The value of information: why continuous ingestion follows

What a signal is worth before you have it

Suppose you face a decision under uncertainty, and someone offers you a look at a signal before you choose. What should you pay for that look? Decision theory gives a precise answer. The value of information is the difference between two expected payoffs: the payoff you get making the best decision with the signal in hand, and the payoff you get making the best decision without it. Nothing more mystical than that. It is a difference of two optimisations, and it can be computed the moment you can specify the decision.

Two properties fall out immediately. First, the value is bounded above by the expected value of perfect information — the payoff of deciding under total certainty minus the payoff of deciding under the uncertainty you actually face. No signal, however detailed, can be worth more than knowing everything, because knowing everything is what perfect information means. Second, the value can be exactly zero. If the signal cannot change which action you would take — if you would drill the well, or hold the stock, or irrigate the field, regardless of what the signal says — then the signal is worthless to you, however novel, however large, however scientifically interesting. Value of information is not a measure of how much you learn. It is a measure of how much a decision moves.

This gives the concept its discipline. It refuses to treat information as a good with intrinsic worth, the way a barrel of oil has worth independent of any particular use. Information is only ever worth something relative to a decision that is still open. Close the decision — commit, or make the outcome irreversible — and the same signal that was priceless a moment before becomes worth nothing. The concept is therefore inseparable from timing: not just what you know, but whether you still have a choice left to apply it to.

Where it came from

Ronald A. Howard formalised the value of information in the mid-1960s, in work that also coined the term "decision analysis." His paradigm case was industrial: whether to drill a wildcat oil well. A prospect with, say, a one-in-five chance of paying off has a negative expected value on its own. A seismic survey costing a few hundred thousand dollars might be worth commissioning — but not because the geology it reveals is intrinsically valuable. It is worth commissioning only if the survey result could flip the drill/no-drill decision. If the company would drill regardless of what the seismic data show, the expected value of that information is zero, and the survey is a waste of money dressed up as diligence.

Howard's formalism sat on older foundations. Abraham Wald's sequential analysis, built in the 1940s for wartime munitions inspection, priced the decision of whether to inspect one more shell before deciding to accept or reject a batch — an early instance of asking what the next data point is worth, rather than assuming more inspection is automatically better. David Blackwell's 1953 comparison of experiments gave the deeper result: one information structure can be shown to dominate another for every possible decision-maker, independent of their specific payoffs, which is what makes value of information a property of the signal and the decision problem jointly, not a matter of taste.

The concept then propagated into fields with hard money and hard lives attached. Clinical trials schedule interim looks at accumulating data using boundaries — O'Brien–Fleming spending functions, for instance — that permit a monitoring committee to stop a trial early for efficacy at a very strict threshold, while keeping the overall false-positive rate near the conventional five per cent. Each scheduled look is a purchase: the option to stop sooner, at the cost of statistical power spent on looking. Electricity markets do something structurally identical when they price forecast horizon. A wind forecast that improves six-hour-ahead accuracy by a few points is worth something not because meteorology is admirable but because it changes which generating units get committed, and in markets where a five-minute price can clear at $2,000 per megawatt-hour against a day-ahead price of $40, that changed commitment is worth real money.

The turn

Large Language Models, Large World Models and Large Universe Models are usually ranked by what they can do — language, then embodied scenes, then something more encompassing. Value of information suggests a different ranking: by what their information costs, and when that cost is paid.

A Large Language Model holds a corpus frozen at a training cutoff. Its information is free at query time — you already have it, no signal need arrive — but its value against any decision sensitive to what has changed since the cutoff decays toward zero as the world drifts from the snapshot. The seismic survey analogy is exact: a report on the geology as of five years ago is worth nothing to a drill decision if the field has since been drained.

A Large World Model buys information at the moment of action — observing a scene while it is present, which is precisely where value of information is highest, since a decision is live and the signal can still change it. But the purchase is narrow and temporary: only what the current scene emits, and only for as long as it is being watched. Close the scene and the position lapses, exactly as a decision closes and the same information goes to zero.

A Large Universe Model is the position that holds streams open past any single decision — maintaining revisable beliefs, with provenance tracking where each belief came from, so that a signal is already present, at the price already paid, when a decision becomes live. Provenance is not decoration here; it is required, because pricing a signal against a decision requires a likelihood, and a likelihood requires knowing how reliable the source is. This is the economic content of the third position: not more knowledge, but a standing subscription against decisions not yet identified.

What is not being claimed

The claim reduces every argument for continuous ingestion to an expected-value-of-information calculation, and that calculation has a ceiling: the expected value of perfect information. There is no fourth category of evidence past "perfect information about every live stream," because that phrase is the analytic maximum of the quantity in question. What remains beyond it is not new kinds of signal but better likelihoods, cheaper sensing, faster propagation — refinements within the ceiling, not above it.

The common misreading says the opposite of this: that more data is always worth more, so a system that ingests continuously must dominate one that does not, by definition. Value of information refutes that directly. A signal worth nothing stays worth nothing no matter how much of it there is, and once sampling costs are subtracted, net value routinely goes negative well before perfection is approached. The defensible claim is narrower and less flattering: continuous, provenance-tracked intake is the terminal position on the axis of what may be observed, not a guarantee that observing more pays.

Three objections earn a full hearing, because at least one of them should narrow the claim rather than merely qualify it.

Expected value of information only exists inside a fully specified decision model — known actions, known payoffs, known likelihoods. Open-world systems rarely have any of these. Calling continuous ingestion "priced" borrows a rigour the setting cannot support.

This is correct as stated, and it does narrow the claim. What survives is the structure, not the number: information has value only through decisions, and that value is bounded, even where the full computation cannot be run. In practice the computation is done on narrow slices — this well, this dispatch interval, this interim analysis — and those slices are exactly where continuous ingestion gets defended or refuted with evidence rather than intuition. Where no slice can be named at all, the honest position is that the ingestion is unpriced, and should be justified on option value, if at all — not smuggled in as decision-theoretic pricing it hasn't earned.

The framework says nothing about cost. Continuous streams carry acquisition, storage, reconciliation and attention costs that scale with volume, while marginal value falls fast. The optimum is nearly always partial observation with a stopping rule, not everything, continuously.

Also correct, and this is the discipline the whole thesis needs rather than a threat to it. Net value of information — gross value minus sampling cost — peaks well short of perfection in almost every real case; sequential sampling theory exists because of exactly this. "Everything, continuously" names the outer boundary of what can be observed, the way perfect information names the outer boundary of what can be known. Real systems live inside that boundary and choose a stopping point. The claim is about where the boundary sits, not about where any sensible system should operate relative to it.

Monotonicity fails outside ideal single-agent Bayesian settings. Information can arrive faster than decisions can absorb it, producing alarm fatigue or premature commitment; in strategic settings, information becoming common knowledge can destroy value for everyone holding it.

This is genuine, and it is documented — information disclosure collapsing insurance markets, trials stopped early because looking too often inflates false positives. The reply is that these are failures of decision architecture and of miscalibrated likelihoods, not indictments of intake itself. They argue for provenance, calibration, and explicit rules for when to ignore a signal — which is precisely what separates a Large Universe Model, as an argued category, from an undifferentiated firehose.

What the concept establishes is narrow and should stay narrow: continuous, provenance-tracked intake is the last rung on the ladder of what can be observed, because "everything, continuously" is the terminal case of the quantity that decision theory bounds. What it does not establish is that opening any particular stream pays, that more looking beats a well-chosen stopping rule, or that intelligence itself has nowhere further to go. Those are separate, ordinary, often unflattering calculations — and value of information is precisely the tool for refusing to skip them.