How Scoring Works

SentiDex uses LMSR (Logarithmic Market Scoring Rule) to price attention positions. LMSR is a well-studied automated market maker used in prediction markets for its efficiency and incentive properties.

LMSR basics

In an LMSR market, each outcome $i$ has a quantity $q_i$ representing shares outstanding. The cost function is:

C(\mathbf{q}) = b \cdot \ln\!\left(\sum_{i} e^{q_i / b}\right)

where $b$ is the liquidity parameter — a higher $b$ means deeper liquidity and lower price impact per trade.

The implied price (attention share) of position $i$ is:

p_i = \frac{e^{q_i / b}}{\displaystyle\sum_{j} e^{q_j / b}}

Prices always sum to 1 across all positions (including the reserve):

\sum_{i} p_i = 1

What prices mean

A position price of $p_i = 0.35$ means the market implies 35% of attention is flowing to category $i$ . This is not a binary event probability — it is a continuous measure of relative attention allocation.

Priors

When a market is initialised, each position receives a prior $r_i$ — a starting weight expressed in basis points that sets the baseline before any trades occur. Priors must satisfy:

\sum_{i} r_i + r_{\text{reserve}} = 10{,}000 \text{ bps}

The initial quantity vector is derived from the priors so that $p_i(0) = r_i / 10{,}000$ .

Example — "What is Crypto For?" initialisation:

Position	Prior (bps)	Starting $p_i$
MONY	1415	14.15%
DEFI	1413	14.13%
TOKN	1060	10.60%
STBL	848	8.48%
INFR	707	7.07%
SOVR	423	4.23%
PMK	600	6.00%
SDEX	400	4.00%
Reserve	2000	20.00%
…	…	…

Trading mechanics

When you buy shares of position $i$ , the market moves from quantity vector $\mathbf{q}$ to $\mathbf{q}'$ where $q_i' > q_i$ and all other quantities are unchanged.

The cost of any trade is path-independent:

\text{cost} = C(\mathbf{q}') - C(\mathbf{q})

Expanding for a single-position buy of $\Delta$ shares in position $i$ :

\text{cost} = b \cdot \ln\!\left(\frac{\displaystyle\sum_{j} e^{q_j/b} + (e^{\Delta/b} - 1)\,e^{q_i/b}}{\displaystyle\sum_{j} e^{q_j/b}}\right)

For a sell of $\Delta$ shares the same formula applies with $\Delta < 0$ , yielding a negative cost (i.e. a credit to the seller).

Price impact

The marginal price impact of buying $\Delta$ shares of position $i$ increases with $\Delta$ and decreases with $b$ . For small trades relative to $b$ , the price moves approximately:

\Delta p_i \approx \frac{\Delta}{b} \cdot p_i (1 - p_i)

This means price impact is largest when $p_i = 0.5$ and smallest at the extremes — a useful property for thinly-held positions.

Settlement

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Settlement mechanics are being finalised. This section will be updated when the settlement spec is published.

At market close, the SentiDex attention index determines the winning allocation. If the realised attention share of position $i$ is $\hat{p}_i$ , then each share of position $i$ pays out:

\text{payout per share} = \hat{p}_i \cdot \frac{\text{total pool}}{\text{total shares}_i}

Attention Markets Getting Started