AMM Trading

AMM-Based Trading

Polarise uses an Automated Market Maker (AMM) mechanism to enable real-time participation, liquidity, and dynamic weighting within interactive assets such as Discussion Threads and other option-based social interactions.

Instead of relying on an order book, Polarise uses the Logarithmic Market Scoring Rule (LMSR) to automatically adjust pricing and weighting based on participant activity. This allows users to allocate support to different options according to their views, while the system continuously updates relative weights as activity changes.

Because LMSR does not require a counterparty, participation can occur at any time. Even the first participant in a thread can allocate support immediately, with the system providing a quoted price and instant execution. This design ensures continuous liquidity, similar to how AMM-based decentralized exchanges operate.

How LMSR Works

LMSR determines prices based on the total amount of participation allocated to each option. Rather than fixed values, option weights evolve dynamically as users interact, reflecting collective sentiment in real time.

The pricing mechanism is defined by the following components:

• C(…): The cost function representing the total cost required for the market maker to maintain the current distribution of shares.

• n: Total number of possible outcomes in the market (for Yes/No markets, n = 2).

• qi: The number of shares purchased for option i (can be interpreted as “vote weight” or “stake amount”).

• b: The liquidity parameter. A higher b makes the market more stable, meaning prices react less sharply to new trades.

• C(q): The cost of moving the market from the current state to a new state q.

Key Property of LMSR

A core property of LMSR is that the sum of all option weights always equals 1 (∑Pᵢ = 1).

When additional support is allocated to one option, its relative weight increases, while the weights of other options adjust downward proportionally. This preserves a consistent total distribution and ensures that changes always reflect relative, not absolute, shifts in participation.

This mechanism allows Polarise to maintain real-time responsiveness, continuous liquidity, and transparent weighting across interactive social assets without relying on centralized matching or external counterparties.