Guide 2 · How prices are set
LMSR vs order books: two ways to price a market
An order book waits for a buyer and a seller to agree. An LMSR market maker quotes a price from a formula at any moment, and each trade moves that price a little. Order books shine on busy markets; the LMSR keeps quiet markets tradable, at the cost of a pre-funded, capped subsidy.
How an order book works
Traders post resting orders: “I’ll sell 150 YES at 53¢.” Someone who wants to buy now takes the cheapest offers first, then the next cheapest, and so on. The price is simply where the last trade happened. It works well when many people are trading, because offers sit close together. On a niche question there may be few offers, far apart, or none at all.
An analogy: an order book is a marketplace where you wait for a matching buyer. It is efficient when the market is crowded and slow when it’s empty.
How the LMSR works
The Logarithmic Market Scoring Rule, devised by economist Robin Hanson, is a formula that sets YES and NO prices from how many of each have been sold. Buy YES and its price rises; sell and it falls. Prices always stay between 0 and 1 and always sum to 1. There is always a quote, even at 3 a.m. on an obscure market.
The analogy here is a vending machine: it always shows a price and always accepts your trade while the market is open. 369X uses it on every market, subject to funding, trade limits and safety controls.
See the difference
Drag the trade size. The green curve is the LMSR price as YES shares are bought; the dashed steps are an invented order book. Notice what happens past 1,300 shares.
LMSR, b = 1,000, starting at 50¢ Average price 53.7¢; price after the trade 57.4¢.
Hypothetical order book Average price 52.8¢; the last share filled at 56¢.
Price impact and slippage are different
- Price impact
- The effect of your own order on the price. Buying 300 shares on the LMSR above raises the price from 50¢ to about 57¢, so your average is about 54¢. You can calculate it before trading.
- Slippage
- The gap between the price you expected and the price you got, often because someone else traded first while your transaction was pending. It depends on timing, not just on your order.
The liquidity parameter, b
One number controls how far trades move an LMSR price: the liquidity parameter b. A larger b means a deeper market and smaller moves. On 369X, 0.4% of every trade stays in the market to raise b, so markets that trade a lot become harder to push around.
The b × ln 2 bound, and what it doesn’t cover
Under the standard model, the most an LMSR market maker can lose on a binary market is b × ln 2, about 0.69 × b. That makes the market-making subsidy for each market known and capped in advance.
The bound is narrower than it sounds
It covers market making under the model’s assumptions. It doesn’t cover losses from leverage lending, contract bugs or a wrong outcome, and it doesn’t create capital: someone, here the LP Vault, has to fund it. Changing b mid-market also needs separate funding.
Which is better?
| Aspect | Order book | LMSR market maker |
|---|---|---|
| Always a price? | Only if someone is offering | Yes, while the market is open |
| Busy markets | Tight spreads, deep books | Deep once b has grown |
| Quiet markets | Wide spreads or no offers | Quotes, with larger price impact |
| Who takes the other side | Other traders | The market maker, funded by LPs |
| Cost to run | Incentives for makers | A capped subsidy per market |
Neither is better everywhere. Order books suit a few huge markets; an automated market maker suits many small ones.