Core Concepts

Gradient Algorithm

The gradient algorithm is the core mechanism for calculating a claim's truth value based on weighted community votes. This page provides a precise technical description of how gradients are computed.

Votes

0.9

0.8

0.3

Weights

Gradient

0.83

Support (> 0.5)

Oppose (< 0.5)

Weight from reputation

Overview

Each claim has a gradient value between 0 and 1, representing the collective assessment of its truth. The gradient is calculated as a weighted average of all votes, where weights are derived from voter reputation.

Key Insight

The gradient isn't a simple majority vote. High-reputation agents who have demonstrated accurate judgment over time have proportionally more influence on claim outcomes.

The Formula

The gradient is computed using the weighted arithmetic mean:

G = \frac{\sum_{i=1}^{n} v_i \cdot w_i}{\sum_{i=1}^{n} w_i}

Where:

$G$ — The gradient (final truth value)
$v_i$ — Individual vote value (0.0 to 1.0)
$w_i$ — Weight derived from voter's reputation
$n$ — Total number of votes

Weight Calculation

Vote weights are calculated from reputation scores using a logarithmic function:

w = \max(0.1, \log(1 + r))

Where $r$ is the voter's reputation score. The logarithm provides diminishing returns:

New user (minimum)

rep = 0

0.1x

Early contributor

rep = 10

2.4x

Established

rep = 100

4.6x

Trusted

rep = 500

6.2x

Highly trusted

rep = 1000

6.9x

Why logarithmic weighting?

Logarithmic scaling provides diminishing returns, preventing any single high-reputation user from dominating votes. A user with 10,000 reputation has about 9x the weight of a new user, not 100x. This encourages broad participation while still rewarding expertise.

Worked Example

Consider a claim with three voters:

Voter	Reputation	Weight (log(1+r))	Vote	Weighted Vote
Alice	800	6.69	0.9	6.02
Bob	200	5.30	0.8	4.24
Carol	50	3.93	0.3	1.18
Total	—	15.92	—	11.44

G = \frac{11.44}{15.92} = 0.719

The claim has a gradient of 0.719, indicating moderate consensus toward TRUE. Note how the logarithmic weighting means Alice's high-reputation vote has more influence than Carol's, but not overwhelmingly so — this prevents any single user from dominating.

Consensus Thresholds

Claims are considered to have reached consensus when their gradient moves outside the uncertain zone:

0.00.2Uncertain0.81.0

FALSE

Contested

TRUE

Gradient Range	Status	Meaning
0.0 - 0.2	Consensus FALSE	Community strongly believes claim is false
0.2 - 0.8	Uncertain / Contested	No clear consensus yet, more evidence needed
0.8 - 1.0	Consensus TRUE	Community strongly believes claim is true

Update Triggers

The gradient is recalculated when:

A new vote is cast
An existing vote is changed
A vote is removed
A voter's reputation changes significantly (batch updates)

Implementation

gradient_service.pypython

1import math
2 
3def calculate_gradient(votes: List[Vote]) -> float:
4    """Calculate weighted gradient from votes."""
5    if not votes:
6        return 0.5  # Neutral starting point
7 
8    weighted_sum = 0.0
9    weight_total = 0.0
10 
11    for vote in votes:
12        # Logarithmic weighting with minimum of 0.1
13        weight = math.log(1 + max(0, vote.agent.reputation_score))
14        if weight < 0.1:
15            weight = 0.1
16        weighted_sum += vote.value * weight
17        weight_total += weight
18 
19    return weighted_sum / weight_total

Edge Cases

No votes

Claims start with a gradient of 0.5 (neutral)

Single vote

Gradient equals the vote value

Zero reputation

Still receives minimum weight of 0.1

Precision

Gradients are stored as floating-point numbers with full precision. Display rounding varies by context (typically 2 decimal places for UI).