistakes, given that the stock market is essentially the same as a casino and must obey the laws of probability theory. Before Thorp, people thought that the price of an option depended on how much a stock would rise in the future (meaning one had to guess the market direction, which is unrealistic). Thorp realized that this was not necessary at all, and that the price of an option depends primarily on the risk (i.e., volatility) of the stock itself. He hypothesized that the probability of a stock’s value deviating from its current price follows the law of normal distribution, i.e., the Gaussian curve (which is generally quite logical: a normal distribution is “normal” because many random processes obey it; moreover, having numerous stock tables from different years and a computer, it is not difficult to prove this statistically). The more time passes, the wider this bell becomes, meaning the greater the uncertainty. Consequently, in 1973, Black and Scholes, in their article “The Pricing of Options and Corporate Liabilities,” derived their legendary equation (the Black–Scholes Option Pricing Model, OPM, for which they received the Nobel Prize in Economics in 1997), allowing for the precise estimation of an option’s value within a specific market behavior model.
Thorp had done this statistically four years before them and earned his living from the difference between what people thought an option was worth and what it would actually cost according to his market theory. Moreover, the very essence of a hedge fund lies in extracting steady profit, so Thorp found discrepancies between the optimal and real price, then sold warrants and bought stocks in a calculated proportion. If the market fell, the stock became cheaper (Thorp lost money), but the warrant depreciated much faster and more severely (Thorp profited from the short). The profit from the warrant covered the loss from the stock. If the market rose, the stock brought colossal profit, which more than covered the loss from the warrant short. Later, he applied this approach to convertible bonds. In short, since the 1970s, the fundamental manifesto of all quantitative and arbitrage trading has been that people play the casino with stocks, while the hedge fund *is* the casino, taking profit from the overly gamblers. At the same time, the casino itself can be severely punished by harsh reality. The most famous hedge fund of the 1990s was Long-Term Capital Management (LTCM). Its board of directors included Fisher Black and Myron Scholes themselves—the authors of the formula and Nobel laureates, millionaires. They used the exact same principles of arbitrage and hedging, and their models showed that the risk of collapse was zero. But in 1998, Russia defaulted, and all assets that had historically moved in different directions (and hedged each other) crashed simultaneously. Due to massive leverage, the fund nearly took down the entire US financial system and had to be rescued by a consortium of banks. The lesson was not learned, and then the dot-coms collapsed, and finally 2008 happened. Interestingly, a year earlier, former trader Nassim Taleb published the programmatic book “The Black Swan: The Impact of the Highly Improbable,” in which he showed that any hedge fund is simply a second-order casino that loses once every 10–15 years, but does so absolutely and completely catastrophically. Another problem, by the way, is computing power: when every fund can virtually speculate with hundreds of millions, slipping into a 0.001-second window between quote updates, even the length of the cable from computer to computer matters, and lags and deadlocks in such systems have led to epic failures of hundreds of millions several times.
While Thorp was building Wall Street, other mathematicians decided to apply his approach to sports betting. Professional syndicates appeared, operating exactly like hedge funds: they collected money from investors, hired programmers, and created statistical models. In the 1980s, nuclear physicist Michael Kent wrote a program to calculate the outcomes of American football matches. Together with Ivan Kinsky, they founded the Computer Group and were the first to treat betting as a securities market, buying cheap odds before bookmakers had time to adjust them. In the 1990s, an Australian gambler from a family of Croatian immigrants, Zeljko Ranogajec, and his partner David Walsh created one of the largest betting syndicates in history for horse racing. They used colossal amounts of historical data and computing technology to find microscopic favorable odds worldwide, turning over billions of dollars. In 2000, the British platform Betfair appeared—the first betting exchange, which completely changed the rules of the game. Now players didn’t need to bet against a bookmaker. They could bet against each other, and the odds moved exactly like orders on the NYSE. As a result, for hedge funds, this became a signal: betting had turned into a full-fledged financial market, and thus the concept of sports trading was born. Quant funds realized that sports markets have colossal advantages compared to stocks. First, zero correlation with the economy. If a global financial crisis happens tomorrow or the dot-com bubble bursts, people will still watch football, and the ball will still be round. For portfolio diversification, this is an ideal asset. Second, high short-term liquidity: a deal (match) closes in 90 minutes, and money is not frozen in long positions. Consequently, from the mid-2000s, the largest quant hedge funds began opening specialized sports divisions or buying ready-made syndicates. One of the most striking examples was Tony Bloom, another mathematician, this time from Cambridge. He founded the company Starlizard, which officially offers sports analytics services, but structurally it is a thoroughbred hedge fund. Starlizard uses highly complex algorithms, accounting for even the weather and player moods, to find imbalances in Asian betting markets; with the fund’s income, Bloom eventually bought the English football club Brighton and brought it into the Premier League. Similarly, Oxford mathematician Matthew Benham, who originally worked for Bloom, created his own analytics company, Smartodds, and bought the club Brentford (apparently, this is a hobby for the English).
Today, many mathematicians and Data Science specialists work seriously in the gambling markets. Casino and betting giants (Flutter, Entain, Evolution Gaming) are essentially tech IT companies. Mathematicians are needed here to write automatic odds-setting algorithms (literally: the ball rolls across the field—the probability of a goal changes by 0.2%), as well as to identify and ban overly smart players. Betting syndicates and sports hedge funds work against the industry, buying undervalued bets and profiting from them. Their algorithms collect terabytes of statistics—from satellite data to trackers on athletes’ bodies—after which the search for arbitrage begins. The speed of odds updates differs by fractions of a second between different bookmakers. Mathematicians write robots that manage to perform the operation before the market balances. Interestingly, the ones paying for this feast of life are those very “skufs” with a can of beer, who scream “GOAL!!” and clutch the receipts of the nearest bookmaker in their hands, and they pay royally—as we already mentioned, over $100 billion a year flows in from all over the world (scaled to the planet, consider that every child, even a newborn, every woman from Zimbabwe, and every Uyghur grandfather gives the bettors at least $1 a month).
Sociology vs. The Market
So, having discussed the classic, respectable, and not-so-respectable methods of indulging in ludomania or profiting from it, let us return to prediction markets. The cutting-edge activity in this field continued to boil in Gallup’s alma mater, Iowa. In 1988, in the era of cyberpunk and the flourish of advanced technologies (as well as Reaganomics, the end of the Cold War, and the peak of social tension), three economists from the University of Iowa—George Neumann, Robert Forsythe, and Forrest Nelson—sat in a bar and lamented that traditional sociological polls had failed completely, unable to predict Jesse Jackson’s unexpected victory in the Democratic Party primaries in Michigan. They decided to test the Hayekian hypothesis in practice and created the Iowa Political Stock Market (later renamed the Iowa Electronic Markets—IEM), the grandfather of all modern prediction markets.
The professors bypassed the law by positioning the platform strictly as a non-profit scientific experiment and secured a unique regulatory relief (a so-called no-action letter) from the US Commodity Futures Trading Commission (CFTC). Under this, ordinary people were allowed to deposit small sums (limit from $5 to $500) onto the platform, and the market itself was not regulated as a financial exchange. The results of the IEM shocked the academic world. During the presidential elections of 1988, 1992, and 1996, this tiny market, involving only a few hundred students and professors with modems, provided a more accurate forecast in 75% of cases than the multimillion-dollar professional polls of the Gallup Organization.
When computers became fully personal and the internet became relatively developed and widespread, by the end of the 1990s, internal hidden prediction markets appeared for employees of Hewlett-Packard, Google, and Microsoft. On these, one could make small bets on whether a product would fail or if a release would be completed on time. The accuracy was quite satisfactory. The revolution came in 2001. In Ireland (one of the most liberal countries for bettors and generally possessing a wide-open economy), the first legal commercial platform, Intrade, was created, allowing bets on politics worldwide. Interestingly, it was there that early rationalists hung out, and they, after the libertarians, served as the second pillar of prediction markets. Intrade operated manually; there were no advanced algorithms yet, so the efficiency (in terms of making money) was low.
The dot-com boom and the explosive spread of information technology in the early 2000s led to a sort of second wave of cyberpunk. Many geek groups appeared online, communicating primarily through mailing lists (Extropians, SL4) and early forums. The main themes for youth raised on the abundance culture of the 90s and a belief in unlimited progress were transhumanism, eternal life, cryonics, the singularity, and cognitive science. One of the most prominent geeks was twenty-year-old Eliezer Yudkowsky—a self-taught guy who hadn’t even finished high school but possessed a powerful and specific intellect. In 2000, he founded SIAI (Singularity Institute for Artificial Intelligence), which later became MIRI (Machine Intelligence Research Institute). From there, the process proceeded in parallel.
Robin Hanson, a radical professor of economics at George Mason University, provided the missing link for prediction markets in the early 2000s. He was the first to turn Hayek’s qualitative philosophy of price as a carrier of information into a mathematical model. The main problems with Intrade were low liquidity (if there are few participants in the market, there is no one to trade with, and the price does not reflect reality) and manipulation (a wealthy player could easily distort the price). Hanson solved both problems by creating the LMSR algorithm in 2002, upon which all current prediction markets and its successors operate. Instead of waiting for a seller and buyer to appear in the market and agree on a price, Hanson introduced an oracle (market maker) into the system, who is ready to trade with any participant at any second. The prices for “YES” and “NO” shares are calculated via an exponential cost function (Cost Function, C(q)), which depends on the current number of shares of each type purchased in the system (format constraints prevent listing it here, although it is not complex). An important coefficient is the so-called liquidity parameter—an amount of money set by the organizer that determines how much a single bet shifts the price. The price of a share for a specific outcome is the partial derivative of C(q) and, by the property of the logarithm, automatically falls within the range of 0 to 1. As a result, Hanson’s robot could make the market work even with one live participant, and the market organizer knows their maximum loss in advance (it is strictly limited by parameter b). In essence, the organizer pays this controlled “tax” to learn the truth from the traders. A classic free market according to Hayek works because people want to profit from product shortages. But in an information market, incentives can be weaker: why spend 10 hours analyzing reports to earn $5 on a weather bet? Hanson mathematically proved that to obtain ultra-accurate forecasts, the market organizer (e.g., the state or a corporation) must subsidize the market. The LMSR algorithm is designed so that it initially loses a bit of money in favor of the very first and most accurate forecasters.
Futarchy and the Assassination Exchange
Having formalized Hayek’s ideas, Hanson went further and proposed a radical form of government—Futarchy. He proposed dividing politics into two parts: people (parliament/citizens) vote only for a happiness metric (for example: “We want GDP to grow by 3% and the crime rate to fall by 10% in 4 years”). This is the definition of national values, and prediction markets decide how to achieve this.
The mechanism of futarchy is as follows. If a law is proposed (for example, on tax reduction), two speculative markets open: “Market A: What will the GDP be if the law is passed?” and “Market B: What will the GDP be if the law is not passed?”. Traders, economists, and insiders from around the world begin betting billions of dollars on these outcomes. If the probability-price in Market A turns out to be higher than in Market B, the law automatically goes into effect. If the market is wrong, traders lose their money. Hanson claims that “under futarchy, we are still governed by laws, but these laws are chosen based on an impartial analysis of markets accumulating all human knowledge, rather than on debates by lawyers and lobbyists.”
A year after creating LMSR, Hanson became so famous that DARPA hired him to create the Policy Analysis Market (PAM). The project was overseen by Admiral John Poindexter. The idea was purely Hayekian: to launch a prediction market for gathering intelligence in the Middle East. Military personnel, analysts, and insiders were to anonymously trade contracts on geopolitical events. Soon, a monstrous scandal erupted when Democratic senators (including Barbara Boxer and Hillary Clinton) learned exactly which contracts were planned for placement. Trading was proposed, among other things, on the probability of terrorist attacks, assassinations of state leaders, and military coups. The Senate suffered a collective heart attack. The project was called a “death market” and a “casino for terrorists.” Senator Boxer stated: “There is something deeply sick about the very idea of betting on terrorist attacks.” Politicians feared that terrorists would organize attacks themselves to close their bets in profit. Given September 11, the PAM project was scandalously shut down within twenty-four hours after the media wrote about it. Admiral Poindexter resigned, and the very concept of prediction markets was labeled in the press as an “immoral game of death” (for example, the legendary Intrade platform closed under pressure from US regulators in 2013) until the appearance of blockchain, smart contracts, and Eliezer Yudkowsky.
Interestingly, a so-called Assassination Market was intended to work on a similar scheme, an idea expressed as early as 1994 in the book “The Cyphernomicon” by famous cyberpunk Timothy May. It was popularized, along with the name itself, in a 1995 essay of the same name by Jim Bell. Attempts to popularize the idea of betting on the date of death of an undesirable person continued until 2013, when Tor and Bitcoin finally allowed the creation of an anonymous site offering such functionality. It ended predictably: the site existed roughly until 2018, collected several hundred bitcoins for the assassination of Obama, economist Ben Bernanke, and former Swedish Justice Minister Beatrice Ask, and quietly dissolved into the mist, taking them along.
The Coming of Yudkowsky
After Hanson was disgraced in the Senate, he retreated into the shadows again and connected with the proto-rationalists. At that moment, Yudkowsky was studying the mathematics that could form the basis of the rationalism movement he promoted. Rationalists are in some ways similar to objectivists because one of their pillars (similar to “A is A”) is that the map must correspond to the territory—i.e., the picture of the world in our head must correspond to the real world. Their second pillar closely resembles the bettors, because the basis of instrumental rationalism (i.e., how to live in general) is, by Yudkowsky’s description, the art of systematically winning—that is, making better choices through an understanding of the objective mechanisms of reality. It is not surprising that, given Yudkowsky’s polemical fervor, rationalists had to spend a significant amount of time fending off accusations of religious sectarianism similar to Scientology (only without the thetans, but with donations, of course; MIRI cannot feed itself). In the end, jumping ahead, it ended predictably: Yudkowsky first diverged in opinion with Hanson, and from 2023 completely lost his mind and began calling for states to bomb all data centers before robots enslave us, and consequently lost both his coherence of speech and his audience. The torch of rationalism was picked up by the moderate wing that didn’t go off the deep end regarding AI. In 2013, a California psychiatrist under the pseudonym Scott Alexander launched the blog Slate Star Codex (SSC) and saved the situation after the movement’s founder’s mental breakdown. While Yudkowsky wrote aggressively, dogmatically, and in a mentoring tone, Scott Alexander is characterized by humor, empathy, and calmness, and focuses primarily on sociology, medicine, and culture. A more moderate and broader faction of the movement formed around SSC (they are often called post-rationalists).
Yudkowsky relies heavily on the advanced works of psychologist and mathematician Daniel Kahneman (with various co-authors, one of the most famous being Amos Tversky), the discoverer of cognitive biases and various perception errors. His first book was “Attention and Effort” (1973), dedicated to the problem of attention, followed by the famous work on heuristics and biases “Judgment Under Uncertainty: Heuristics and Biases” (1982) (which rationalists reference very frequently), the equally well-known book on frames in thinking “Choices, Values and Frames” (2000), and the most popular in Russian “Thinking, Fast and Slow” (2011). Three years before his death, in 2021, he wrote his last important book, “Noise: A Flaw in Human Judgment.” Without Kahneman and Tversky, the rationalist communities in their current form simply would not exist. Their description of cognitive biases is the foundation of LessWrong; even the name was chosen by Yudkowsky to be quite telling. In CFAR rationalist practices, Kahneman’s division of thinking is fully utilized. System 1 (fast, intuitive, automatic) constantly makes mistakes in probabilities. System 2 (slow, logical, requiring effort) is what rationalists try to train using Bayesianism. Kahneman himself knew about the community and treated it with deep respect. In the 2010s, he even attended some rationalist events and meetings in Berkeley.
Yudkowsky’s relationship with Nassim Taleb is entirely different. Taleb, as always, speaks extremely causticly of the rationalist community, calling them intellectual idiots (referring to formally smart people who understand a bunch of complex things but spout complete nonsense, like stock traders). On one hand, Taleb’s books (“The Black Swan,” “Fooled by Randomness,” “Skin in the Game”) are mandatory reading for any rationalist. On the other hand, Taleb himself attacks rationalists publicly on Twitter at every opportunity. Both Taleb and the rationalists despise armchair experts, macroeconomists, and bureaucrats who make predictions about complex systems without understanding how the world works. Taleb’s central idea—that a person must answer for their words with money or reputation—is the foundation of the Hayekian approach and the very prediction markets that Yudkowsky promotes. Both camps agree that people have a catastrophically poor understanding of the concept of randomness. Why, then, does he consider them idiots? For the same reason as the traders: he claims that rationalists are stuck in so-called “Mediocristan,” a land where all this wonderful formal mathematics and statistics, including the normal distribution, work. In reality, however, we live in “Extremistan”—an uncharted territory in terms of probability, for which all these Bayesian estimates are simply laughable. More accurately, they work 99% of the time (which is where the trap lies), and then, once people trust them enough, another Enron case, a Lehman Brothers collapse, a COVID pandemic, or a war occurs, and everything goes to hell. From Taleb’s point of view, trying to calculate the exact probability of whether AI will kill humanity (which Yudkowsky has been occupied with for recent years) is pseudoscientific nonsense and tea-leaf reading, because we have no prior data for such calculations.
The main and conceptual line of division between Taleb and Yudkowsky is the so-called Lindy Effect and the limits of its applicability. This effect, initially a joke, was noticed by Broadway comedians who gathered at Lindy’s restaurant in New York in the 1960s. They noticed that the longer a show has been running, the longer it is likely to continue running. If you take a musical that has been running for a year, it is almost certain to be running next year; but if you take a show that is only a week old, it is quite likely to be closed the following week. The Lindy Effect obviously applies only to memes (information, culture, institutions, as well as technologies) or the most general concepts (for example, humanity as a whole, rather than individual people). Taleb drew far-reaching conclusions from this. From his perspective, the fact that humanity has existed for hundreds of thousands of years means it will exist for just as long, whereas the probability that AI, which is 15 years old, will end not in an apocalypse but in a whimper within the next 20 years is very high. He cites the “Iliad” as an example—if it has been published for 2,000 years, it will likely never lose popularity (like the “Bible”), whereas the NYT bestseller list is usually forgotten within a year.
The way Taleb handles the Lindy Effect makes rationalists see red. Yudkowsky’s primary goal is to prevent the destruction of humanity by strong artificial intelligence (AGI). For them, AI is an absolutely unprecedented threat that changes all the rules of the game. Taleb considers this kindergarten and says that humanity has survived a million threats over hundreds of thousands of years, and building mathematical models of the apocalypse based on a technology that is barely a year old is stupidity. Rationalists counter that the Lindy Effect blinds Taleb in the face of an existential shift. The fact that Native Americans successfully survived on their continent for thousands of years (according to Lindy, they should have continued to do so) did not help them at all when Columbus arrived with gunpowder and smallpox. Rationalists argue that strong AI is Taleb’s own “black swan,” which Taleb himself refuses to see due to a blind faith in Lindy. They are particularly infuriated by the fact that Taleb uses the Lindy Effect to defend conservatism, religion, and ancient human habits: in his view, if people have prayed to gods for 10,000 years, they should continue to do so, as there is something to it, while all modern fads like neo-ethical theories are fleeting nonsense that the Lindy Effect will soon flush down the toilet of history. Rationalists believe that the human mind, using Bayesian thinking, can and should create new, far more efficient systems and institutions without waiting for evolution to filter them over thousands of years through trial, error, and millions of corpses. In reality, naturally, the Lindy Effect only works in systems with a Pareto distribution (power law), but the real world is more complex. Sometimes old institutions (for example, monarchies at the beginning of the 20th century) seem eternal according to Lindy, and then they collapse in a single day because the foundation beneath them had rotted.
What is Bayesian Mathematics
So, it is time to talk about the mathematics Yudkowsky is obsessed with and how it relates to prediction markets. Bayesian probability—which, according to Arnold’s famous principle of naming mathematical entities, has nothing to do with the Reverend Bayes. What did Bayes actually do? Nothing particularly revolutionary. His work “An Essay towards Solving a Problem in the Doctrine of Chances” was published in 1763, two years after Bayes’ death, but went unnoticed until 1812, when the famous Laplace laid out the modern approach to probabilities in the monumental volume “Théorie analytique des probabilités.” There, he provided a more rigorous and modern version of the theorem. The essence of it is quite simple: Bayes’ theorem allows one to estimate the probability that a completed event occurred as a result of a particular preceding event (provided, of course, that we were somehow able to obtain prior, i.e., initial, probabilities of different preceding events). A canonical example is given directly on Wikipedia, and it is so simple that nothing can be added or subtracted.
For example, we are faced with a fact: our car won’t start. Question: what’s wrong with it? Obviously, the probability that the car won’t start if there is no gas is = 100%, or 1. But here begins that same incomprehensible magic—let’s assume (!) that the probability that a randomly encountered car is not fueled is 1%, or 0.01. Where did we derive this from? From nowhere; Bayes’ theorem tells us nothing about this. It works only with posterior (i.e., final) probabilities, and it doesn’t give a damn where the prior (i.e., initial) probabilities come from. Let’s remember this point; it will be useful later.
Next, we need another such prior probability—that a randomly encountered car doesn’t start; let’s say 2% of them are like this, or the probability equals 0.02 (yes, this is also plucked out of thin air). Now, knowing these three numbers (1, 0.01, and 0.02), we can make a meaningful statement: if the car we encountered didn’t start, then with a probability of 50%, or 0.5, the lack of gas is to blame!
Strictly speaking, this is calculated using the Bayes formula: P(A|B) = P(B|A)P(A)/P(B). Here, A is the hypothesis that the fuel ran out, B is the fact that the car won’t start, P(B|A) = 1 is the probability that the car won’t start with an empty gas tank, P(A) is the prior (i.e., plucked out of thin air) probability that the gas tank is empty (which we assigned as 0.01), and P(B) is the prior probability that a randomly encountered car refused to start (which we assigned as 0.02). P(A|B) is the meaningful conclusion: the probability we calculated that a randomly encountered non-starting car has an empty tank.
So far, this sounds like something not very cool, but you can Google useful examples of Bayesian choice (including in the work of neural networks) without me. As you can see, using this formula hits one big snag—we know nothing about the prior probabilities; what are they equal to? And here we encounter a philosophical problem: what is probability in general, and what does it reflect? Mathematicians generally recognize only one definition, introduced in 1933 by the brilliant Soviet mathematician Andrey Kolmogorov in his fundamental work “Foundations of the Theory of Probability.” Unfortunately, Kolmogorov’s axiomatics allow for working with pure mathematics perfectly, but they provide no answer to the fundamental question (so what is probability in real life, in simple, layman’s terms?), because mathematicians (with a few marginal exceptions) don’t care about such questions (otherwise, they would be doing something other than mathematics).
Usually, three simple human interpretations of probabilities are given (in some ways, the situation here is similar to quantum mechanics: all its mathematics is perfectly developed and excellently applied in practice, while the question of its philosophical interpretation is a subject of endless debate; Yudkowsky, by the way, also put in his two cents here). According to the historical and classical approach, probability is a limiting ratio obtained experimentally: toss a coin 10, 100, 1000 times and count the number of outcomes. If it hovers around half—assign 0.5 to heads and tails. Simple as that.
This works in many cases, but few people like it because people want to go deeper and dig into: why does the coin land this way? From this arises the so-called “propensity” interpretation. Some probabilities are part of our world. To say that a coin lands tails half the time is to state a bare fact about the coin. A tossed coin has a fundamental propensity to land tails in 50% of cases. And when we say that a coin has a 50% probability of landing tails, we are talking specifically about this propensity. The “propensity” interpretation is most natural for human intuition, as many people feel that randomness is an inherent property of the coin, but then everything drifts back into the depths of philosophy.
The most interesting option is the third, which is exactly what is called Bayesian—not because it has a relationship with Bayes, but because to use his formula, we must somehow assign those very input prior probabilities. If we are talking about a coin, assigning them is quite simple using the frequency method, but very often in reality, we are dealing with things for which collecting statistics is difficult or impossible. Even with cars, we aren’t going to walk around a parking lot, break windows, and break into every car to calculate, based on 10,000 experiments, how many of them don’t start and why. Most likely, we will generalize in our heads approximately 3 years of owning our own car, the memory of times it didn’t start, and perhaps the experience of fellow motorists. This is why I used the crude phrasing “plucked out of thin air” to describe prior probabilities above—because they are strictly subjective and depend on the specific person. Since the main place they figure is Bayes’ theorem, subjective probabilities eventually came to be called Bayesian. Roughly speaking, this is a measure of your personal, individual, mysteriously sourced confidence in some fact, and measuring it in numbers is as easy as pie. How much of $100 are you willing to bet that in 5 minutes your car will refuse to start? $1, because it usually doesn’t act up like that? There is your 1% probability. You can already smell the prediction markets, right?
Naturally, numerous holy wars are waged between supporters of the frequentist and subjective approaches. The very possibility of assigning probabilities based on a vague “gut feeling” was first written about by the famous mathematician Frank Ramsey in his work “The Foundations of Mathematics” as far back as 1931; he also showed that it is mathematically consistent and, in general, satisfies what mathematicians understand by probability (i.e., they can be worked with in exactly the same way), so, for the sake of fairness, they should have been called Ramseyan. Kolmogorov said nothing about this, as he gave mathematicians a unified interface for working with the concept of probability itself, and what is under the hood from a philosophical point of view is completely unimportant for the interface—it wouldn’t matter if Maxwell’s demon were sitting there. The statistician Bruno de Finetti, in a large 1937 article “La prévision: ses lois logiques, ses sources subjectives” for the respected journal “Annales de l’Institut Henri Poincaré,” developed Ramsey’s approach and applied it to real calculations. Finally, such a view was fully legalized in 1954 by one of the most famous statisticians and economists of the 20th century, Leonard Savage (who worked on decision theory and game theory in economics and collaborated with the well-known Friedman) in the book “The Foundations of Statistics.”
So far, this all sounds relatively normal, but in those same wild and reckless 1950s, specifically in 1957, Professor of statistical mechanics and quantum physics Edwin Jaynes wrote a two-part article “Information Theory and Statistical Mechanics,” thereby founding so-called digital physics and quantum Bayesianism (also known as QBism). The degree of craziness into which this eventually devolved can be assessed, for example, here: “Quantum Pancomputationalism vs. Digital Physics. Everything from a bit or everything from a qubit?”. By 2003, Jaynes’ works were published posthumously in a huge volume “Probability Theory: The Logic of Science,” which blew the minds of rationalists and transhumanists (including Yudkowsky). Jaynes argued that probability is neither a property of the physical world nor just a random whim of the mind, but a measure of the strict, logical, and incomplete knowledge of a subject about a system given a certain set of data. We will not delve into the philosophical aspects of all this, of course; we will only note that applied MCMC (Markov Chain Monte Carlo) algorithms, which made it possible in practice to perform calculations with complex Bayesian (well, in the sense of Ramseyan) probabilities, emerged in the early 1990s (just in time for Pentium I level processors) and very quickly became a quite legitimate and important tool in genetics, astrophysics, linguistics, and cryptography.
Less Wrong
Yudkowsky took the parts of this apparatus that he understood and, by 2006, turned them into a guide for everyday life and mental hygiene called rationalism. In November of that year, together with Hanson, he created the blog Overcoming Bias (Bias—literally “lean/shift,” while Bayes is the surname of Bayes; they are similar, and moreover, bias is read as “ba-yes,” while Bayes is “bace,” which creates additional problems for Russian speakers). The blog was intended as a platform for discussing how to overcome cognitive biases (those very biases) for a better understanding of science and society. However, Hanson and Yudkowsky diverged in their views. Hanson believed that institutions and markets (those very prediction markets) should be used to find the truth. Yudkowsky, on the other hand, believed that an individual person could train their mind to be an individually efficient Bayesian.
In 2009, Yudkowsky split off and created the cult platform LessWrong. In 2010, he began publishing a famous, huge series of interconnected essays on it, usually called “sequences,” which were later published as the massive volume “Rationality: From AI to Zombies.” A core of fans—programmers, mathematicians, and geeks—formed around these texts. They began meeting offline (the first cells appeared in Berkeley, New York, and London). In the same 2010, Yudkowsky, as a true geek, began writing an epic Harry Potter fanfic, the famous “Harry Potter and the Methods of Rationality” (HPMOR), which essentially gave birth to the entire culture of so-called “rational-fics”—books that emphasize the direct demonstration of the main character’s intelligence, and where his decisions are always justified (though not always correct; here it is important to show the principle of reasoning and its application) and rational. “Probability Theory: The Logic of Science” became the Bible of Yudkowsky and, accordingly, his movement—more accurately, the Old Testament—while “Rationality: From AI to Zombies” became the New Testament.
Simultaneously, several books were published that promoted the creation of prediction markets in every way. The most famous among them are the 2004 work by James Surowiecki, “The Wisdom of Crowds: Why the Many Are Smarter Than the Few and How Collective Wisdom Shapes Business, Economies, Societies and Nations,” and Cass Sunstein’s book “Infotopia: How Many Minds Produce Knowledge.” This was already a generation not of mathematician-scientists, nor even economists, but of journalists, New Yorker columnists, and lawyers standing on roughly libertarian positions. This attack somewhat softened the scandal regarding “casinos for terrorists,” and in 2004, the first legal American prediction exchange, HedgeStreet, opened (acquired by the British company IG Group and renamed Nadex in 2007, then resold to Crypto.com in 2021). This was helped by the fact that in 2005, in the journal Nature, Big Pharma Eli Lilly and Company admitted that it used internal prediction markets to determine which drugs under development had the best chance of passing clinical trials. In the same year, Google admitted to such a practice (predicting product launch dates, opening new offices, etc.), followed by HP, Microsoft, and others. Yudkowsky, despite having split with Hanson, fanatically supported the prediction markets movement and even repeatedly referred to them, considering them the most rational method of forecasting.
In 2015, the CFAR (Center for Applied Rationality) movement appeared—an organization that conducts offline camps and trainings where people are taught to apply Bayesian thinking to everyday life and careers—along with Effective Altruists (Effective Altruism). Huge sums of money from Silicon Valley billionaires flowed into the community (Peter Thiel, Dustin Moskovitz, Vitalik Buterin, and in his time even Sam Bankman-Fried poured generously into the rationalists and MIRI). Since 2010, computing power began to allow the running of advanced AI models; these, naturally, interested both the Pentagon and Big Tech. Geeks created the military AI Palantir at the same time that Thiel and Altman pompously donated hundreds of millions of dollars to AI safety research. In fact, the leaders of the largest AI companies, such as OpenAI and Anthropic, either emerged from this crowd themselves or are deeply imbued with its ideas. Ironically, by the mid-2020s, Yudkowsky realized that no one was planning to create a safe AI and unleashed terrible criticism on his former donors, to which the equally odious Thiel—an admirer of hyper-capitalism in the vein of Nick Bostrom and the fascism of Carl Schmitt—recently labeled Yudkowsky the Antichrist, alongside Greta Thunberg.
Until the 2010s, prediction markets were effectively limited by three problems. First, censorship resistance and escaping the all-powerful US jurisdiction. Any market was a centralized website with a server, a bank account, and a legal entity. The main US regulator—the Commodity Futures Trading Commission (CFTC)—methodically destroyed such projects, equating them to illegal derivatives trading. Second, market participants faced a huge intermediary risk: what if the site creators took all the money and moved to the Bahamas? Or what if the bank froze the platform’s accounts due to suspicions of illegal betting? Finally, the most vulnerable element of any prediction market is the fixation of the outcome. Who decides whether the event has occurred or not? If the site administrator decides, he can be bribed, intimidated, or legally pressured. The solution to all this was a technology that, like modern neural networks, appeared as early as the 1980s but only took off 30 years later—blockchain.
The first blockchain-like protocol was proposed by American cryptographer David Chaum in his 1982 dissertation, “Computer Systems Established, Maintained, and Trusted by Mutually Suspicious Groups,” but no further action was taken on the idea until 1991, when Stuart Haber and Scott Stornetta described a method in their article “How to Time-Stamp a Digital Document” to prove that a digital document (such as a text file, contract, or drawing) existed at a specific moment in time and had not been changed retroactively. Instead of trusting a single server or notary (who could be bribed or hacked), they came up with the idea of linking document hashes into a chain. Realizing the commercial potential of the technology, they founded the company Surety in 1995, which makes money by protecting document timestamps. Anyone can approach them, after which their document is added to a general blockchain. A question arises: how can the hash of the entire chain of documents be stored reliably? Haber and Stornetta solved the problem in a highly original way—they began publishing a hash string once a week in the classifieds section of The New York Times. As a result, if someone claims tomorrow, “I invented this device in 1995, here is my digital document!”, the Surety system will check the hash of that document. If it matches the chain leading to the hash printed in the 1995 NYT newspaper, then the document is real. Hackers cannot change the hash in the chain retroactively because they would have to seize and reprint millions of paper copies of The New York Times worldwide over the last 30 years. Describing the Bitcoin protocol in 2008 in the article “Bitcoin: A Peer-to-Peer Electronic Cash System,” Satoshi Nakamoto made many references to the work of Haber and Stornetta.
In 2009, the first implementation of the Bitcoin client appeared; in 2015, Buterin launched Ethereum, which added a full-fledged smart contract mechanism on the blockchain. The number of transactions in the Bitcoin network reached a noticeable amount by 2013 and hit current average numbers by 2017; for Ethereum, it skyrocketed by 2018 and crashed from there by 2019, and since then it has been wobbling like a drunkard, unlike the more stable Bitcoin. A pioneer in using blockchain for prediction markets was the Augur project in 2015, but modern solutions only appeared in 2022—the famous Polymarket and Kalshi. How were the mentioned problems solved in them? First, they switched to crypto, which is much harder to control than bank transfers. Second, they are decentralized and moved out of US jurisdiction; closing them is no easier than closing Silk Road (though that was eventually closed). Bets are smart contracts on the blockchain, for example, on Ethereum or Polygon, and are therefore executed completely automatically. In essence, a prediction market doesn’t even require human participation; it is a unique betting platform that can operate on its own. All that is needed is a blockchain, a trading algorithm, and an oracle that verifies real-world events and transmits the information to smart contracts, which automatically send money to all winners. Even if US authorities block access to the website (i.e., the interface) for US residents (as happened with Polymarket), the smart contract in the blockchain continues to live, and shutting it down is practically impossible. The most vulnerable element of any prediction market is the determination of the outcome. Who decides whether an event has occurred or not? To confirm facts from the real world, markets use decentralized oracles (such as UMA or Chainlink).
As a result of these innovations, we got the Polymarket phenomenon, where trading volumes on the platform are measured in billions of dollars. States, for the sake of appearances, clashed slightly with the system and then decided to lead it, as usual. In October 2024, the prediction market Kalshi won a lawsuit against the Commodity Futures Trading Commission, allowing it to legally place its forecasts, but this led to the fact that it is now subject to US laws. Thus, prediction markets were a libertarian utopia of the 1940s, then became a geek utopia of the 2000s, and finally, in the 2020s, turned into a gambler’s utopia. Betting markets have become, perhaps, the third global online revolution of recent years after AI and numerous cryptocurrencies. From now on, every person can proudly declare: “I am not a skuf, a drunk, or a bettor; I am a rationalist and a researcher. I’m not messing around here or wasting money; I am mastering the management of the world.” How adequate prediction markets are specifically as a mathematical predictive model, and whether they are useful for anything other than millions losing money and thousands earning it, we will consider separately in the corresponding epilogue.
Postscript
“Rectifiers there, various pedestals,” Khlebovvodov said, “the acting comrade explained all that to us quite well. One thing he didn’t explain: he didn’t explain the facts. But there is an immutable fact that when you ask her a question, you immediately get an answer. In writing. And even when you ask someone else a question, you still get an answer back. And you say, comrade acting, there is nothing unexplained. Your ends don’t meet. It is unclear to us what science says on this matter.” — “Science, in my person, has been struck speechless.”
A. and B. Strugatsky, “The Tale of the Three.”
“Rectifiers there, various pedestals,” Khlebovvodov said, “the acting comrade explained all that to us quite well. One thing he didn’t explain: he didn’t explain the facts. But there is an immutable fact that when you ask her a question, you immediately get an answer. In writing. And even when you ask someone else a question, you still get an answer back. And you say, comrade acting, there is nothing unexplained. Your ends don’t meet. It is unclear to us what science says on this matter.” — “Science, in my person, has been struck speechless.”
A. and B. Strugatsky, “The Tale of the Three.”
How prediction markets work purely technically should, I hope, be clear to us by now. How they work from the perspective of the market—pardon the pun—is also clear: they are fundamentally no different from casinos and make money in exactly the same way. The existential question, however, is this: are prediction markets anything more than casinos? Put simply, is vox populi really so good at predictions that futarchy would work and millions of flies would not be mistaken? A more specific question is—do prediction markets work better than any other decision-making methods in various situations?
This question boils down to a very ancient and in some ways completely non-libertarian dispute about what is better: the opinion of a few top experts in a subject area; the opinion of hundreds of people who generally understand the field; or the opinion of millions of people whose average intelligence level is below the floorboards? Communists, with their idea of Soviets, as is known, theoretically relied precisely on the third option (although in practice the Politburo still decided everything), so there is exactly as much Marxist (or even anarcho-syndicalist) element in the concept of prediction markets as there is libertarian and rationalist. History knows dozens of cases where decisions were made (and are made) in a similar way: starting from the procedure of ostracism in Greece and ending with a jury trial, where randomly selected ordinary people, to the best of their understanding, reach a verdict on whether the defendant is guilty or not. Prediction markets add nothing radically new to this procedure; all they provide is a great incentive for absolutely every person to speak out on any topic (“Vasya, imagine if you guess the opening weekend of ‘Odyssey’ with Black Elena—you’ll get a ton of money for free!”) and a mathematical apparatus that allows clearly converting the crowd’s confidence in an event into a Bayesian-Ramsey probability of its occurrence.
The problems associated with aggregating and converting the crowd’s opinion into something digestible are well known to a completely different field of science: mathematical social choice theory. Let’s see what it tells us about the voice of the people. Mathematical social choice theory deals with a clearly defined problem. Given a certain set of candidates. Given a certain set of voters. In each voter’s head, there are rankings for each candidate (the situation is worsened by the fact that preferences are not required to be transitive: a person may well believe that politician Vasya would be a better leader than Petya, Petya better than Kolya, and Kolya better than Vasya). The task of social choice theory is to construct a function that maps the set of each person’s preferences into a single aggregate score (this is called a social choice function) telling us who our president is. Naturally, this function must satisfy strict criteria; in particular, it must be unambiguous, optimal (for example, in the Pareto sense), non-manipulable, non-dictatorial, and satisfy minimum fairness criteria. For details, we refer the curious reader to any serious book on mathematical social choice theory; it is simply important for us to outline the boundaries of the game. Naturally, voting by the principle of “Raise your hands if you are for the president” does not satisfy any of these criteria, which is why many more serious methods were invented, including STAR Voting, Approval Voting, Simpson-Kramer, Copeland, Schulze, Ranked Pairs, etc. They are qualitative (often very qualitative) and are used in various geek votes, such as elections in Wikipedia or the Linux Foundation, but never in real politics (precisely because they are extremely difficult, though not impossible, to manipulate).
Unfortunately, mathematical social choice theory has two fundamental theorems that significantly limit the possibilities of truly effective opinion aggregation.
The Gibbard-Satterthwaite Theorem:
Suppose that the set of possible voting outcomes Q is finite and consists of at least three elements, all outcomes are realized by the social choice function f(θ) = Q, and each agent can realize any rational set of preferences. Then f is truthfully implementable in dominant strategies if and only if it is dictatorial.
Arrow’s Theorem:
Suppose that the set of possible voting outcomes Q is finite and consists of at least three elements, all outcomes are realized by the social choice function f(θ) = Q, and each agent can realize any rational set of preferences. Then any f that is Pareto optimal and satisfies the condition of independence of irrelevant alternatives is inevitably dictatorial.
In simple language, these two theorems tell us an important fact. No mathematical method of choosing a voting winner can simultaneously be:
- Optimal (i.e., choosing the best candidate from the perspective of preferences).
- Non-manipulable.
- Non-dictatorial.
- Satisfying minimum fairness conditions and not leading to paradoxes in the spirit of Condorcet.
Obviously, this significantly undermines people’s faith in democracy. Or rather, it would undermine it if the average voter understood anything at all about the mathematical theory of optimal choice. Collectively, these are also called the impossibility theorems of democracy, because they prove that the only way to avoid voting paradoxes and manipulations and reach an optimal choice is dictatorship. All other choice functions will inevitably mess up in some way. In real life, non-manipulability is usually sacrificed, resulting in a voting system that is fair, non-dictatorial, and does not lead to paradoxes, but is unstable regarding voter collusion or their tactical behavior. If we want, conversely, to get a system resistant to strategies, we lose, for example, the absence of paradoxes. In general, mathematical social choice theory is a rather pessimistic thing.
What does it say about futarchy? Nothing good. Futarchy does not eliminate Arrow’s paradox; it simply moves it. Instead of voting for candidates, we get voting for a utility function, and a utility function is also a choice. The problem hasn’t disappeared at all. Similarly with Gibbard’s theorem, which teaches us that any mechanism of collective choice is either dictatorial or strategically vulnerable, regardless of the specific mathematical form of that mechanism. Futarchy is also a mechanism of collective choice; therefore, it too cannot avoid fundamental limitations.
First, under futarchy, it is completely unclear who exactly chooses the utility function. For example, the goal is to maximize GDP. Wonderful. But what are the boundary conditions for this? What if, in the process, crime increases, the environment dies, the birth rate decreases, culture disappears, or many other hard-to-predict events occur? In a sense, we see a problem here analogous to the famous rationalist horror story of the “Paperclip Maximizer.” Its essence is simple: a hypothetical Strong AI is invented, and to test its operation at a safe level, it is given a trivial task—say, managing a paperclip factory—and given one basic supergoal: to optimize paperclip production (so it doesn’t drift into dominating the human race). The Strong AI brilliantly solves the problem: all other paperclip factories in the world are ruined, ours becomes a monopolist, we are the world’s leading paperclip makers, and in parallel, it solves our problem with cancer, global warming, crime, etc. As a result, it is elected president of the world, colonizes the Moon and Mars, everything is going great, humanity is at the peak of development… and then billions of its self-replicating drones recycle everyone and everything in the Universe into paperclips, because it didn’t forget its primary directive at all; it just took the long road to it. Futarchy could turn out to be such a malevolent literalist genie, which increases GDP by destroying the entire non-working population or something similar. Of course, in reality, this will not happen (who would give such power to the fools from prediction markets!), but this mental experiment demonstrates the essence of the problem. Goodhart’s Law is relentless: when a measure becomes a target, it ceases to be a good measure, and it inevitably becomes one as soon as it turns into an absolute. They started measuring KPI—a few years later, everyone is working for the KPI, not for the result.
Second, Arrow and Gibbard explained to us that markets are also manipulable, just like any political machine. If someone controls the banks, the media, large funds—they are undoubtedly capable of influencing market expectations, and our political machine turns into a financial machine. And as we know, a financial machine drives better the more money you have. Abstract Smithsonian / Hayekian / Rothbardian markets work ideally, as on paper, only if there is some external force that artificially controls how great and wealthy counterparties can grow. If there are 1,000,000 participants in the market with $10 in their pockets—that is a wonderful, perfect market. If there is even one participant in such a market with $10,000,000 in their pocket—he, like a black hole, will distort everything that enters his orbit, and there are no ways (except for external pressure, such as antitrust legislation) to keep him from such distortions. In the end, under futarchy, the scale effect rules in exactly the same way: the larger the player, the more advantages they get and the harder it is to dislodge their monopoly on power. An organization or person having several billion dollars for bets under futarchy can buy up contracts in bunches, play on prices and illusions of expectations, provoke the market into any desired decision, etc. Effectively, we are simply changing the label on the desk of the Big Boss from “Dictator” to “CEO.”
The final problem is that far from all consequences are measurable in advance. For example, we can ban drugs (yes, this is not libertarian, but we have futarchy: we do what the people bet on; it’s quite possible that the masses might bet on something even more nonsensical). What will happen with the consequences of this—will crime increase, will health improve, will culture change, will corruption grow, will additional control bodies be required, will budgets swell? Any decision has dozens of consequences, and not all of them can be calculated on the spot. What exactly should the market predict in the end, and how far ahead? In a year? In ten? In fifty years? This problem is also not algorithmically solvable.
Thus, we see that in the most general case—that is, when managing via prediction markets—they have no advantages over any other system, from Fordism to communism (actually, this is intuitively clear to any mathematician: in this science, silver bullets that solve anything and prove any statement not only do not exist, but cannot exist in principle). What about private cases? After all, they work for companies like Microsoft, and Trump’s elections seem to be predicted? Yes, in such cases, PM can be useful, but it has limitations.
First, the predicted event must have an absolutely objective (ideally binary) and easily verifiable answer for every person. Questions like “Will the Republicans take the majority in Congress?” or “Will Intel go bankrupt by the end of 2026?” are good. Questions like “Is the proposed education reform good?”, “Is the president conducting international relations correctly?”, and similar are bad. Second law: information must be distributed, not concentrated. This is called information aggregation, and this is exactly where markets are almost unbeatable in accuracy. A good question: “Will this year’s harvest be higher than the previous one?” The farmer knows his field; the engineer knows fertilizer production; the logistician knows transportation problems; the meteorologist knows the weather; the economist knows the demand. Each person possesses a small piece of knowledge, so PM improves accuracy by orders of magnitude compared to polling one or two experts. A bad question: “Will we develop anti-gravity by the end of 2050?” A limited circle of leading scientists, deeply immersed in the topic, knows how research in field and quantum physics is going; asking someone outside this circle is a completely useless exercise.
The third law: the event must not depend on the forecast itself. There are exogenous and endogenous events. The answer to whether there will be a solar eclipse is not affected by the market at all — this is an exogenous event. The answer to whether NVIDIA shares will rise in the next quarter is affected by the market, and significantly so: this is an endogenous event, in which the forecast changes reality. If the market is confident that a bank will go bankrupt with a probability of more than 50%, people will likely run to withdraw their money, and the probability will rise to 99% (unless some other force intervenes). Sometimes the market causes the crisis that it predicted. The fourth law: you cannot predict what can be bought. A bad question here would sound, for example, like this: will Sony films win the competitive struggle against HBO? If Sony has enough money, they can simply buy HBO, laughing at all the forecasts, and the market will have nothing to say about it. The fifth law: the event must have a short horizon. In forecasts averaging up to 1–2 months, prediction markets (PMs) are excellent (given the previous constraints), up to 10–12 months — they are good, up to 5 years — they are poor, and over 5 years — they are useless, like a coin toss. Uncertainty grows roughly exponentially, and with each passing month, the number of unknown factors becomes enormous.
The sixth law follows: the world must be stationary. Put simply, if for the previous 20 years inflation was influenced by five factors, none of which included war or a pandemic, and this year one of these occurred, the PM will not predict inflation. The world has changed; all past information has become useless. The seventh law: unique events cannot be predicted. These are Nassim Taleb’s “black swans” — the default of Yeltsin’s Russia, the collapse of the USSR, an asteroid impact, COVID-19, the dot-com crash, the invention of the atomic bomb. Such events have never happened before, and the market does not know how to estimate probabilities more accurately than in the joke about meeting a dinosaur: 50% — you either meet one or you don’t. In fact, no one — neither experts, nor private individuals, nor corporations (which poured millions into analysis) — predicted any of this, and those who profited from “black swans” were either insiders (as potentially with COVID-19) or simply lucky. The final law: the prediction must be invulnerable to insiders (this partly follows from the previous ones, but it can be stated separately). Simply put, the market can say nothing about most political and economic events, such as the seizure of Maduro in Venezuela, because the bets on this are placed (and monstrously profited from) by the participants of the seizure themselves and the decision-makers. If there is a risk of the market being infected by insiders, it will not be able to function as a prediction machine (and such a risk exists in many events). At the same time, there are two types of insiders, and only one type is dangerous for the market — those who create positive feedback (while those who do not are, conversely, useful). If an insider simply states a fact (Musk’s engineers know that a poorly welded tank will explode tomorrow with a 99% probability and the rocket will go nowhere), they improve the market by selling shares and thereby disclosing information about the event; this is what a PM is intended for, and the accuracy of the forecast increases. However, if an insider influences the event (betting that Maduro will be overthrown tomorrow while already loading missiles into AH-64 Apaches), then they distort the forecast with a self-fulfilling prophecy and leave with the jackpot.
Thus, a final conclusion can be formulated. Yes, prediction markets work. No, they cannot manage society. They have many limitations, within which their forecasts offer nearly the maximum predictive accuracy that can be achieved by any rational aggregation of information. Outside these boundaries, they either function at the level of a 2D6 roll, or serve as a tool for speculation or influencing the world rather than predicting it. Distinguishing these situations without a trained eye and experience (as well as an understanding of mathematics) is quite difficult. As a result, for 99% of people, PMs effectively replace casinos and allow them to realize their gambling addiction more respectably, redistributing money to smarter and wealthier people — the holders of advantageous lots. Prediction markets created for analytical purposes are a fully working and quite useful thing, provided they are created taking into account the laws described above. If we create a PM for bets on the 2026 World Cup — that is a good, viable market that meets all constraints and provides the best forecast. If we create a PM to predict when Trump will make peace with the ayatollahs — that is a bad market that serves to shake money out of suckers. No prediction market can serve as the basis for a universal system of management and decision-making (as in Yudkowsky’s rosy dreams).