truth scoring
The scoring layer of the cybergraph: how Bayesian Truth Serum (Prelec, 2004) extracts honest private signals from neurons, how those scores accumulate into karma, and how the protocol makes honesty the selected equilibrium — truthful reporting is a Bayes-Nash equilibrium, and the surprisingly-popular divergence with honest-majority-by-stake selects it over coordinated consensus (see strong-truthfulness).
BTS score formula
Each participant submits two things: a personal belief (probability distribution over outcomes) and a prediction of the aggregate of others' beliefs.
The score for agent $i$:
$$s_i = \underbrace{D_{KL}(p_i \,\|\, \bar{m}_{-i}) - D_{KL}(p_i \,\|\, \bar{p}_{-i})}_{\text{information gain}} - \underbrace{D_{KL}(\bar{p}_{-i} \,\|\, m_i)}_{\text{prediction accuracy}}$$
where:
- $p_i$ is the agent's true belief
- $m_i$ is their prediction of others' aggregate beliefs
- $\bar{p}_{-i}$ is the geometric mean of others' actual beliefs
- $\bar{m}_{-i}$ is the geometric mean of others' predictions
The information gain term captures how much the agent's belief differed from what others predicted, corrected by what others actually believed. The prediction accuracy term rewards calibration about the collective.
Negative scores indicate noise -- the agent added distortion rather than signal. Stake redistributes from noise producers to signal producers proportional to scores.
what BTS measures
BTS measures information contribution in bits. The KL divergence between the agent's belief and the predicted mean ($D_{KL}(p_i \| \bar{m}_{-i})$) measures the agent's surprise relative to the prior. The correction term ($D_{KL}(p_i \| \bar{p}_{-i})$) removes the portion attributable to consensus rather than private signal.
The net score is the agent's unique informational contribution: what they knew that the group did not already know and did not already expect.
Prelec's equilibrium proof
Prelec proved that truthful reporting of $p_i$ (actual belief) and $m_i$ (actual prediction of others) is a Bayes-Nash equilibrium: no agent can improve their expected score by misreporting either quantity.
The mechanism is incentive-compatible because:
- inflating belief toward popularity loses the information gain component (the belief stops being more popular than predicted once the agent has predicted it into the crowd)
- deflating belief to seem contrarian loses the prediction accuracy component (the agent mispredicts the aggregate)
- the only strategy that consistently maximizes expected score is accurate reporting of both belief and meta-belief
This is why the mechanism is called a "serum" -- it does not rely on virtue. It makes honest reporting a best response through score structure alone. Truthful reporting is a Bayes-Nash equilibrium; it is not automatically the only one. Selection among equilibria -- defeating merely-coordinated consensus -- comes from the surprisingly-popular divergence and the honest-majority-by-stake condition. see strong-truthfulness.
relation to the wisdom of the crowds
The wisdom of the crowds (Galton, 1907) aggregates raw beliefs. It works when errors are independent and cancel. It fails when beliefs are correlated -- when the crowd shares a common bias, errors compound rather than cancel (Condorcet jury theorem requires independence).
BTS corrects for correlated bias by using second-order beliefs (predictions about predictions) to detect and discount systematic distortions. It does not require independent beliefs -- it only requires that truthful agents' private signals are distributed around reality, even if all agents share a common prior.
mapping to cyberlinks
In cyber, the cyberlink IS the BTS input -- no separate submission step required:
| BTS concept | cyberlink field |
|---|---|
| first-order belief $p_i$ | link creation + stake $(\tau, a)$ -- the neuron asserts the connection and stakes on it |
| meta-prediction $m_i$ | valence $v \in \{-1, 0, +1\}$ -- the neuron's prediction of how the ICBS market on this edge will converge |
| agent identity | $\nu$ -- the signing neuron |
Every cyberlink is simultaneously a structural assertion and a BTS prediction, in one atomic act. The scoring engine computes $s_i$ for every neuron from the public graph without any additional input.
the market is the substrate, not the scorer
The first-order channel -- link creation and stake -- moves the ICBS market, which supplies liquidity, commitment, and spam-cost. The market is not a proper scoring rule: its reserve ratio is a biased readout of belief (a true belief of $0.5$ settles near $0.366$, because ICBS prices lie on a circle $p_Y^2 + p_N^2 = \lambda^2$ rather than the simplex $p_Y + p_N = 1$). Truthfulness routes through the serum, never through the market.
The serum scores the valence meta-report, which is strictly proper, and the surprisingly-popular divergence $\bar p_{-i} - \bar m_{-i}$ selects the truthful answer over coordinated consensus. In a resolved market the market becomes proper at settlement and carries the first-order signal; in a perpetual market with no external oracle the serum is the only truth source. see strong-truthfulness.
karma
Karma is the accumulated BTS score history of a neuron -- the record of how much information a neuron has contributed to the collective over time. A neuron that repeatedly links things the market later validates has high karma. A neuron that links noise has low karma.
Karma is non-transferable. It cannot be bought with stake alone. It is earned by consistently being right before the crowd.
High karma means the network has observed a track record of genuine private signals. That track record enters effective adjacency as $\kappa(\nu)$ -- the trust multiplier that amplifies future contributions from consistently honest neurons.
karma in effective adjacency
Karma weights every future link the neuron creates in the tri-kernel effective adjacency:
$$A^{\text{eff}}_{pq} = \sum_\ell \text{stake}(\ell) \times \underbrace{\text{karma}(\nu(\ell))}_{\text{BTS history}} \times f(\text{ICBS price}(\ell))$$
This makes karma an epistemic weight, not merely an economic one. Epistemic capital -- the form of wealth that can only be earned by being right before the crowd.
honesty: three atomic acts
In the cybergraph, honesty is expressed through three acts that form one atomic record:
- Creating the cyberlink -- "I believe this connection exists"
- Setting the stake -- "how strongly I believe it"
- Setting valence -- "my honest prediction of where the market will settle"
Honesty and correctness are independent properties. A neuron is honest when it reports what it actually believes, regardless of whether that belief is accurate. A neuron is correct when its belief matches reality. Honesty is a property of the reporting; correctness is a property of the belief's relationship to the world. BTS does not require correctness -- it requires honesty.
protocol honesty vs epistemic honesty
Protocol honesty: the neuron runs the correct software, signs valid transactions, and follows the consensus rules of nox. This is what the honest majority assumption requires -- more than half of staked weight does not deviate from the protocol. It is enforceable by cryptographic proof: a stark verifies that the state transition is correct. Dishonesty at this level is detectable.
Epistemic honesty: the neuron creates cyberlinks that reflect its actual beliefs -- that the source particle relates to the target particle, that the connection deserves the stake it receives, that valence $v$ accurately encodes its private prediction. This is what Bayesian Truth Serum targets. It is not directly verifiable -- only the outcome (whether the market confirmed the prediction) is observable after the fact.
Both are necessary. Protocol honesty guarantees the computation runs correctly. Epistemic honesty guarantees the computation produces knowledge rather than noise.
why honesty is rational
Bayesian Truth Serum proves that epistemic honesty is a Bayes-Nash equilibrium: when a neuron believes other neurons are reporting honestly, honest reporting is a score-maximizing response. It is an equilibrium, not automatically the only one -- the surprisingly-popular divergence and the honest-majority-by-stake condition select it over coordinated alternatives (see strong-truthfulness).
The logic:
- a neuron that inflates valence toward what it expects the crowd to say loses its information gain (it is no longer more accurate than the predicted mean -- it has predicted itself into the crowd)
- a neuron that sets valence contrarian without genuine private signal loses prediction accuracy (the market does not move where it predicted)
- the only robust strategy is accurate reporting of both first-order belief (link + stake) and meta-belief (valence)
The mechanism extracts private signals even when those signals are wrong, because honest errors are distributed around reality while dishonest reports are biased in self-serving directions. The aggregate of honest-but-imperfect signals converges toward truth faster than any aggregate of strategic-but-precise signals.
the compounding mechanism
Honesty compounds through karma. Each accurate BTS prediction adds to the neuron's accumulated score. High karma means the network has observed a track record of genuine private signals.
A neuron that consistently lies accumulates negative karma. Its future cyberlinks carry diminished weight in the tri-kernel, regardless of stake. Epistemic dishonesty is therefore economically self-defeating in expectation: the mechanism does not punish dishonesty in a single round (a lie can go undetected once), but it punishes it in expectation across rounds, because the honest strategy dominates the dishonest one in expected score.
Consistently right before the crowd → high karma → more adjacency weight per link → more reward per contribution → more resources to stake on the next correct insight.
honesty as the foundation of syntropy
The cybergraph's information measure -- syntropy $J(\phi^*) = D_{KL}(\phi^* \| u)$ -- is produced entirely by the aggregate of honest epistemic acts. Each honest cyberlink is a bit of genuine signal. The tri-kernel converts honest signals into a sharper $\phi^*$. Dishonest links move $\phi^*$ toward noise, lowering syntropy.
A maximally honest graph is a maximally syntropy-generating machine. Honesty is the fuel.
see epistemic-markets for the ICBS market mechanism. see rewards for the reward functions. see knowledge-economy for the full economic design. see veritas for the continuous temporal extension of BTS. see honest majority assumption for the protocol-level complement.