The Latency of Legal Precision

Tax complexity is not a policy failure — it is a Nash equilibrium. The same arms-race dynamics that drive HFT latency drive tax code growth. Both are positive-feedback loops where individual optimization degrades the collective system.

1. The Structural Parallel

Two systems, two centuries apart, converging on the same pathology. The core insight: HFT latency reduction and tax code growth are isomorphic arms races. Both are driven by individual optimization in competitive environments, both produce collective waste, and both resist reform because the equilibrium is stable.

DimensionHFT Latency RaceTax Code Arms Race
PlayersTrading firmsTaxpayers + tax planners
ResourceExecution speedDefinitional ambiguity
InvestmentMicrowave towers, FPGAsTax lawyers, accountants
Individual payoffFaster execution = profitExploited ambiguity = lower tax
Collective outcome$billions spent, microseconds gained, no aggregate benefit$546B/yr compliance, 10M words, no simplification
EquilibriumSpeed-of-light limitLanguage-of-precision limit
Regulatory responseIEX speed bump, SEC reformTax Reform Act 1986, TCJA 2017
Post-reform outcomeArms race resumesCode grows back
Red Queen Dynamics
Both systems exhibit Red Queen dynamics — running faster just to stay in place. HFT firms spend billions to shave microseconds, but no firm gains a durable advantage because competitors match every improvement. Taxpayers spend $546B annually to navigate the code, but no simplification persists because every patch creates new exploitable boundaries. The investment is real. The net positional gain is zero.

2. The Signaling Game

Formalize the tax system as an information-theoretic signaling game.

ComponentSignal-Theoretic RoleTax System Instantiation
SenderEncodes messageTaxpayer (signals economic activity through tax return “language”)
ReceiverDecodes messageIRS (interprets the signal into tax liability)
ChannelTransmission mediumThe IRC (the grammar that maps activity to liability)
NoiseSignal corruptionAmbiguous terms, undefined concepts, inconsistent definitions
CodecEncoding/decoding rulesThe definition machine (§7701 + “for purposes of this section”)

Shannon’s noisy channel theorem: the channel capacity C sets the maximum rate at which information can be reliably transmitted. The IRC is an attempt to increase C — but each patch changes the channel characteristics, introducing new noise at the boundary.

Channel Capacity of the Tax Code
C = maxp(x) I(X; Y)

where X = economic activity, Y = tax liability
The IRC is the codec: p(y|x) shaped by 10M words of definition
Each amendment changes p(y|x), requiring recalculation by all participants
The Constant-Capacity Conjecture
The effective channel capacity has remained roughly constant even as the code has grown 2000× — all the growth is in the codec overhead, not in the signal-to-noise ratio. Tax outcomes are no more predictable today than in 1954 despite 7× more words. The definition overhead ratio inverted (from Rdef ≈ 0.5 to Rdef ≈ 2–3), but the residual ambiguity is unchanged. The codec grew; the channel did not.

3. The Nash Equilibrium

The 2×2 strategic form:

IRS Enforces Strictly IRS Enforces Loosely
Taxpayer Exploits Ambiguity Litigation
Costly for both		 Tax reduction
Taxpayer wins
Taxpayer Complies Simply Clean audit
Both win		 Overpayment
Taxpayer loses

The dominant strategy for the taxpayer is to exploit ambiguity whenever the expected litigation cost is less than the expected tax reduction. The dominant strategy for the IRS is to enforce strictly. But strict enforcement of ambiguous terms produces litigation, which produces case law, which produces codification, which produces new ambiguity.

This is NOT a prisoner’s dilemma. It is a coordination game with asymmetric information where the ambiguity IS the strategic resource. The more ambiguous the code, the more valuable tax expertise becomes, the more incentive to exploit, the more patches needed, the more new ambiguity created. The game is self-reinforcing precisely because the medium of play — English — cannot be made unambiguous.
1 Ambiguous terms exist in the code.
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2 Tax planners exploit the ambiguity (dominant strategy).
↓
3 IRS enforces strictly (dominant strategy).
↓
4 Litigation produces case law clarifying the ambiguity.
↓
5 Congress codifies the case law — using more English words.
↓
6 New words create new boundary ambiguities. Return to step 1.

4. Why Reform Fails

The Tax Reform Act of 1986 is the canonical test case.

1986
Tax Reform Act
+
Net Word Count Change
<10yr
Time to Exceed Pre-Reform Levels
2017
TCJA Repeated the Pattern
Reform AttributeTRA 1986TCJA 2017
Stated goalSimplify the tax codeSimplify the tax code
Immediate effectReduced rates, broadened base, eliminated deductionsReduced rates, changed pass-through rules, limited SALT
Net effect on word countINCREASEDINCREASED
Within 10 yearsWord count exceeded pre-reform levelsRegulatory guidance still accumulating
Mechanism of regrowthNew provisions required new definitionsNew provisions required new definitions

This is a Nash equilibrium reset attempt. You can perturb the equilibrium temporarily by changing the payoff structure — lower rates reduce the incentive to exploit. But the equilibrium reasserts because the channel is still noisy: English is still ambiguous. The simplification itself requires thousands of new words to specify what was removed, what replaced it, and what the new terms mean.

The paradox of simplification in natural language. Every rule you remove must be replaced with a rule specifying what happens in its absence. Every new rule uses English words that require definition. The act of simplification in a natural-language legal system is inherently inflationary. You cannot deflate the code without deflating the language — and you cannot deflate the language.

5. The HFT Overlay

Two curves on the same axes. One growing exponentially. One shrinking exponentially. Both driven by the same dynamics.

Mirror Curves: Tax Code Growth vs. HFT Latency Reduction
Left axis (blue): IRC word count, growing from ~5,000 (1913) to ~10M (2024). Right axis (red): HFT execution latency, shrinking from ~1,000ms (1995) to ~0.5μs (2024). Both are exponential curves driven by competitive optimization. The tax code grows because each participant adds definitional complexity. HFT latency shrinks because each participant invests in speed. Neither reaches a stable equilibrium — both are bounded only by physical limits (the precision of language; the speed of light).

6. The $546 Billion Codec

The annual operating cost of running the codec that converts ambiguous English into deterministic tax liability.

7.9B
Hours on Tax Compliance
$413B
Lost Productivity
$133B
Out-of-Pocket (Accountants, Software, Lawyers)
$546B
Total Annual Compliance Cost

This is larger than the GDP of most countries. This is the operating cost of a codec — a system for translating ambiguous natural language into deterministic numerical outputs. Every dollar is spent on the same underlying problem: reducing information asymmetry between what a taxpayer did and what they owe.

HFT Infrastructure
~$5–10B
Microwave networks, co-location, FPGAs, custom ASICs

The total capital investment in reducing execution latency from seconds to microseconds across the entire global HFT industry.

Tax Compliance Infrastructure
~$546B
Accountants, lawyers, software, 7.9 billion hours

The annual operating cost of converting ambiguous English into deterministic tax liability. Recurring every year. The tax codec is 50–100× more expensive than the HFT codec.

The Codec Cost Ratio
Both systems spend resources on the same underlying problem: reducing information asymmetry in a competitive environment. The HFT codec converts market information into execution decisions. The tax codec converts economic activity into tax liability. The tax codec is 50–100× more expensive — because natural language is a far noisier channel than a market data feed, and the tax code must be run by 150 million participants rather than a few hundred firms.

7. The Escape

Three possible escapes from the equilibrium.

ESCAPE 1
Change the Grammar

Write tax law in a formal specification language (TLA+, Alloy, or a purpose-built DSL) instead of English. Definitional overhead drops to zero — formal languages have no ambiguity by construction. Every term has exactly one meaning. Every rule is mechanically verifiable.

The HFT parallel: FIX protocol replaced ambiguous phone orders with deterministic message formats. It worked.

Cost: no human can read it. Democratic accountability requires that law be accessible to the governed. A tax code in TLA+ is technically superior and politically impossible.
ESCAPE 2
Change the Payoff Structure

Flat tax, consumption tax, or automated tax. If there is nothing to optimize against, the arms race stops. A flat rate on consumption has near-zero definitional overhead — no income categories, no deductions, no phase-outs, no “for purposes of this section.”

The HFT parallel: IEX’s speed bump changed the payoff structure by making the last microsecond worthless. It worked for IEX’s exchange but didn’t stop the industry-wide race.

Cost: massive political resistance. Every deduction is someone’s incentive. The mortgage interest deduction alone has a constituency of 65 million homeowners.
ESCAPE 3
Accept the Equilibrium

Recognize that complexity is the stable state of any competitive system with ambiguous rules. Stop trying to simplify the code. Instead, invest in better codecs: AI tax preparation, automated compliance, machine-readable tax rules that run alongside the English text.

The HFT parallel: most firms accepted the latency race and invested in better technology rather than lobbying for structural reform. The arms race continued, but the cost per unit of performance dropped.

Cost: concedes that the tax code will never be simple. Shifts the burden from simplification to tooling. Potentially increases dependence on proprietary compliance systems.
You cannot escape a Nash equilibrium by wishing it away. You can only change the payoff matrix. And changing the payoff matrix of the US tax code is a political problem, not a linguistic one — which is exactly what the critical review correctly identified.
Uncertainty