The textbook description of federal administrative law goes as follows:

• Since all lawmaking authority is vested by the Constitution in Congress, Congress first passes a law. If the law requires some element of administration (e.g., the law prohibits marijuana possession, subject to fines or imprisonment carried out by federal investigation and prosecution) it can delegate a particular authority to the executive for this purpose.

• That authority may include some determination of particulars to make the law actionable, which they often do through issuance of a regulation: something that looks much like a law, and is understood to be binding on the public like a law, but is executed without direct congressional involvement (including voting).

• In the case of many of these regulations they must be issued subject to prescribed procedural manners which can include availability to the public and ability for any person to provide input.

This is the broadest, simplest description of how a binding policy decision goes from legislative consideration to executive implementation. What follows focuses on the last stage, which for the most significant category of regulations involves a misunderstood internal administration process, drawing on longtime direct experience in the federal regulatory production function, especially time in the executive branch office overseeing much of it.

An actual rulemaking example case study helps to lay out the competing forces which broadly explain the path of travel from inception to finalization for federal regulations.

Without consideration of these variables within the regulatory production function, those interested in administrative law and reforms of administrative state institutions are limited to at best a partial understanding and at worst an incorrect understanding.

Do a Better Job, Congress

There’s an inevitable interpretation problem the executive branch needs to solve with almost any law. In theory, Congress could pass a law involving Article II administration that is so specific there is no decision space to which discretion is applicable.1

For example, say a statute prohibits private fishing of a particular type of fish: it specifies the individual species using its scientific name and proscribes weight in tenths of grams, below which the law applies.

Questions will still remain unanswered – such is law - for three reasons:

1. In prudential terms, specificity is inversely correlated to likelihood of passage. Ambiguity is the handmaiden of compromise and therefore passage.

2. There is always some parameter or aspect that is unforeseeable. You might think that would not be the case for some things, but even niche policy issues end up running up against some unknowable aspect of the future—new technologies, the effect of weather, or indeed just a future law or regulation.

3. Even earnest attempts at precision fall into imprecise application, especially in unavoidable questions of enforcement discretion, that can even run in the complete opposite direction of the policy aim.

Pass the Farm Bill ‘pon the Left Hand Side

Take the “Hemp Rule.” The 2018 Farm Bill (Agriculture Improvement Act of 2018) directed the USDA to establish a regulatory framework for legal domestic production of the crop hemp, which they eventually did (largely) through a regulation the following year (Establishment of a Domestic Hemp Production Program). One can stipulate there’s a lot there in the law’s directive. But limiting focus on a particular part will not sacrifice the generality of the point.

On the first day in the White House office tasked with overseeing the administration’s regulatory output, there sat on my desk a several-hundred page draft of the proposed USDA hemp program. As I would quickly learn, it turns out what people refer to as “hemp” is actually “cannabis,” which is illegal to grow under other laws and regulations. This new law simply established a legal definition of hemp (as a subset of cannabis) and deemed that legal.

The congressional authors and advocates of this law were responding to an increasing commercial interest in growing, processing, and manufacturing of products made with hemp, and wanted to encourage a growing market by providing an explicit legal structure. But not wanting to fully legalize weed, they established the following federal definition:

The term ‘hemp’ means the plant Cannabis sativa L. and any part of that plant, including the seeds thereof and all derivatives, extracts, cannabinoids, isomers, acids, salts, and salts of isomers, whether growing or not, with a delta9 tetrahydrocannabinol concentration of not more than 0.3 percent on a dry weight basis.2

(ed. The Salts of Isomers sounds like a lost P.G. Wodehouse novel)

That is a remarkably precise definition. Whatever judges, scholars, and wonks bemoan about congressional dereliction in statutory construction, they can’t possibly expect more than this:

• a scientific name of the supercategory from which the subject is subcategorized

• a long list of adjacent and derivative elements

• most importantly a cutoff down to the tenth of a percent. An extreme level of precision by any measure

The problem is that even here there is still room for discretion. Because the structure of the law is carving out a subset of an article, possession of which remains illegal often at great legal risk, margins of error are important here. Does “0.3 percent” possibly include anything greater than 0.3? Say, 0.4? If not, what about 0.39? 0.31? Is it proper to assume 0.3 means 0.3000…?

Wherever you draw that line, keeping in mind the significant sanction applicable to anything above it (so-called “hot hemp”), is it reasonable to presume full unwavering enforcement of anything above it?

Say a farmer, knowledgeable and diligent in the techniques of controlling plant growth and their production of certain chemicals, nonetheless grows crops that just barely cross the threshold. Maybe due to unseasonable weather (because plants don’t read statutes).

1. What if they could show it was unintentional? should they have a defense?

2. What if on the entire farm, one small portion is noncompliant?

3. In any case, does every plant or stalk need to be tested to demonstrate compliance (possibly hundreds of acres)?

4. If not, what’s the sampling methodology?

5. What's the disposal procedure for hot hemp?

These are not hypothetical questions, but actual ones that came up.

Executive discretion inexorably enters administration of the law somewhere. Political considerations as well, but it is worth noting that the primary congressional advocates for the law preferred as capacious and flexible an implementation as possible.3

In short, even seemingly clear direction and granular consideration leaves unanswered questions for the executive branch.

How, then, do those questions get answered?

The Three Axes of Administration

A naïve explanation of how administrations land on various policy decisions will either imbue: (1) the president with comprehensive decision-making direction, or (2) individual agencies/offices internally directing decisions in their limited sphere of authority. Instead, the canons of Presidential Administration tell us that it is much more complicated, involving various internal leverages, authorities, and competing interests. This process is usually referred to as the “interagency process” but it’s not very descriptive.

For regulatory outputs there are broadly three variables, variously constraining and driving decisions. A meaningful understanding of these interdependent elements is a necessary condition for productive influence and effective reforms of federal regulatory policy–the realm of federal policy making up the lion’s share of all of Washington’s policy production.

Policy Preferences

This may seem circular: how can policy preferences be merely amongst other variables driving policy? At the highest, broadest level, one presumes a given administration has a concordant policy agenda. The president ran on a particular agenda, distinct from their opponents, and at various stages the campaign followed by the transition team added specifics to the rhetoric, and so on. Even if that’s true to some extent, as one goes further into policy specificity into narrower and narrower questions, there will be disagreement.

In the context of the hemp rule, one could fairly characterize the Administration’s overarching policy direction as one of deregulation—directionally, lower costs imposed by the government and more room for the market to operate. But that is not enough to unify everyone in an Administration, because it still permits different ideas of what that means, competing ways to go about it, and ultimately (as is always the case) how to manage competing priorities.

The aforementioned interest in establishing as wide a berth for the emerging industry ran up against law enforcement concerns. Cultural acceptance of cannabis and other psychoactive substances was perhaps reaching a peak, but the Administration also bore a strong interest in appearing tough on crime and strict enforcement of the law, especially drug laws. The concern wasn’t so much on criminal behavior around hemp itself, but rather its adjacency and unavoidable interaction with drug interdiction efforts. Regardless of whether one is sympathetic to these concerns, it is a credible issue that is not obviously dispensed with.

Even though a single agency (more accurately a sub-agency office within an agency) is nominally responsible for authorship of the rule in question, multiple agencies can come to the drafting table with pertinent concerns and questions (as well as their own expertise). And really even within an agency, there can be unresolved disagreements that are illegible to everyone but for a few people. All of this has to be resolved one way or another before the rule goes out the door. The ultimate outcome might subordinate some disputes, but the goal is to find a compromise.

For illustrative purposes, assume that everyone involved generally agrees on the preferred direction of the policy. They can still disagree on how best to achieve it—on the specific wording and structure that more or less effectively accomplishes the shared goal.

Political Incentives

The second variable which enters the regulatory production function is political in nature. Every public policy choice implicates tradeoffs. Some are explicitly representable through comparative statics revealing welfare gains and losses for different groups, demographics, industries, or regions. Even a universal uniform tax cut will affect inequality in some way; modify incentives leading to long term changes in growth; and, of course, under certain conditions, benefit current populations at the expense of future ones.

The way these tradeoffs are negotiated in the American system, controlling for ideological priors (themselves not entirely exogenous to the policy production function), is through what we broadly call politics. At the macro level, it’s through elections that decide which coalitions of groups will be given preferred treatment in the tradeoff showdown. At the micro policy level, in Congress it is sorted out through negotiation between individual members and caucuses subject to institutional structures. Something similar happens in the executive branch, but with different electoral constraints. But many of the same coalitional dynamics are at play in both.

Farmers (I use that word loosely) are an organized interest group in a small number of districts. They play an outsized role in shaping policy preferences in some key states, and a somewhat peripheral role in most other states. So for that small number of agriculture-heavy districts and states, accommodation of agriculture interests are a necessary part of a winning coalition. Additionally, the long history of the industry, and to a degree the bipartisan favorability of the group’s “brand,” has led to a federal agency pretty much oriented toward it across administrations, even across partisan shifts. To be sure, between partisan shifts, rebalancing of incentives occurs between sub-groups within the larger agriculture industry: large industrial vs. smaller producers, export-dependent vs. localized sellers, newer “natural” growers vs. pesticide users, ethanol vs. everyone.

So with the hemp rule, it being a somewhat nascent node in the larger special interest, there was not much of the more mature intra-interest frictions to speak of. The congressional provision had wide bipartisan support, and the agency was glad to facilitate the aim.

But many rules pose tradeoffs between highly opposed groups even within the same industry: incumbents vs. startups, alternative energy vs. coal-based, etc. Even if a Democratic administration will reflect different rank-ordering of interests than a Republican one, those interests will almost all be reflected somewhere across the government in some way.

Timing is also a political variable in two ways:

1. There may be political benefits for issuing a rule quicker or slower—say, closer to an election when it will be most salient—or timed to come out on the day of the State of the Union.

2. Prioritization is partly a timing question. Multiple agencies may agree on the substance, but if it requires resources to implement, that comes at some opportunity cost of other initiatives. One cabinet secretary will say to another: “I’m very supportive of this thing you’re doing and we can definitely be helpful in making it successful, but I just can’t take our people off this other top priority of the President. Better we hold off for a bit.”4

Relatedly, the president may be the final decider between differing viewpoints, but several offices within the White House, many with very wide and undefined remits, will have an opportunity to weigh in. Some of these explicitly focus entirely on political concerns, not as an adjunct concern to other considerations. Because of the often ambiguous scope of these offices and individuals, combined with their literal proximity to the Oval Office, they play an important role in shaping policy, including siding with one position or the other in an interagency disagreement.

Here again, as in the earlier case of competing policy preferences, Congress is a participant in negotiating among political interests. While having no formal role in the interagency process exactly, Congress does maintain a line of communication. In particular, chamber leaderships and committee chairs want to ensure that their statutory handiwork becomes a regulatory showpiece. White House and other agency staff have an incentive to listen and, in some circumstances, push for those congressional views. At any given time, there are ongoing negotiations around other legislation, appropriations, nominations, etc., providing political leverage for those outside the interagency process to push their way in.

The same goes for outside stakeholders: industries and their trade associations, advocacy organizations, and individuals. They each may have their own direct connections with various nodes in the bureaucracy. But they also have a formal mechanism at specific stages to lobby on the record through so-called 12866 Meetings and public comment.

Successfully mediating the various policy questions and negotiating between the various political constituencies is the objective of this sometimes messy interagency process and drafting. For any published regulation of significant importance, assume an extensive deliberation occurred in the background.

Yet there’s one more variable influencing the shape of the final regulatory output left to solve

But is this legal?

So various forces push on the pending policy product this way and that, policy arguments go back and forth and sometimes run into political constraints…what else is there?

The rule has to be defended in court. This is the trickiest of the three variables to cleanly conceptualize, since it is fairly interactive with the other two in a way they are not with each other.

The legality question is not a matter of “yes” or “no.” The idea of legality rarely if ever exists as a binary state. This is why we have scores of lawyers and hundreds of courts. As in the hemp example, reasonable people, including litigating attorneys, can disagree about exactly what is allowable or not based on the legislative text. Various canons of statutory interpretation all focus on how to go about drawing meaning from laws. So let’s stipulate this variable is not about deciding whether to intentionally break the law or not.

Instead, it is about determining what the law means. And that is a variable, because there will inexorably be different answers all plausibly describable as “legal.”

This legality question is intertwined in a complicated way (as opposed to in a simple way like Nigel Tufnel’s piano etude in D minor) because choosing among the answers is both a policy question and a political question.

Formally, there are offices in DOJ, the White House, and across agencies possessing relevant expertise to help determine the bounds of legality of a potential regulation. This question – what is and isn’t legally defensible – is all about discovering the scope of the decision space. Without eventually outlining this dimension, you won’t know where you’re aiming. Knowing the limits of what policies are allowable (which is not a predefined or determinative outcome) sets the boundaries on what policy options are “on the table.”

With hemp, who’s to say the Farm Bill language presumptively excludes 0.99 percent? We might base our answer on a layman’s common sense framing. And that’s one possible mode of interpretation: the reasonable person standard. But does it apply in this context? Are there other statutes providing an applicable example? Court opinions which, say, rounded up to an integer in an instructive context? Other precedents imposing a standard methodology? In the same way that no statute can answer every possible question, now someone has to make a decision to answer at least some of the questions, and to do that we first need to lay out the boundaries within which we can draw.

This can include a party to the interagency process making the case that the decision space should be much bigger than conventional wisdom. To be clear, this is not a means to invite illegality. Every Administration, every agency, at some point has put forward novel applications of authorizing laws. There are high-profile examples where those novel applications are explicitly deemed illegal by a court, but most go unnoticed except for niche specialists in one field or another. The idea of applying a law in a way that lacks a clear antecedent is not by itself an extralegal assertion. This is how old laws can undergird rules on new technologies and circumstances.

Defensibility

The most direct way these analyses inform the deliberations is through determinations of defensibility. The DOJ attorneys in particular are the front line in defending administration actions in court. They have specific experience and context informing “defensibility.”

Note: defensibility is not equivalent to legality. A compelling argument can be made for why an action is clearly permissible via valid authority. But in court asserting that conclusion requires different elements, because of civil procedure and the like, which may not be easily available.

On a different rule, we ran into another type of legal constraint: treaties. I am not an expert on the obligations of the U.S. government with respect to treaties vis-a-vis domestic law. But treaties serve as a kind of law. And if a policy action appears to run up against any of those obligations, someone from the government will let you know. You would be surprised how often and on what topics this comes up.

A related issue is national security. Certainly the actual statutes pertinent to that, but internal practices governing government practices are not always so directly correspondent to a specific law. For all intents and purposes, these practices function as implicit law and if a policy action threatens to “violate” them that will carry weight.

Finally, there’s a pointedly political aspect that is nonetheless subject to a legal question. Embedded within defensibility are other questions: How likely is this rule to be challenged? Who is likely to undertake the cost and be able to show standing to challenge? When is a possible adverse judicial action likely to happen?

The COVID Emergency Case

A sui generis example illustrates how the answer to these defensibility questions manifest in the eventual action, and how inextricably interdependent the three broad variables are—and therefore how resistant they are to discrete categorization.

COVID-19 constituted an emergency, requiring many novel deployments of existing laws not specifically constructed for this purpose. Not just pandemic preparedness and national emergency laws, but everything from interstate highway operations, to pharmaceutical manufacturing inspections, to tax incidence on alcohol. They all implicated adjustments in regulatory schemes in no obvious way extended from underlying laws.

In one case, a fairly significant potential action presented a large policy benefit as well as a political one. The authority to undertake it was shaky at best, and a near-consensus formed that if challenged, it would not be defensible. However, there was no obvious party likely to demonstrate standing in any expeditious way. But beyond that, to the best of anyone’s ability to predict, there was no one with any compelling political incentive to challenge. And further, the temporal impact of the policy meant the outcome of a future challenge would be moot by the time of a final decision.

Conclusion

Matthew Stephenson’s 2006 Harvard Law Review article provides “a positive theoretical analysis of the relationship between the textual plausibility of an administrative agency’s statutory interpretation” and strategic agency decision-making. Likely the first to do so (and elsewhere in his 2006 Administrative Law Review article), he posits an agency with a single goal of withstanding judicial review (the objective function). The agency acts strategically to meet this threshold condition by optimizing across two endogenous instruments: statutory interpretation and procedural formality.

Further in their response to Stephenson, Emerson Tiller and Frank B. Cross contend there are further considerations in the decision function of both the agency and the court, that more properly accounted for would more accurately reflect observed regulatory policymaking behavior.

That work is largely the inspiration for this essay, in particular the formalization contained in the appendix. That is, trying to describe structurally the within-agency (or within-administration) optimization and interaction of potentially competing decision margins. Whereas Stephenson focuses on the extra-administrative game between agency and court, I limit the regulatory result as emerging from three intra-administration factors. Both consider margins that are costly to each other. His court is a strategic actor in the reduced-form game. Here I remove that actor, but add a political dimension to the internal optimization. And where Tiller & Cross require some consideration for policy durability, I permit for a term-limit parameter which changes the relative weights of the three dimensions.

In 2006, I lacked the necessary experience to describe a plausible structural model of agency rulemaking. But in what precedes I hope I can finally build on testable claims about the production function of administrative laws.5

Future direction would for instance identify the sub-games which themselves determine the policy preference function, explicitly incorporate Congress as an independent but interdependent player in the normal form game, and ultimately work toward a unified Constitutional theory of administrative law (Congress + Agencies + Courts).

The author is a writer and musician in the Bay Area, and currently a harvest intern at a winery.

Appendix: Formal Model

The following formalizes the agency’s decision problem described above, with the exception that we stipulate the administration’s policy preference as exogenous to allow for a closed-form solution. Endogenizing U(P) would preclude a closed-form solution, consistent with the “three-body problem” framing.

Parameters.

• L – administration’s distance from ideal policy position, toward greater legal defensibility (choice variable)

• A – administration’s distance from ideal policy position, toward greater political payoff (choice variable)

• x_P, x_A, x_L – realized policy, political, and legal payoffs

• x_P0, x_A0, x_L0 – baseline levels at ideal policy position (i.e., L = A = 0)

• w_P, w_A, w_L – the administration’s relative weights on each variable

• c_L, c_A – marginal cost to policy of legal and political payoffs

• γ_LL, γ_AA – slope of marginal cost on each margin alone

• γ_LA – slope of cross-marginal cost (positive means pursuing one makes the other more expensive, negative means cheaper, zero means no interaction)

• t – elapsed time, increasing as gets closer to term-limit (t ∈ [0,1]; 0 = start of term, 1 = end of term)

• w_L(t), w_A(t) – weights as functions of term-limit (w_L’ > 0; w_A’ < 0)

Objective Function. The administration chooses L and A to maximize the weighted sum of the three goals, net of constants:

First-order conditions. Differentiating with respect to each margin and setting equal to zero:

Regularity condition. For an interior maximum, the cost curves must be convex:

Closed-form solution. Solving the FOCs jointly, the optimal legal and political accommodation are given by:

Independent margins. When the two margins don’t compete for the same policy room (γLA=0), this collapses to the standard tangency condition (optimum defined as where marginal rate of substitution equals the “price” ratio of the two tradeoffs), applied separately to each variable:

Term-limit dynamic. Letting the weights vary with time horizon, the independent-margins case gives the rate of change of realized policy achievement as the term limit approaches:

The two terms pull in opposite directions: rising importance of legal durability drags on policy intensity; diminishing political concerns works the opposite way. If we observe policy maximalism towards the end of the term-limit, the model explains this as freed up political capital increasing faster than legal moderating.

Threshold Condition. This holds if and only if:

If this inequality fails, the prediction reverses: administrations become more legally conservative and less policy-ambitious as a term limit nears. Determining direction is an empirical question about the relative rates at which political urgency fades and legacy urgency rises, testable across administrations’ final years. Neither outcome is determinative a priori.

5

In fact for some five years I had Stephenson’s equilibrium conditions written on my Senate office white board:

Recap

Assume the AI makes some mistakes, yet we don’t know exactly how often. The company reviews the AI’s decisions, but human effort isn’t set-it-and-forget-it — we respond to incentives. So management offers bonuses for every AI mistake caught. As a result, over time the company ends up in either:

• Employees maintain full effort; they eventually learn the AI agent’s actual error rate; or

• Employee effort collapses to zero; they eventually believe a false AI error rate, resulting in unexplained losses.

Assumptions are fairly conservative and informed by real experiments, including actual corporate experience.

….with the exception of the AI’s accuracy we which treated a fixed error rate.

Now we allow the accuracy rate to improve. Which is fairly reasonable given the advancements in reinforcement-learning (RL).

To wit:

Over the last year, many such evaluations have found that agents are now able to make progress on tasks where success is easily verifiable, prompting speculation that we are on the verge of RSI.

— AI As Normal Technology, Aug. 5, 2026

The claim by and , part of a fascinating post on experiments in recursive self-improvement (“the automation of AI research using AI agents”), question-begs whether RL is sufficiently effective (trustworthy?) to move on to abstract, open-ended tasks.1 This model assumes a simple repetitive task, fully verifiable, and elsewhere plainly states the obvious: “as things stand, any work given to AI will require human review to make sure it’s up to organizational standards.”

This question — how ought an organization exploit agentic AI — is operative and underexplored. The task remains the same (simple, verifiable) but now the AI model improves in one of two ways:

1. fixed rate over time; or

2. variable based on human feedback

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Solutions (Bottom Line)

The problems remain the same (explained below) but also point to fixes:

1. ballooning bonuses for successful reviews

2. constantly rotating review teams

They are not costless though.

Graphic Results

Formal Model (Extension-1): The AI Keeps Getting Better

Narrative Description

A fixed error rate is unrealistic. Many of these systems do improve over time, whether through retraining, better data, or just model version iteration. So what if the AI is actually getting better, on its own schedule, independent of anything the analyst or management does?

Here we add a separate force pulling in the opposite direction of human attention decay: the AI’s true error rate falls exogenously.

Formal Description

Parameters (existing)

ε_t - the AI model’s true error rate, directly unobservable to management and analysts

ε̂_t - belief of ε_t, equal to prior period’s observed error detection rate

L - fixed loss to management per undetected error

γ - analyst’s convex cost of effort

π - bonus to analyst for every caught error

v_t - effort (vigilance) level; from non-zero to one. The probability an error is caught

δ_t - the analyst’s decay parameter, getting smaller over time

δ_tv_t* ≡ effective effort level

r_t - the threshold condition (where things go south or not)

Parameter (new)

ρ ∈ (0,1) - AI model’s given improvement rate term

The AI model’s actual error rate process is now defined as:

ε_t​ = ε₀​ρ^t

The recursion combines this with analyst attention decay (rewriting with k ≡ π^*/γ):

Result. Effort still tracks error belief up to a point: v_t = min⁡(1, kε̂_t-1). Define the analyst effort threshold as ε̄ ≡ 1/k = 2γ/L (determined by analyst incentive bonus):

• When true error ε_t > ε̄ effort is maximized;

• When true error ε_t < ε̄ — when the error rate falls low enough (gets good enough) — maximum effort is not worthwhile for the analyst (the chance of bonus payment isn’t good enough).

Because ε₀ (initial error rate) and ρ (improvement rate) are stipulated and fixed terms, the point at which this threshold gets crossed is calculable:

After that point in time, belief declines → effort declines, and attention decay compounds the descent.

Implication. From the outside you can’t tell the difference between an AI that merits less scrutiny (saving time) and an analyst whose vigilance has quietly faded on its own. Override rates and time-per-case are indistinguishable. A company doing everything right and one being fooled look exactly the same.2

To be fair, despite our model setup, the model’s true starting error rate and precise rate of improvement may not be practicably knowable. But the point is these regimes exist and with sufficient data/information a company can characterize the inflection point where you cross from one to the other.

A company winding down its review because the AI earned it, and one winding down because reviews are getting soft, produce exactly the same numbers.

Formal Model (Extension2): When Effort Teaches the AI

Narrative Description

Now the AI agent, still with an initial error rate, improves through human correction. Every caught error is the thing that makes it better. Human feedback remember is subject to endogenous effort. Obviously more errors caught → more improvement. But finding them takes work, and more work as the AI improves.

Formal Description

New Parameter

λ ∈ (0,1) - how effective the AI model improves from identified errors by humans

The model’s true error rate is determined by a combination of the analyst’s vigilance level in the previous period (how likely they are to catch an error) and our new term:

Three things now determine each other jointly, period over period:

1. Vigilance (effort) ← prior belief of the model’s actual error rate

2. Belief ← current true error, the analyst’s attention decay, and effort

3. True error ← prior true error, analyst effort, and the model’s feedback improvement efficiency

There’s no closed-form solution since we need to solve a recursion with three conditions. However, as shown in the graphics above, with some chosen parameters we can display the dynamics over time.

Result. Compounding effects:

Attention decay suppresses actual effort below what the analyst believes they’re delivering (same as earlier model where the AI doesn’t improve)

→ lower realized effort now affects the AI model’s actual performance improvement

→ slower improvement (fewer errors caught means fewer opportunities to feedback the system)

→ lower ceiling on what belief can ever converge to, even if effort later recovers

→ true error always > zero (always some positive error residual)

Attention decay does not just slow this process down. It leaves the system stuck at a strictly worse permanent error rate than the no-decay case would have reached, because the window for real improvement closes sooner.

Implication. In every version of this model built so far, the human side’s failure was a failure of measurement, a belief drifting away from an unchanging or a moving truth. Analyst fatigue doesn’t just lose track of how good the AI is. Given enough time, they can be the reason it never gets as good as it could have.

Memo to management. There are some potential solutions here, but some underlying limitations.

Necessary information:

• model’s true starting error rate. Whatever the consultant/vendor says, the stochastic nature means the best we can do is probabilities, and maybe widely dispersed ones at that

• company’s loss per error. If the task is simple enough, this can be contained to a definable set. But companies often don’t have this info on hand as much as you’d think.

Solution:

• increasing bonuses. Incentive has to scale to compensate for the belief that errors are harder to find.

• rotating reviews. It’s easy enough to measure how long people are spending on reviews (though employees hate it). But acknowledging attention decay is pretty universal, so keep teams rotating pretty often to cutoff fatigue earlier. However this imposes some additional organizational cost.

The author is nonresident senior fellow at

Who approved this decision?

Maybe you saw that recent story where a bank deployed an AI agent?

“…[It] approved a $1.4 million commercial line of credit. No human reviewed it. No human knew it had happened…nobody was sure exactly who was accountable.

Six weeks later, the agent was rolled back to a lower autonomy tier. Not for a model reason…The decision was operational: The people supervising the agent had stopped looking at the screen.”

There’s a self-limiting paradox at play in agentic AI quality, fed by a natural human tendency. When a company launches an AI system, the general cycle goes:

1. Human oversight begins diligently (“management says carefully review every case”).

2. Periodic reports show increasing accuracy across analyst reviews. Override rates starting at 14% go to 8% eventually migrating all the way to 2% after a few months.

3. The company feels increasingly confident in the system’s accuracy, with good reason! They become more productive by speeding up reviews.

4. PROFITS!

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But our analysts spend less and less time on each review, for two reasons:

• Statistically, overrides only occur about 1-in-50 cases. Fairly infrequent. Plus experience has taught them where to look for mistakes. “This must be how we exploit productivity gains from AI,” she thinks. “It’s supposed to make us quicker.”

• Productivity aside, humans suffer attention decay.1 Eventually tasks like looking for a rare occurrence results in declining diligence. What psychologists call “vigilance decrement.”

It turns out our mistake rate only looks like it dropped to 2% because HUMANS missed more of them. Type II errors increased. The false sense of improvement combined with our own tendency made us worse off.

That’s all before adding in task fatigue. I wanted to see if I could model this and extrapolate out where (if anywhere) it ends up.

Conductor: “This is Bottom Line. Last stop before Math-town!”

RESULT: We find you’re basically either in “hell yah!” or “dear god!” territory. Through no fault of anyone, you go speeding toward:

full effort and accurate assessment of the AI model

OR

zero effort and full confidence in an inaccurate assessment.

→ Losses pile up and you have no idea why

Graphic Results

Formal Model

Narrative Description

The intuition is we have a principal-agent problem (literally). At first I thought it was between the analyst and the AI agent, but realized it’s the same old manager-employee. The AI agent is mechanical. Putting aside operating costs, the agent isn’t subject to fatigue, or incentives to shirk.2 Its productivity is entirely a function of its internal design quality and human review effort.

We imagine a company like above. The agent automatically processes cases (applications) which analysts subject to review. Per the story, companies control the frequency of reviews but analysts choose the intensity: total time on each review.

Reviews are not costless, nor are errors.

• ANALYST: bears a cost based on how diligently they review, but they also get some payoff from every error caught (a bonus).

• MANAGEMENT: bears a fixed cost for each error that gets missed. They choose the size of bonus for actual detected errors.

• AI AGENT: doesn’t choose anything, but it’s true accuracy at any time is unknown to humans, who can only make estimates based on observations (i.e., the more you review the more you know).

THIS SETUP ALSO FULLY MIRRORS A BUG BOUNTY PROGRAM, LIKE A FIRM CONTRACTING WITH WHITE HAT HACKERS USING AN AI AGENT.

Formal Description

Parameters

ε - the AI model’s true error rate (fixed), directly unobservable to management and analysts

ε̂_t - belief of ε, equal to prior period’s observed error detection rate

L - fixed loss to management per undetected error

γ - analyst’s convex cost of effort

π - bonus to analyst for every caught error

v - effort (vigilance) level; from non-zero to one. The probability an error is caught

Analyst problem. The analyst chooses diligence v ∈ (0,1] to maximize:

yielding an optimum effort v*:

In equilibrium, effort follows beliefs about the model’s error rate. As belief about AI error rate ⬆️ → effort ⬆️

Management problem. Management's expected cost per case is made up of bonuses plus loss from undetected errors:

Substituting the analyst’s optimal response effort, yields in equilibrium an optimal bonus level:

Bonus level is purely a function of how big the loss from an error is, nothing else.

Error rate belief is based on prior period’s observed error rate, which is itself a function of the true error rate and review effort level.

Substituting the analyst's optimal response v* along with the optimal bonus expression π* gives a first-order recursion:

Result. There are two possible outcomes and they are both corner solutions.

• Good: When the cost of effort γ is sufficiently cheap, and the loss from errors L sufficiently large such that r > 1, analysts converge to maximum effort and belief of the AI model’s accuracy moves to the actual accuracy (ε̂_t = ε), whatever that may happen to be.

• Bad: When effort is costly relative to loss from errors such that r < 1, analyst effort collapses to 0 very quickly in response to believing the model has a higher accuracy. It quickly collapses toward 0 (ε̂_t → 0).3

Implication. No stable equilibrium exists in-between. It doesn’t matter where your starting assumptions are. The software’s vendor may sell you on some amazing accuracy, or the skeptical manager could declare “this thing is definitely 100% wrong,” at the outset. In the bad outcome, you get a few periods of informative data and after that you’re cooked. But in the good outcome it’s the same thing but the other way and you end up at a stable productive place.

Memo for Management.

• For a real-world case, the loss term L is not something easily manipulated by anyone. An AI makes a bad loan decision, it was randomly drawn from the pile — they can’t ahead of time pull a lever to change the cost to the bank. However, somewhat unintuitively, they could limit the AI’s scope to just the highest dollar loans, increasing that pool’s average cost which increases the optimal bonus. That probably sounds scary to a typical bank management.

• The other part is the “cost” of detection. Fortunately, this is a reducible factor. Models generally are becoming more user-friendly, more intuitive, more natural language fluent. Also adjacent processes are not fixed. Businesses like our hypothetical bank are built on process improvements: workflows, data management, employee training, etc. Things they invest in all the time.

Ultimately it also depends on the actual quality of the model, there too they're overall improving. But quality is just not fully knowable ex ante. You’re left relying on someone else’s evaluation, and in a world without standardization to boot.

Formal Model (Extension): Attention Decay

Narrative Description

The setup is the same, except now we account for attention decay. Looking for a needle in a haystack gets tiring after awhile. Even a well-meaning analyst exerts the optimal amount of effort per their incentives, but unknowingly their vigilance becomes less effective over time.

You can think of effort v as representing the number of minutes they spend on each review, but those minutes are less effective the more they do. And they don’t realize it.

Formal Description

New Parameters

δ_t ∈ (0,1] - the decay parameter, declining over time; multiplied by effort level

δ_tv_t* ≡ effective effort level

r_t - the threshold condition as before

The analyst continues to solve for v_t* (now time-varying to accommodate decay) that maximizes their payoff expression, but they do not observe this time-decaying effort δ_tv_t* is what’s actually being applied.

The recursion condition becomes:

Result. The possible results are same as before, with good and bad edge equilibriums, but now the threshold is moving.

It’s still defined at r_t ≶ 1. But since δ_t is declining, temporarily being in the good space (r_t > 1 ) can flip into the bad one (r_t < 1). Even without anything else changing. And once crossing into the bad-outcome space, the collapse is geometric and never recovers.

Two analysts, one with and one without the decay condition, would be indistinguishable, to themselves and others.

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The author is nonresident senior fellow at

Elsewhere I explored a bargaining model describing a legislative body with a one or near one-seat majority, resembling the current makeup of the House of Representatives. Some plausible assumptions are necessary but I believe the model credibly describes the nature of individual caucus holdouts’ leverage in such a scenario based on predictions mirroring recent bill negotiations.

But that model treated the negotiation as existing between “leadership” and a mutually exclusive faction of individual holdouts, each bargaining separately for their own desired outcome.

A recent paper by colleagues and explores how what we would more properly think of as factions have and can function in Congress. Putting aside their normative claims for now, it prompted me to consider extending the earlier model to more realistically account for factions in a legislative bargaining model.

First I briefly recap the consistent elements which carry over and then restate the implications.

Then I describe the extension and characterize it’s predictions for legislative outcomes.

Base Bargaining Model

F is the set of pivotal holdout members — members who can’t be substituted for alternative bargainers. Each individual holdout is indexed i. Membership in F_i is established beforehand. Leadership (L) acts as the sole proposer.

Variables:

• x — the policy outcome, running from 0 (leadership’s baseline bill, no concessions) to 1 (a fully-conceded bill matching a holdout’s ideal).

• u_i(x) — holdout i‘s payoff from the bill passing at concession level x; utility increasing in x.

• c_i(t) — holdout i‘s own cost of delay, as a function of time t remaining before the deadline. A safe-seat member has a low, close-to-flat c_i(t); a vulnerable-seat member has a steep one.

• d_i — the disagreement point: what member i gets if bargaining collapses entirely and no deal is reached.

• c_L(x) — leadership’s cost of granting concession x, increasing in x.

• c_L(t) — leadership’s own cost of delay. Convexly increasing in t.

• π(t) — the probability, at time t, bargaining collapses to the disagreement point rather than resolving at baseline.

• x_i* — holdout i‘s equilibrium reservation demand: the minimum concession they’ll accept.

Implications:

• An individual holdout’s leverage is determined by:

  • cost of delay (idiosyncratic to the member)

  • divisibility (a characteristic of the bill itself)

  • ratio of cost of concession (leadership) to value of concession (holdout)

• Leadership cost of delay non-linearly increasing (convexity) - this is an assumption built in to the model

Extension: Multiple Factions, One Shared Capacity

The base model treated the bill as a single scalar x and F as one holdout vector. Not all bills are single-ask, and once you look at recent cases side by side, two structurally different kinds of concession show up — and the base model’s existing machinery can tell them apart without adding anything new.

A SALT-cap fight and a Speaker election are different kinds of bargain. SALT is divisible: only members from high-tax states actually value it; a member from a no-income-tax state is indifferent.1 A Speaker vote is indivisible: it’s binary, and pays off identically to every member who backs the winning side regardless of how many others join them.

The bill becomes a vector, X = (x₁, ..., x_D), allowing severable dimensions, each one of the two types above.

Divisible dimensions get a support set — the subset of members who actually have a stake.

Outside F_j, u_i(x_j) = 0, the member is indifferent. Each divisible dimension then runs the original scalar bargain, unmodified, restricted to its own F_j. The faction on this dimension is the set of members for whom the concession is worth something.

Indivisible dimensions are where a faction’s size becomes the live question, and here the existing budget constraint (2n + p < m) supplies the threshold, just read from the faction’s side rather than leadership’s:

Below k_min, adding members increases the faction’s blocking weight. At k_min, the faction is already sufficient — leadership can’t pass the bill without them — and additional members past that point buy the faction nothing.

w_F(k) is the aggregate “blocking” leverage. Extraction per member peaks exactly at sufficiency and dilutes past it.

Because leadership’s tolerance — c_L(t), and the same vote-budget constraint — is one finite resource, dimensions with completely disjoint memberships and zero utility overlap are still implicitly drawing on the same capacity. Satisfying one dimension’s demand consumes some of what’s available for every other active dimension:

A bill with a single indivisible dimension at the one-seat margin collapses k_min to 1 — a faction of one is sufficient — and the extension returns the original single-holdout result unchanged.

The extension applies to margins wide enough that multiple severable asks can be live at once, but narrow enough that a rival coalition still can’t credibly bid for defectors.

Comparative statics (testable directional claims)

1. The number of concurrently active factions on a bill tracks the number of severable, divisible dimensions it carries — not the size of the margin.

2. A concession granted on one dimension tightens what’s available on every other simultaneously active dimension, even where factions share no members and no overlapping preferences, because leadership’s capacity is one shared, finite resource. Early concessions will be bigger.

3. An indivisible vote (e.g., Speaker vote) collapses to the base model’s single-faction case, with per-member extraction maximized at exactly the sufficiency threshold and falling past it.

Conclusion

Most of this is intuitive once stated, but a couple of things fall out that aren’t:

• The relevant predictor of how contested a bill will be isn’t the margin alone, it’s how many severable asks the bill happens to bundle. A wide majority carrying one clean, indivisible ask (a debt-ceiling raise with a single up-or-down rider) behaves like a razor-thin majority with one holdout — the margin matters less than the bill’s structure.

• “The faction” isn’t a fixed roster across bills — it’s whoever has a stake in that bill’s specific dimension. The functional membership on a SALT fight and on a debt-ceiling rider can be entirely different people, even when press coverage uses the same caucus label for both.2

• Bundling is a lever leadership can pull deliberately, not just a feature of how a bill happens to get written. Combining several divisible asks into one vehicle forces factions that would otherwise bargain independently to draw on the same finite capacity — which can dilute any single faction’s leverage, or just as easily create a more fragile package that any one faction can sink.

Predictions

1. OBBBA-style tax bills: where there are several divisible elements (SALT, sector carve-outs), concessions should land unevenly by order of resolution — factions that lock in early get closer to their ask; factions still bargaining once earlier concessions have drawn down leadership’s capacity settle for less, independent of their own underlying leverage.

2. A debt-ceiling bill carrying a single rider: treat it as the indivisible case — expect a faction size near k_min among holdouts, no internal division of the concession, and a resolution profile matching the original model's shutdown/deadline predictions (clustered near the binding constraint) rather than the OBBBA pattern above.

3. Appropriations omnibuses: holding margin constant, expect smaller per-faction concessions as the number of bundled asks rises — a crowding effect distinct from the deadline-clustering prediction from the base model.

That’s the band Wallner and Dayton are actually describing: DSG, RSC, Freedom Caucus and 2023 Speaker fight — none of them one-vote margins. The model’s prediction for that regime: a bloc holding at exactly k_min (Freedom Caucus, enough to deny McCarthy, no more) should out-extract, per member, a larger bloc with equivalent aggregate blocking power but more internal heterogeneity (RSC, historically).

The author is Nonresident Senior Fellow at the Foundation for American Innovation

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In a recent newsletter I scratched out a simple growth model showing how “regulation” (broadly defined) could be conducive to economic growth by facilitating innovation.

The basic intuition is this: a portion of labor focuses on things like scientific research and discovery which produces the new ideas which we call innovation. But in a new emergent field, a portion of these PhDs and other high-skilled workers have to spend time reconciling different methods and terminology so those new ideas can maximally recombine and build on each other to produce the next innovative iteration. A form of regulation can reduce this “translation drag” as a coordination mechanism: defining terms, establishing common measurement rubrics, facilitating interoperability, and so on.

Nobel-laureate Paul Romer’s canonical endogenous growth theory provides a tractable model on which to scaffold this idea. His includes a variable to account for specialized labor devoted to discovery of new ideas which is a core driver of economic growth in his story.

Below I briefly restate his base model before explaining two extensions introducing regulation as a variable in different ways.

Here regulation is a broadly applicable term, and later allows for non-governmental regulation such as self-regulatory organizations or quasi-private institutions.1

Base Romer model (w/ knowledge spillover)

Narrative description: labor devoted to adding to the stock of knowledge is the source of innovation-driven growth. Beyond the actual amount of labor, this is subject to the effectiveness of this work (research), and degree to which new ideas feed into and interact with other ideas.

Formal description:

A = knowledge stock, L_A​ = total pool of skilled R&D labor, δ = research productivity, β = knowledge-spillover parameter.2

Implication: growth depends on A which increases in level one-time through an increase in R&D labor if β < 1, or in growth rate if β = 1.

Extension 1 — regulation as coordination

Narrative description: in the absence of regulation, a portion of skilled R&D labor gets peeled off to work on interpretation, translation of existing ideas in lieu of producing new ones, creating translational drag on growth potential. Regulation can reduce translational drag but imposes it’s own cost (compliance). The effect of regulation is a priori ambiguous.

Formal description: instead of R&D labor (L_A) going entirely to production of the knowledge stock, some is peeled off into resolving knowledge frictions. The diverted R&D labor (L_R) then is characterized as:

θ = share of skilled labor (L_A) going to knowledge production, bounded by θ(R) ∈ [0,1]. R is the regulatory level: at R = 0 no regulation and maximum translational drag; at R = 1, maximum regulatory drag.

Effective knowledge-producing labor is the remainder, L_A − L_R = θ(R)L_A​, giving:

θ(R) can be further decomposed as:

T(R) = translational drag (decreasing in R), C(R) = compliance drag (increasing in R). Optimal R* maximizes θ(R):

Implication: Regulation’s effect on growth (via innovation) is optimally ambiguous, but non-zero. At R = 0, some of L_A​ is occupied with reducing translational drag. Adding regulation from zero frees more labor into direct knowledge production faster than it adds compliance burden. There is an optimal R* where the two marginal effects exactly offset which is an improvement in innovation from the baseline no regulation case.

Extension 2 — government v. industry regulation

Narrative description: There are now two types of regulatory regimes. (1) government-issued OR (2) industry-issued, via a Self-Regulatory Organization (SRO) or similar standards-setting body.3 One regime is chosen exclusively.

Government rules lead to 100 percent adoption across the industry, but will be further from a theoretical ideal set of rules (being more intermediated by political incentives and other frictions). SRO regulation is closer to the ideal in substance, but has only partial adoption (never fully reaching 100 percent).4

Formal description: Regulation R is now split into government (R_g) and voluntary (R_v). Both are subject to different coefficients for adoption level a and substantive quality (fidelity) φ. Under either regime, the other is set to zero.

• Adoption: a_v(R_v) ∈ [0, ā], ā < 1; a_g​= 1

• Fidelity: φ_g​, φ_v​ ∈ [0,1], φ_v > φ_g (note: phi renders slightly differently in LaTeX below)

Adoption and fidelity both discount the effective quantity of regulation entering a single shared drag-reduction function τ, which is common to both channels, lower-bounded by 0, characterized by decreasing marginal returns.

Only one regulatory regime operates (government-issued OR SRO-issued):

Under government regulation, translation and compliance costs are given by:

So total combined effect is:

Which optimizes at R_g* such that (same as Extension 1, before expanding):

Under voluntary regulation, translation and compliance costs are given by:

Combines as:

Optimizes such that (requiring cross-partials since adoption is now also a factor):

First-order conditions for each given by:
R_g:

R_v

Government is optimal when:

Voluntary is optimal when:

Implication: Government regulation is preferable when the translational drag it removes, net of what it costs to comply, exceeds what the best voluntary standard could net after accounting for the same tradeoff. Because of universal compliance, every dollar of Cg​ is paid, and every unit of τ is realized.

Voluntary regulation is preferable when it’s fidelity advantage (φ_v​>φ_g) is sufficient to compensate for adoption holdouts.

Empirical question: to what degree is SRO/industry-developed regulation higher quality than mandatory government-issued regulation. We assume it is higher-quality to some degree in the model but the magnitude is important here. It has to compensate for what’s lost to non-adoption (free-riders).

If you suppose the policy regime is such that industry-developed rules are “voluntary” in the sense of how they are developed and who can participate, but nonetheless legally binding, then this approach will always be superior.

Hypothetical Illustration: (assuming baseline growth ≈ 3%, δ = 0.08, L_A ​= 1, A^β-1 = 1)

g_A(R_g) / g_A(R_v) / g_A(0)

The author is Nonresident Senior Fellow at the Foundation for American Innovation

How much damage can one Representative do?

James Wallner’s new concise essay (“The Tiny Rule That Can Paralyze Congress”) breaks down the peculiarities of House pathways for partisan bills in a tight margin majority.1 I’m not much interested in politics per se, only how it constrains the policy choice set.

Which got me thinking about the bargaining dynamics of a one vote or near one-vote margin majority, and whether a model could functionally describe such a Congress in a way that tells us something about how different types of votes will unfold.2 The result is somewhat intuitive, even obvious, predictions but also some less intuitive testable claims from a closed-form normal game. And that it tracks our observed recent history is a soft indicator of plausibility.

Modeling the situation

The foundation

The literature on bargaining and specifically bargaining in a legislative structure is extensive. There are some canonical and robust foundations on which to build.

• Riker’s (1962) “Minimum Winning Coalition”3 theory describes a rational proposer minimizing coalition size to maximize each member’s share of a fixed surplus.

  • Baron and Ferejohn (1989)4 formalizes Riker’s theoretical model and supports the MWC outcome.

• Groseclose and Snyder (1996)5 offer a consistent bargaining setup except with a rival proposer which predicts competitive bidding to “buy” pivotal votes. Ultimately I do not believe this describes the current House makeup because it requires the competing coalition (in this case Democratic minority) to demonstrate a non-zero value in buying off a defector. However it is instructive for recent specific examples, one of which I witnessed first hand (more below).

• The Rubinstein (1982)6 characterization is a generalizable alternating-turn bargaining game revealing that parameterizing “impatience” (cost of delay) is critical to describing an equilibrium. Again the premise, per Riker, is there is a fixed surplus from which to distribute shares, to which delays in a successful outcome (this case passing a bill) imposes differing costs on the bargaining parties and therefore affecting leverage.

  • Observable delay indicates incomplete/private information and information revelation models per Kennan and Wilson (1993)7 (strikes as costly signals of credible commitment).

• I believe the model describes equally a situation where there is a single pivotal marginal vote or more than one (within some bound well outside the current situation) because it does not rely on sole holdup power as a sufficient condition to establish bargaining leverage. Shapley and Shubik8, Banzhaf9, and Owen10 are canonical contributions supporting legislative bargaining as not a purely individual, but effectively coalitional blocs game.

Structural elements from the above inform the model.

The Model: Narrative Description

The players

In this model we imagine “leadership” is the proposer, with the implicit ability to set the agenda by limiting floor consideration of other legislation. Negotiating with leadership is a “faction” of holdouts. The faction isn’t a unified or otherwise coordinated bloc (though it can be). It is collectively the undetermined number of individual members, each unrestricted to have their own preferences. But we can include them singularly in one vector without loss of generality.11

The bill

They’re bargaining over the outcome of a single bill with a range of policy outcomes. At one end is leadership’s ideal outcome, and at the other is the holdout’s. Because the collective faction is a heterogeneous set of individual holdouts, the policy range is an index that allows the variable to represent the preferred outcome for that member specifically.

Accordingly, a holdout’s ideal is at one end of the outcome range, but there is some point below that sufficient for an agreement because holdout is not costless (“constraints”).

The constraints

Both leadership and holdouts bear some cost from delay, individuated for the holdouts. The latter’s cost is tied to electoral risk: for example a super-safe district, high reelection expectation, means the member can bear more delay at less cost. Leadership may bear more of the cost of missing a debt limit deadline, forcing a government shutdown, or inability to get on to other substantive priorities, because they bear a broader caucus-wide electoral incentive to show a functioning majority.

They also of course bear some cost in moving from their preferred policy outcome toward a holdout’s. Also more time goes by, there’s an underlying increase in the likelihood of breakdown and no one gets anything.

The Model: Formal Description

Players

F is the set of pivotal holdout members — members who can’t be substituted for alternative bargainers. Each individual holdout is indexed i. Membership in F_i is established beforehand. Leadership (L) acts as the sole proposer.

Variables:

• x — the policy outcome, running from 0 (leadership’s baseline bill, no concessions) to 1 (a fully-conceded bill matching a holdout’s ideal).

• u_i(x) — holdout i‘s payoff from the bill passing at concession level x; utility increasing in x.

• c_i(t) — holdout i‘s own cost of delay, as a function of time t remaining before the deadline. A safe-seat member has a low, close-to-flat c_i(t); a vulnerable-seat member has a steep one.

• d_i — the disagreement point: what member i gets if bargaining collapses entirely and no deal is reached.

• c_L(x) — leadership’s cost of granting concession x; increasing in x.

• c_L(t) — leadership’s own cost of delay; convexly increasing in t.

• π(t) — the probability, at time t, bargaining collapses to the disagreement point rather than resolving at baseline.

• x_i* — holdout i‘s equilibrium reservation demand: the minimum concession they’ll accept.

The holdout equation says member i accepts a given offer only if the payoff from that offer, net of current delay, is at least as good as their risk-weighted expected payoff from walking away.

Division vs. size are two separate levers.

• Division is governed by the ratio of leadership’s cost of delay to the holdout’s own — the more impatient leadership is relative to the holdout, the more of the available concession goes to the holdout.

• Size is governed by the ratio of how much the holdout values a unit of concession relative to how much it costs leadership to grant it. A concession can be cheap for leadership and valuable to the holdout.

The budget constraint is the vote-counting condition: n is the number of GOP holdouts casting an outright “no”, p is the number “present” or “absent,” m is the raw seat margin (R − D). A “no” costs the coalition two points of margin, a “present/absent” costs one, and leadership’s total tolerance is the margin minus one.

Comparative statics (testable directional claims):

1. leadership’s rising cost of delay near a deadline increases level of concession.

2. a holdout’s own rising cost of delay decreases what they extract.

3. a more favorable ratio of the holdout’s valuation to leadership’s cost of granting it (i.e., more divisibility) increases what they extract, independent of patience.

Payoff Matrix

“Lawler case” refers to Rep. Lawler’s demands nearing passage of the 2025 tax bill (OBBBA). In contrast to Rep. Luna, he is in arguably the most competitive district in the country which makes the implied cost of blowing up the bill incredibly high. But in our model a comprehensive tax bill is highly “divisible” and offered a large payoff (SALT deduction) if he is successful (which he was).

Conclusion

Okay so most of that you could draw from intuition, not exactly pathbreaking. But here’s a couple implications that are perhaps not so obvious:

• News reporting tends to focus on the naive partisan margin at any given time as shorthand for the bargaining dynamics. In a sense that tells you who is “in the room” as a candidate for being pivotal vote but it is incomplete. Two (or more) members can be equally likely to be pivotal (“pivotality” in the literature) but get widely different results.

• It is determined by:

  • cost of delay (idiosyncratic to the member)

  • divisibility (a characteristic of the bill itself)

  • ratio of cost of concession (leadership) to value of concession (holdout)

• Leadership cost of delay non-linearly increasing (convexity) - this is an assumption built in to the model

• High drama like shutdowns and extended speakership ballots are the result of imperfect information, a means of information revelation. In earlier times of old-fashioned logrolling, leadership already has a good idea of how much it costs to “buy” a member’s vote.

Predictions

1. NDAA/SAVE Act: House leadership offered Rep. Luna a package as a single vote, but still remain textually separable. This was the “cheaper” offer which she rejected. She has now signaled credible resolve by bearing real cost and has a safe seat. The model prediction is that we’ll end up with something resembling her ask: the bills are actually linked into the same text to be voted on (NDAA+SAVE). Doesn’t guarantee Senate can’t undo it but they do now bear a higher cost of doing so.

2. Appropriations/shutdowns: less clean and fairly familiar. Concessions will cluster in the final 24-72 hours before deadlines.

3. FISA: because as I understand it much of the FISC certifications effectively run through March 2027, we haven’t approached the meaningful deadline which is why we didn’t see much bargaining/concession - leadership’s cost function never reached the spiking point. We’ll see that happen in the Spring.

Potential Empirical Testing & Extensions

Empirical

• Input Cook PVI scores to specify the electoral risk parameter (which inputs to delay cost). Compare predicted level of concessions with actual ones for sample of major bill fights.

• The literature has multiple methodologies for computing a “power index” by tabulating across conceivable winning coalitions, based on voting pattern, what is a given member’s pivotality. The model then provides a testable prediction going forward.

Extensions

• Like James points out the unfolding of coalitions and bargaining is not fully instrumented by votes, but all the procedural maneuvering and minutiae strategically deployed leading up to a vote (or preventing altogether). This accounts for none of that. Could be possible to introduce some elements as an additional leadership lever.

• d is what a holdout gets in a no-deal scenario, but it’s exogenous right now. Possibly it can be derived endogenously from an election subgame.

• Policy space exists across a one-dimensional scalar x. Of course not always the case so could be made multi-dimensional but increases complexity considerably.

• This represents a one-shot normal form game. In a repeated game you can include carryover effects which feed equilibrium strategy, like credibility or reputation.

[ maybe you have thoughts]

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