---
produced: 2026-07-08
title: The standardization value model - formulas relating the Coordination Problem, Complexity Budget, GitHub Test, Reach Test, Return on Complexity, Interaction Tax, Standardization Penalty, and Standardization Dividend
---

# The Standardization Value Model

Every library proposal puts the same question to the committee: should this component be added to the C++ standard library? The default answer is no. A proposal earns yes by demonstrating, with evidence, that its Standardization Dividend is large and that its Return on Complexity beats every competing use of the budget.

## Terms

| Term | Meaning |
|---|---|
| Coordination Problem | The class of problem that justifies standardization: a concept everybody needs but every library implements differently |
| Complexity Budget | The finite resource of specification the standard can carry; every addition spends it |
| The GitHub Test | The threshold question: what does standardization deliver that downloading the library does not |
| Reach Test | The audience question: how large is the constituency that collects the benefit |
| Return on Complexity (ROC) | Value delivered per unit of Complexity Budget spent |
| Interaction Tax | The permanent ongoing cost each component imposes on everything standardized after it |
| Standardization Penalty | The immediate loss of value on entry: the component can no longer compete or evolve in the marketplace |
| Standardization Dividend | The net payout to the community: gross benefit times reach, minus committee cost, Penalty, and Tax |

## Variables

| Symbol | Meaning | Operationalizes | Estimated by |
|---|---|---|---|
| $B$ | Gross benefit per beneficiary per year beyond mere availability | The GitHub Test | Field reports, interface-boundary evidence |
| $N(t)$ | Beneficiaries at time $t$ | Reach Test | Census: surveys, download and dependency counts |
| $\delta$ | Fraction of value forfeited to ossification, $0 \le \delta \le 1$ | Standardization Penalty | Domain velocity times freeze horizon |
| $k$ | Complexity spent: wording, names, interactions | Complexity Budget spend | The proposal's wording section |
| $K$ | Total budget the standard can carry, $\sum_i k_i \le K$ | Complexity Budget | Page, clause, and name growth data |
| $\tau$ | Annual cost per unit of complexity imposed on everything after | Interaction Tax rate | Post-adoption fix-paper counts, cross-feature wording |
| $C_0$ | Fixed admission cost: committee hours, review, displaced floor time | Cost of admission | Docket and throughput data |
| $r$ | Time discount rate | - | - |

## Formulas

**The GitHub Test** is the threshold condition:

$$B = B_{\text{standardized}} - B_{\text{downloadable}} > 0$$

If everything the component offers is captured by downloading it, $B = 0$ and no other number matters. This is the default no, stated as arithmetic.

**The Standardization Penalty** relates in-standard value to ecosystem value:

$$V_{\text{std}} = (1 - \delta) \cdot V_{\text{ecosystem}}, \qquad \delta \approx f(v \cdot L)$$

where $v$ is the domain's evolution velocity and $L$ is the effective freeze horizon: release cycle plus implementation lag plus ABI eternity. Hash maps and regex live in high velocity domains, so $\delta \to 1$. Strings live in a low velocity domain, so $\delta$ is small. The penalty is not a constant; it is a property of the domain, measurable from ecosystem release cadence.

**The annual dividend flow** of an admitted component:

$$d(t) = (1-\delta) \cdot B \cdot N(t) \; - \; \tau k$$

Benefit net of Penalty, minus the Interaction Tax the component levies on the rest of the standard every year, forever.

**The Standardization Dividend** is the present value of that stream minus admission:

$$D = \sum_{t} \frac{d(t)}{(1+r)^t} \; - \; C_0$$

**Return on Complexity:**

$$\mathrm{ROC} = \frac{D}{k}$$

**The admission rule.** Because the budget is finite, the hurdle is not $D > 0$:

$$\text{admit iff } \mathrm{ROC} \ge \lambda$$

where $\lambda$ is the shadow price of the Complexity Budget: the return of the best proposal this admission displaces. Positive is not the bar. Better than every competitor for the same budget is the bar. This is the opportunity cost of committee time as one inequality.

**The per-release portfolio dividend.** A standard revision is a portfolio:

$$D(\text{C++}XX) = \sum_{i \,\in\, \text{admitted}} D_i$$

This is a retrospective instrument: score each release's portfolio and ask whether the committee's return per cycle is rising or falling.

## The scaling law

For a convenience component, value scales with the nodes:

$$B \cdot N \propto N$$

For a vocabulary component, value lives in the links: pairs of independently authored libraries that can now interoperate:

$$B \cdot N \propto N^2$$

Only components whose value scales with the square of adoption reliably outrun $\delta$, $\tau k$, and $C_0$. Linear algebra happens inside a codebase: linear scaling, download it. Strings cross every interface boundary: quadratic scaling, standardize them. Networking qualifies on both axes: sockets appear at interface boundaries and $N$ is nearly the whole user base.

## The ordinal sufficiency principle

The admission rule is intrinsically comparative: $\lambda$ is the return of the displaced proposal, so the model never requires absolute values, only rankings. Order of magnitude estimates suffice to rank when gaps are large, and the gaps are large: a component serving everyone who connects to the internet versus a component serving one specialty container's users is a difference no estimation error can flip. Soft numbers beat no numbers. The objection "these cannot be measured precisely" is an argument against false precision, not against measurement.

## The evidentiary checklist

Every variable is an evidence obligation. A proposing paper must supply:

| Requirement | Establishes | Form |
|---|---|---|
| Field reports from years of real deployment | $B$, and the domain velocity behind $\delta$ | The bulk of the paper |
| Reach census with scaling class | $N$, and whether value scales as $N$ or $N^2$ | Surveys, dependency counts, cross-library interface evidence |
| Complexity estimate | $k$ | Wording size, name count, interaction survey |
| Docket comparison | $\lambda$ | Why this proposal over the alternatives competing for the same budget |

A paper that is all design supplies none of these. Design is not evidence.

## Caveat

$B$, $\tau$, and $\delta$ are order of magnitude instruments, not precise quantities. Their power is that they force proposals to state estimates that can be argued about, and they make ignoring opportunity cost structurally impossible rather than merely embarrassing.