The Probability Market

Alpha Vector (α)

The state of the market is a Dirichlet concentration vector representing cumulative evidence. It is always strictly positive.

Public Consensus (q)

This is the public Probability Density Function (PDF) shown to users, defined as:

qᵢ = αᵢ / Σα

Buy: Submitting a Belief Curve

A buy operation applies collateral along the user’s belief vector. The engine performs the following:

• Update State: α ← α + C · p

• Compute Potential: ΔA = A(after) − A(before)

• Mint Claims: Create information claim m = μ · ΔA

• Record: Store p, m, and metadata in the ticket

Note: Early contributors earn disproportionate claim rewards due to the concavity of the potential function.

Sell: Exiting a Position

Selling reverses the exact informational update. The process ensures a deterministic, fair valuation and an actionable exit from the parimutuel system.

• Reversibility: The exit must follow the original belief vector p.

• Solver: The engine solves g(t) = 0 for t*, where g(t) represents the energy-balance equation.

• Uniqueness: Monotonicity ensures a unique solution.

• Safety: Checks enforce that α never crosses safe floors.

Settlement (Given x*)

Settlement uses the final value x* to redistribute the pool. The process is numerically stable, deterministic, and resistant to manipulation.

The mechanism uses:

• Log-sum-exp density evaluation at x*

• Eligibility filters

• Tempered softmax accuracy weighting

• Claim-share weighting

• Deterministic redistribution of the remaining pool

The Reality Market

Purpose

To determine a single settlement value x* for a continuous prediction market, using adversarial capital rather than oracle governance.

Closure (Bond) Agents

• Role: Assert an x* value they believe to be true.

• Capital: Locked until resolution.

• Incentive: They compete for the Bounty prize.

Continuance (Bounty) Agents

• Role: Fund the bounty and prevent premature closure with "no" capital.

• Incentive: They compete for the SlashPool.

Market Lifecycle

1. Pre-Clearance

   Closure and bounty accumulate. Assertions can be made and disputed freely.

2. Clearance

   Achieved when the ratio of Closure/Bounty ratio ≥ threshold. The market enters a monitoring phase.

3. Dwell Period

   The ratio must remain above the threshold for a required duration.

4. Finalisation

   The final value x*is determined by the capital-weighted median of active closure assertions.

5. Slashing

   Assertions falling outside the MAD-based epsilon band around x* are penalised.

6. Distribution

   • Accurate closure agents receive the ContinuancePrize.

   • Continuance agents receive the SlashPool.

   • All capital is unlocked and the RM terminates.

Key Properties

• Propositive: Agents may assert any x*

• Adversarial: Designed to leverage selfish behaviour for truth-finding

• Fast finalisation: Once information stabilises, convergence is rapid

• Manipulation-resistant: Capital requirements grow with uncertainty through linkage to underlying Probability Market

• Dynamic Security: Clearance condition determines budget for Closure/Continuance

• Developer-agnostic: Can be hosted by FS or any builder

Developer Options

Nothing in FS forces developers to run a full prediction stack, ensuring flexibility. Developers can:

• Ignore RM entirely and use FS-hosted resolution.

• Expose RM elements for power users.

• Build their own RM frontends.

• Integrate RM data only.

• Create alternative vertical-specific RM experiences.

Summary: Developers have full control over the UI/UX, knowing that markets will inherently self-resolve.