Prediction Market Mechanism Design: Why the LS-LMSR Is the Best Market Maker for Forecasting

A prediction market is a financial market designed to elicit and aggregate information from diverse participants to forecast future events. By allowing traders to buy and sell contracts tied to specific outcomes, these markets transform individual beliefs into quantifiable probability estimates, providing valuable forecasts for everything from election results to product launches to scientific discoveries.

The power of prediction markets lies in their ability to aggregate information from participants with varying levels of knowledge and often conflicting views. When someone believes the market's current probability estimate for an event is incorrect, they can profit by trading contracts to push the price—and thus the implied probability—toward what they believe to be the true likelihood. Through this process of price discovery, prediction markets can produce remarkably accurate forecasts, even for complex events where expert opinions diverge significantly.

However, creating effective prediction markets requires careful mechanism design—the engineering of market rules and incentives to ensure that traders are motivated to reveal their true beliefs rather than manipulate prices or withhold information. This article explores the evolution and technical foundations of prediction market mechanisms, from early parimutuel betting systems to modern automated market makers.

What prediction markets are for

The price of an event contract is the market's probability that the event happens. A contract that pays ₿100 if the event happens and trades at ₿50 gives the event a 50% chance. A full range of contracts, one for every possible outcome, gives the full probability distribution.

Event contracts can also hedge against undesirable outcomes. A Bitcoin holder who loses money if the price falls can buy contracts that pay if Bitcoin falls. If the price drops, the contracts pay out and offset the loss.

Forecasting and hedging each set a requirement for the market's mechanism. For the price to be an accurate forecast, traders must reveal what they believe as soon as they believe it. For the market to work as a hedge, traders must be able to buy or sell at any time, in any size, at a price known in advance. A mechanism that fails either requirement fails as a prediction market.

What is prediction market mechanism design?

Mechanism design is inverse game theory. Game theory takes the rules of a game and predicts how players behave; mechanism design takes the behavior a designer wants, here honest trading on private information, and derives the rules that produce it. A mechanism is incentive compatible when trading on one's true belief is the most profitable strategy, which makes the price an honest forecast. Otherwise traders gain by waiting, hiding information or bluffing, and the price inherits those distortions.

Five properties separate strong prediction market designs from weak ones:

• Incentive compatibility. Trading toward one's true belief earns the most.
• Continuous liquidity. A trader can always buy or sell at a quoted price.
• Bounded subsidy. The operator pays traders for information with a fixed amount it knows before the market opens.
• Path independence. A large order costs the same in one piece or in many, and a trader can exit by selling back.
• Liquidity sensitivity. Each trade moves the price less as more money enters the market.

Parimutuel markets

A parimutuel market pools every stake into one pot. After the outcome is known, the pot is split among the winning stakes in proportion to their size, net of a fee. If the pot holds T dollars, the winning outcome attracted M dollars and the fee rate is τ, each winning dollar returns (1 − τ) × T / M. Racetracks have paid out this way since the nineteenth century.

The operator of a parimutuel pool carries no event risk. Losing stakes fund the winners, so the house keeps its fee whatever happens.

The weakness of the parimutuel pool is timing. The payout depends on the final mix of stakes, so the odds a trader sees before the close are only an estimate. An informed trader who bets early reveals information that later bettors can use against them. The rational strategy is to wait until the last moment. A forecast drawn from a pool that fills in the final minute says little before that minute. Figure 1 shows a pool in which informed money arrives in the final ten minutes.

Parimutuel bettors also cannot exit. A stake stays in the pool until the outcome is known, so a hedger cannot lock in a gain or cut a loss as conditions change. Parimutuel prices also show a well-documented favorite-longshot bias. Unlikely outcomes tend to be overpriced, and likely outcomes tend to be underpriced.

The dynamic parimutuel market was designed to fix the timing problem [1]. Its share price rises as more people buy, so early buyers pay less, and shares can be resold before the outcome. The fix is partial. Game-theoretic analysis shows that a trader in a dynamic parimutuel market can still profit by withholding information when they expect other traders to receive better information later [2].

Limit order books and the continuous double auction

A limit order book is the mechanism behind every stock exchange. Traders post bids to buy and asks to sell, and a trade happens when a bid meets an ask. The gap between the best bid and the best ask is the spread. Economists call this matching process a continuous double auction. Most large prediction markets today run on order books. Figure 2 shows a thin order book for a Yes contract.

An order book is a zero-sum game between traders. Every dollar one trader wins, another trader loses. The no-trade theorem describes where that logic leads. When rational traders who share the same starting beliefs meet in a zero-sum market, they will not trade at all, however different their private information [3]. Any offer signals to the other side that the offering trader knows something, and that signal kills the trade.

Real order books escape the theorem only because some traders trade for reasons other than information. Even then, the order book does not reward honesty. A trader with exclusive information earns more by leaking it into the price slowly through many small orders than by revealing it all at once [3]. Posting a limit order also gives information away free to anyone who sees it. In a thin market, that cost brings little benefit, so informed traders stay away. Thin markets then stay thin, because traders avoid markets where other traders are scarce [4].

The problem multiplies for quantitative questions. A forecast of where Bitcoin will close needs a contract on every price range. A market with 500 price ranges would need 500 order books, each with its own buyers and sellers. Most of those books would sit empty, and an empty book gives neither a forecast nor a hedge. The largest order-book prediction market of the late 2000s, Intrade, drew millions of dollars on its popular contracts while thousands of its other contracts traded too thinly to reveal anything [5].

Market scoring rules: paying for honest forecasts

The alternative to the order book starts with the scoring rule. A scoring rule is a formula that grades a probability forecast once the outcome is known. A scoring rule is called proper when a forecaster maximizes their expected score by reporting exactly what they believe. The logarithmic scoring rule is the best-known proper rule. It pays b × ln(r), where r is the probability the forecaster gave to the outcome that actually happened. A forecaster who shades their report up or down lowers their own expected score.

A market scoring rule turns a proper scoring rule into a market [6]. The market opens with a forecast set by the operator. Any trader can replace the current forecast with their own at any time. When the outcome is known, each trader is paid the score of their forecast minus the score of the forecast they replaced.

The payments in a market scoring rule cancel in sequence. Each trader pays the score of the forecast before theirs and collects the score of their own. The operator ends up paying only the gap between the score of the final forecast and the score of the opening forecast. Under the logarithmic rule with n outcomes, that gap can never exceed b × ln(n). The operator therefore knows its largest possible loss before the market opens.

That bounded loss is a subsidy. It is the price the operator pays for information. The subsidy turns a zero-sum game into a positive-sum one, which gives every informed trader a reason to join. Even a single informed trader can profit by correcting the market, which is impossible in an order book with no one on the other side [3].

The LMSR as a cost function market maker

Writing out a full probability distribution is awkward for traders. A cost function market maker presents the same scoring rule as ordinary buying and selling. The market lists a contract on every outcome that pays $1 if that outcome happens. An automated market maker stands ready to buy or sell any of these contracts at any time. It tracks q, the number of contracts outstanding on each outcome, and a single cost function C(q) records the total traders have paid in.

The LMSR cost function for n outcomes is:

C(q) = b × ln( e^q₁/b + e^q₂/b + … + e^qₙ/b )

A trade that moves the market from state q to state q′ costs C(q′) − C(q). The price of outcome i is the slope of the cost function along q_i:

p_i = e^qᵢ/b ÷ ( e^q₁/b + e^q₂/b + … + e^qₙ/b )

LMSR prices are always positive and always sum to $1, so each price reads directly as a probability. Buying contracts on an outcome raises its price and lowers the others. Every purchase is mathematically the same act as replacing the old forecast with a new one under the logarithmic scoring rule [7].

The liquidity parameter b sets how far prices move per contract. Figure 3 shows the price of a Yes contract in a two-outcome LMSR market for three values of b.

A small b makes an LMSR market jumpy. With b = 50, buying 150 net contracts moves the price from 50% to 95%. A large b makes the market stiff. With b = 200, the same purchase moves the price only to 68%, and the operator's worst-case loss doubles.

The cost of any trade is the area under the price curve between the starting state and the ending state. Figure 4 shows a purchase of 150 Yes contracts in a market with b = 100.

Because the cost depends only on where the trade starts and ends, the order of trades does not matter. A trader pays the same $100.83 whether they buy the 150 contracts at once or one at a time. Selling the 150 contracts back returns the market to 50 cents and refunds the same amount. A hedger can therefore enter or exit a position at any time, at a price known in advance.

Why the LMSR beats parimutuel pools and order books

The LMSR passes the forecasting test that the parimutuel pool and the order book fail.

A trader who considers only their own next trade earns the most under the LMSR by moving the price exactly to their own belief. Buying past that point loses money on the extra contracts. Stopping short of it leaves expected profit on the table. This property comes straight from the logarithmic scoring rule and is called myopic incentive compatibility.

A forward-looking trader could in principle try to bluff. A bluffer pushes the price the wrong way to mislead others, then profits by correcting it later. Game-theoretic analysis of the LMSR shows that bluffing fails when traders' private signals are independent once the true outcome is known [3]. In that setting, trading immediately to one's true belief is the unique equilibrium. Bluffing does not pay, and waiting does not pay either. The guarantee depends on that independence condition. When traders' signals are only informative in combination, bluffing can return, and a version of the LMSR that discounts later trades still drives the price toward full information at an exponential rate [3].

The LMSR also solves the liquidity problem. The automated market maker quotes a price on every outcome at all times, so no trader ever waits for a counterparty. This holds for two outcomes and for two thousand. A 64-team tournament has about 9.2 quintillion possible brackets, and a market on every bracket would be unworkable without automated pricing [5].

A deeper result explains why the forecast improves over time. Cost function market makers are mathematically equivalent to no-regret learning algorithms from machine learning [7]. The LMSR's prices are the weights of the multiplicative-weights algorithm, a standard method for combining the predictions of many experts. The market maker's bounded loss translates into a no-regret guarantee. Over many rounds, the market's forecast performs nearly as well as the best single forecaster in hindsight.

The LMSR and its relatives have proven themselves in production. LMSR markets have run at Inkling Markets, Consensus Point, Yahoo!, Microsoft and the Gates Hillman Prediction Market at Carnegie Mellon University. WeatherBill, which sold custom weather insurance, and Bet365, the sports bookmaker, built proprietary automated market makers to quote instant prices across thousands or millions of customizable contracts [5].

Where the LMSR falls short

The LMSR's weakness is its single fixed parameter b. The operator must choose b before the market opens, before anyone knows how much interest the market will attract. Researchers who studied LMSR deployments described setting b as more art than science [5].

A b that is too small lets the first large trader push prices to extremes. The forecast then looks noisy, and a single wealthy trader can dominate it. A b that is too large freezes prices, so informed traders struggle to profit from what they know. A large b also raises the operator's worst-case loss of b × ln(n).

The deeper flaw of the LMSR is that its price response never changes. In an LMSR, the 1,000,001st dollar moves the price exactly as much as the first dollar [5]. A market that has absorbed trades from thousands of people is as easy to push as a market that opened a minute ago. A market that has absorbed more information should be harder to move, in the same way that the thousandth flip of a coin changes an estimate of its bias far less than the first flip.

The LMSR also loses money by design. Its prices always sum to exactly $1, so the market maker has no spread to earn. An LMSR operator expects to pay out part of b × ln(n) in every market. Most early LMSR deployments ran on play money for this reason [5].

The LS-LMSR: a market maker that deepens with volume

The liquidity-sensitive LMSR keeps the LMSR cost function and lets b grow with the market [5]:

b(q) = α × ( q₁ + q₂ + … + qₙ )

The constant α is small. As traders buy contracts, the total number outstanding rises, b rises with it, and each new trade moves the price less. Figure 5 shows the effect in a two-outcome market.

Figure 6 compares the two designs directly. It shows how far the price moves when a trader buys 100 contracts in an even two-outcome market of a given size.

The original LS-LMSR paper proves four properties of this design [5].

Prices respond to liquidity. A thin market stays responsive, so early traders can move the price cheaply with new information. A thick market becomes hard to push around, which protects a mature forecast from any single large trade.

The subsidy can be small. The operator's worst-case loss is the cost of the opening state, C(q⁰). As the opening liquidity shrinks toward zero, so does the worst-case loss. An operator can open a market with a small subsidy and let traders supply the depth.

The market maker can earn a spread. LS-LMSR prices sum to slightly more than $1, between 1 and 1 + α × n × ln(n). The excess acts as a spread. The spread is widest when the market knows little and narrows as the forecast sharpens. Setting α = v ÷ (n × ln n) caps the spread at a chosen commission rate v, in the same way a bookmaker sets its margin. The spread lets the market maker run at a profit across a wide range of outcomes, so the market can sustain itself with real money.

Prices stay path independent. Every trade is still priced off a single convex cost function. A large order costs the same whether placed at once or in pieces, and a purchase followed by a sale returns the market to where it started. The truthful-trading result for this design is set out in the Glimpse whitepaper [8].

The LS-LMSR also sits at the frontier of what is mathematically possible. No market maker can be path independent, free of arbitrage and liquidity sensitive at the same time [5]. Free of arbitrage here means prices that always sum to exactly $1. Every design must give up at least one of the three properties. The order book gives up path independence. The LMSR gives up liquidity sensitivity. The LS-LMSR gives up only the exact $1 sum, by a small margin the operator controls through α. Traders already pay a spread in every real market, so this is the cheapest of the three properties to lose.

Glimpse: the LS-LMSR on prices and quantities

The LMSR family proved itself on yes-or-no questions, sports and weather. Glimpse is testing the LS-LMSR on a new frontier of prediction markets, built on prices and other quantitative outcomes. The Glimpse design is the quantile LS-LMSR, or QLS-LMSR, set out in the Glimpse whitepaper [8].

Each Glimpse market splits the price axis into 500 ranges. Each range has a contract that pays 100 sats ($0.08 USD) if the price settles inside it. One cost function prices all 500 ranges together, so the full probability distribution is always live and always tradable. A trader can buy a single range or a band of adjacent ranges in one transaction. The price of each range, divided by 100, is the market's probability that the price settles there.

Glimpse's hourly markets open with 80 contracts on every range. That opening state costs 24,000 sats ($20 USD), and it is the most Glimpse can lose on the market. At opening, the market's depth b is about 26 contracts. Once traders hold ten times the opening number of contracts, b reaches about 257. A fixed LMSR with that depth across 500 ranges would put 160,000 sats ($135 USD) at risk in every market. The LS-LMSR reaches the same depth while its worst-case loss stays at 24,000 sats ($20 USD).

The market also behaves like a learning ensemble. When traders size their bets by the Kelly criterion, the market price equals the average of their beliefs weighted by their bankrolls [9]. Settlement then shifts bankroll toward the traders who forecast well, in the same way Bayes' rule shifts weight toward accurate models [9]. The forecast is most accurate in the long run when traders risk only a small fraction of their wealth on each bet [10]. Small bets let traders with different views survive, and their combined beliefs keep the price close to the true probability. Hourly markets with small subsidies and small bets are built for exactly this pattern.

The forecast works

Glimpse runs hourly prediction markets on Bitcoin and gold around the clock, and it scores each forecast against the price at settlement. Measured 72 hours before resolution, the Glimpse Bitcoin price forecast has a hit rate above 85%. Measured at the same horizon, the Glimpse gold price forecast has a hit rate of 95%.

The same markets serve hedgers. A Bitcoin holder worried about a fall can buy the ranges below a chosen price for a given hour. Each contract pays 100 sats ($0.08 USD) if Bitcoin settles in that band. The cost function quotes the hedge instantly at any size, and the hedger can sell it back before settlement if the risk passes.

How the five prediction market mechanisms compare

The table scores each mechanism against the five properties set out at the start of this article. The dynamic parimutuel market appears as its own column, since it fixes some of the parimutuel pool's problems and leaves others in place.

Property	Parimutuel	Dynamic parimutuel	Order book (CDA)	LMSR	LS-LMSR
Incentive compatibility	No. Rewards waiting until the close.	No. Rewards holding back information.	No. Rewards leaking information slowly.	Yes	Yes
Continuous liquidity	Partial. Buy only, with no exit before the outcome.	Partial. Always buy, but selling needs a resale buyer.	No. Every trade needs a counterparty.	Yes	Yes
Bounded subsidy	No. Bettors only redistribute each other's money.	Yes. Capped at the seed.	No. Zero-sum between traders.	Partial. Capped at b × ln(n), which rises with depth.	Yes. Capped at the opening cost, which can be small.
Path independence	No. The payout depends on the final pool.	Partial. Purchases are path independent, payouts are not.	No. Every round trip pays the spread.	Yes	Yes
Liquidity sensitivity	Partial. Big pools move less, but payouts stay unknown.	Yes	Partial. Depth depends on who posts orders.	No. Every trade moves the price the same amount.	Yes

The LS-LMSR is the only mechanism that scores Yes on all five properties. The parimutuel pool and the order book fail the forecasting test of incentive compatibility. The dynamic parimutuel market fails it too. The LMSR passes the forecasting test but fails liquidity sensitivity, and its subsidy grows with every increase in depth. The LS-LMSR keeps everything the LMSR does well and adds the two things it lacks. Its depth grows with volume, and its worst-case loss stays fixed at a small opening subsidy.

Common questions

What is prediction market mechanism design?

Prediction market mechanism design is the engineering of a market's trading and payout rules so that traders profit most by revealing their true beliefs. A well-designed mechanism produces an accurate forecast and gives hedgers a counterparty at any time.

What is the LS-LMSR?

The LS-LMSR, or liquidity-sensitive logarithmic market scoring rule, is an automated market maker for prediction markets. It prices every outcome from one cost function and lets its liquidity parameter grow with the number of contracts outstanding. Prices move less as volume grows, and the operator's worst-case loss stays fixed at the cost of the opening state.

Why is the LMSR better than an order book for prediction markets?

The LMSR rewards traders for moving the price to their true belief, and it always quotes a price on every outcome. An order book rewards informed traders for leaking information slowly, and it needs a counterparty for every trade. Markets with many outcomes leave most order books empty.

Why is the LS-LMSR better than the LMSR?

The LMSR moves the same amount for a given trade no matter how large the market grows, and its operator must guess the right liquidity before trading opens. The LS-LMSR adjusts its liquidity automatically with volume. It runs on a small fixed subsidy and can earn a spread, so it can operate with real money.

How accurate is the Glimpse forecast?

Measured 72 hours before resolution, the Glimpse Bitcoin price forecast has a hit rate above 85%, and the Glimpse gold price forecast has a hit rate of 95%.

See the forecast

Anyone can view the live Glimpse forecasts for Bitcoin and gold for free on the Glimpse forecast page. The full mathematics of the QLS-LMSR is in the Glimpse whitepaper. Anyone with bitcoin can add their own view to the forecast by placing a bet.

No forecast is a guarantee. Do your own research before you trade.

References

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4. Y. Chen, D. M. Pennock. "A Utility Framework for Bounded-Loss Market Makers." Conference on Uncertainty in Artificial Intelligence (2007).
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7. Y. Chen, J. Wortman Vaughan. "A New Understanding of Prediction Markets via No-Regret Learning." ACM Conference on Electronic Commerce (2010).
8. J. Pierog. "Quantile Prediction Markets on Bitcoin." Glimpse whitepaper (2026).
9. A. Beygelzimer, J. Langford, D. M. Pennock. "Learning Performance of Prediction Markets with Kelly Bettors." International Conference on Autonomous Agents and Multiagent Systems (2012).
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