The formula, annotated.
The Payment Algorithm deep dive shows you the shape — good minus harm, open and weighted. This page shows you the actual machinery: the published equation, every variable, every dial, and a worked calculation you can check by hand.
ProvenanceWhere this comes from
What follows annotates the Net Benefit Reward Algorithm Proposal, version 7.1 — the last iteration the Copiosis project published, distributed as an open technical document and explicitly marked as superseding every earlier version. The proposal was open-source by design: anyone could read it, critique it, and propose changes.
Everything on this page restates that published material in fresh words and notation. Where the historical record is ambiguous or incomplete, we say so rather than smooth it over.
The equationNBR, in one line
Read it as a sentence: the reward equals a sustainability-and-reach multiplier, times the sum of what consumers gained and what the world gained. Three structural choices do most of the work:
- The left side multiplies the right side. Consumer delight can't rescue an act that torches resources or reaches no one — the Production Demand Balance scales the entire benefit sum, so sustainability and reach gate every reward.
- Benefit variables run from −1 to +1. Harm isn't a footnote; it's negative territory on the same scale. Enough of it drives the bracket — and the reward — to zero or below, and a non-positive result simply pays nothing.
- Reach is logarithmic. Serving a million people beats serving a hundred, but not by 10,000× — the natural log damps runaway rewards for sheer scale, keeping ordinary local work meaningfully rewarded.
The inputsEvery variable, defined
| Var | Name | What it measures | Scale |
|---|---|---|---|
| ra | Resource abundance | Sustainability: the rate resources are consumed versus the rate they're replaced over the measurement window. Renewable, plentiful inputs score high; depleting scarce stocks scores low. | 0 → no upper bound |
| loge(1 + B/P) | Social impact | Reach: how much of humanity benefits, per producer involved. The log keeps huge audiences from producing runaway numbers; the +1 keeps small audiences from zeroing out. | 0 → damped |
| cs | Consumer satisfaction | The subjective half of consumer benefit: what the people served say they got — asked directly, not assumed by a seller. | −1 → +1 |
| cb | Consumer benefit | The objective half: science's best measure of what the product or service actually did for its consumers — health, time, capability, safety. | −1 → +1 |
| eb | Environmental benefit | Did the result leave the environment more life-supporting or less? Regeneration scores positive; pollution and depletion score negative. | −1 → +1 |
| hb | Human benefit | Did the result make humanity as a whole more resilient or less? Think knowledge, health infrastructure, durable capability — or their erosion. | −1 → +1 |
| Ccs, Ccb, Ceb, Chb | Coefficients | The visible dials: adjustable weights on each benefit term. This is where a society's values enter the math — in public, subject to the citizen-jury process, not hidden inside prices. | set openly |
By handA worked calculation
Take the water-filter designer from the Payment Algorithm page — a low-cost filter giving a small town clean water. Here's the same story with numbers. The figures are illustrative (and we set every coefficient to 1 for clarity); the arithmetic is the real v7.1 structure.
Now poison the story: the filter housing turns out to leach a toxin. Satisfaction stays high for a while (cs = +0.9 — people don't know yet), but measured consumer benefit flips to cb = −0.5, environment to eb = −0.6, human resilience to hb = −0.2. The bracket becomes 0.9 − 0.5 − 0.8 = −0.4 — negative, so no reward at all, no matter how big the multiplier. Popularity cannot outvote measured harm: that's the −1..+1 scales and the additive bracket doing exactly what they were designed to do.
IterationHow the formula evolved
Version 7.1 didn't appear fully formed. The published changelog from 6.1 to 7.1 reads like any healthy open-source project's — and that's the point. Highlights of what changed, and why it mattered:
- Merged: the producer-population and consumer-demand variables collapsed into a single consumer/producer ratio, and social impact moved inside the Production Demand Balance — tying reach to economic efficiency instead of double-counting it as a consumer benefit.
- Multiplied: PDB terms switched from being added to being multiplied — making each one consequential — and the PDB began multiplying the whole benefit sum, giving sustainability veto-like weight.
- Clarified: "consumer subjective benefit" became "consumer satisfaction" to honestly reflect what's being measured (what people report), and "consumer objective benefit" became simply "consumer benefit."
- Simplified: the effort variable was eliminated entirely — rewards track results, not how hard you tried — along with caps and opaque fine-tuning denominators, replaced by the visible coefficients.
Being honestWhat this page can and can't claim
Keep exploringRelated reading
The Payment Algorithm
The plain-language tour of the same machinery — start here if the math above felt like the deep end.
Read this →NBR, in Depth
The reward this number produces — created from nothing, non-transferable, gone when spent.
Read this →The Hard Objections
Gaming, laziness, the dirty jobs — the toughest questions, taken seriously.
Read this →Now see it in motion
A formula is a snapshot. The system around it — juries adjusting the dials, rewards flowing to whole supply chains — is where it comes alive.
Who runs itBack to Deep Dive