← Back to article

Equation 3 · Comparing the Main Approaches to AI Governance and Regulation

What does this equation mean?

Ei≈f(coveragei, enforcementi, ti),ti≪tj for several pairs (i,j)E_i \approx f(\text{coverage}_i,\ \text{enforcement}_i,\ t_i), \qquad t_i \ll t_j \text{ for several pairs } (i, j)

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

This equation gives an approximation: it relates the quantities while allowing an approximation. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

EiE_i

Symbol E_i

EiE_i is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Understand this part →

ff

Symbol f

f is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Understand this part →

ii

Symbol i

i is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Understand this part →

tit_i

Symbol t_i

time-in-force for approach i.

Understand this part →

tjt_j

Symbol t_j

tjt_j is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Understand this part →

jj

Symbol j

j is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Understand this part →

≈

≈

Approximately equal to; the equality is not exact.

Understand this part →

subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Understand this part →

How to interpret it

Its accuracy depends on the assumptions and range of use described in the article.

What the article says around this equation

Start with the plainest problem: elapsed enforcement time. China’s algorithm-filing regime has run since March 2022 — more than four years of registrations, security assessments and enforcement activity. The EU’s high-risk tier, the part of its Act closest in spirit to a general risk-based licence, will not bind most Annex III systems until December 2027 at the earliest [ 3 ] . The UK’s five principles have applied, non-statutorily, since 2023, but a regulator applying a principle it was already free to apply under its existing powers is a different claim from enforcing a new statute. Comparing outcomes today would mean comparing a system with years of live administrative data against one…
Read the full surrounding passage
Start with the plainest problem: elapsed enforcement time. China’s algorithm-filing regime has run since March 2022 — more than four years of registrations, security assessments and enforcement activity. The EU’s high-risk tier, the part of its Act closest in spirit to a general risk-based licence, will not bind most Annex III systems until December 2027 at the earliest [ 3 ] . The UK’s five principles have applied, non-statutorily, since 2023, but a regulator applying a principle it was already free to apply under its existing powers is a different claim from enforcing a new statute. Comparing outcomes today would mean comparing a system with years of live administrative data against one with close to zero years of its central mechanism’s operation, whose independent contribution is hard to isolate from what regulators were doing anyway. Effectiveness is only meaningful once the thing measured has run long enough, under comparable conditions, to produce an outcome — informally, Ei≈f(coveragei, enforcementi, ti),ti≪tj for several pairs (i,j)E_i \approx f(\text{coverage}_i,\ \text{enforcement}_i,\ t_i), \qquad t_i \ll t_j \text{ for several pairs } (i, j). where tit_i is time-in-force for approach i . When tit_i differs by an order of magnitude or more across the set compared, as it does here, no amount of careful measurement of coverage or enforcement intensity fixes the fact that the outcome variable has not had time to be generated for every entrant. This is why no figure in this article, or elsewhere in this publication, ranks these regimes by effectiveness.

Read the equation in its article →

Sources cited in the surrounding passage

These citations give research context. Read each source to check which claims it supports.

Return to Comparing the Main Approaches to AI Governance and Regulation

See this formula across 1 published context →

Browse the mathematical compendium →