In 1968, the American Statistical Association and the National Bureau of Economic Research began a quarterly survey of professional forecasters. Alongside the average forecast, the individual responses made disagreement measurable: not the prediction for inflation or growth, but how far apart the predictions were. The forecasters were reading the same data, using broadly the same models. They disagreed anyway, and through the inflationary 1970s they disagreed more. The question of whether high inflation was temporary or permanent had divided the profession into camps that no longer found each other’s reasoning convincing. The price regime did not settle the argument until Paul Volcker forced the matter at the turn of the 1980s. The argument itself, though, had been visible and measurable for years before the prices turned.
This reverses the usual order of attention. We watch prices and treat the beliefs behind them as private, knowable only after the fact. But beliefs leave a measurable trace of their own: disagreement, which can be counted directly.
What kind of problem is this?
A market regime is a kind of agreement. Through the long low-inflation period that followed Volcker, most participants came to share a working model: central banks could and would control inflation, and growth, not inflation, was the main risk to manage. That working model held for the better part of three decades, and through the low-and-stable-inflation years of the 2000s and 2010s it also held that government bonds would rise when equities fell. It was a settled view about how the world was arranged, and it organised everyone’s behaviour around itself.
When what matters is whether a population of interacting believers will hold together or split apart, and when the early evidence of a split may appear in the spreading of views before it is visible in slow price summaries, that is a specific shape of problem. And the discipline that has thought most rigorously about how the opinions of many interacting agents evolve is opinion dynamics, a branch of the statistical physics of social systems.
So let’s borrow.
This is the multi-model move: recognise the shape of a problem, find the discipline that has thought rigorously about that shape, and import its frameworks deliberately rather than reinventing them from scratch.
Opinion dynamics was developed from the 1970s onward by mathematicians, physicists and social scientists, built for abstract agents who each hold a number, exchange it with others, and update by simple rules. Markets do not satisfy its assumptions cleanly: beliefs are not single numbers, the views are entangled with prices and incentives, and the networks of who listens to whom are unobservable and shifting. But the structural logic transfers: whether a population of interacting believers converges on one view or fractures into stable factions depends not on how far apart they are but on whether their disagreement stays bridgeable, and that leaves a measurable trace in the spread of their views.
Start with the simplest model of social learning, set out by Morris DeGroot in 1974. Imagine a group of people, each holding a number, say their estimate of some uncertain quantity. At each step, every person replaces their number with a weighted average of those held by the people they listen to. DeGroot showed that under broad conditions this process converges. The numbers come together, and the group settles on a single shared value. Repeated averaging, across a connected group, manufactures consensus.
This is a slower mechanism than common knowledge, where shared belief turns on what everyone knows that everyone else knows and can shift in an instant. Gradual averaging instead leaves a continuous, measurable trail of disagreement on the way to agreement.
It is a clean account of why agreement is the normal state. Markets are connected groups revising toward those they respect, and such a group tends to converge; a settled regime is the visible form of that convergence. DeGroot describes for the whole population what active inference describes for the single agent, belief drawn toward coherence.
In its canonical connected and ergodic form, the DeGroot model converges to one value. Real populations form lasting factions instead. To explain that, the model needs one more ingredient.
The missing ingredient was supplied around the year 2000 by Rainer Hegselmann and Ulrich Krause, and independently by Guillaume Deffuant and colleagues. The mechanisms differ in detail: in the Hegselmann-Krause version each agent moves toward the average of everyone within a threshold of its own view; in the Deffuant version, agents meet in random pairs and compromise only when already close. Either way, views beyond the threshold are ignored. The threshold is a confidence bound: the width of disagreement an agent will still take seriously.
In the simplest homogeneous, one-dimensional versions, the confidence bound becomes the decisive parameter. When it is wide, agents listen across the whole range of views, and the population converges to a single consensus, as in DeGroot. When it is narrow, agents listen only to those who already broadly agree with them, and the population fragments into separate clusters. What decides the outcome is not how far apart the views are but whether they stay linked through chains of acceptable disagreement: a wide but continuous spread can still converge, while a narrower distribution can split once a gap opens between camps. These clusters are stable, the competing settled states the system could occupy, defined not by the data but by which conversations remain connected.
The teaching image is a row of people standing on a line, each at the position of their estimate. At each step everyone shuffles toward the average position of the neighbours within earshot. If earshot is wide, the whole row collapses to a single point; if it is narrow, the row breaks into separate huddles that drift apart and then hold.
This is the result worth carrying into markets, because it says something the bare idea of “disagreement” does not. What governs the stability of a consensus is not the level the crowd settles on, nor even how widely its views are spread, but whether that spread is still bridged. The level is what everyone watches; bridgeable disagreement is what lets the agreement survive a shock.
The bond-equity relationship shows this plainly. Through the low-and-stable-inflation years of the 2000s and 2010s it was reliably negative, bonds tending to rise when equities fell, but whether they do is not fixed; it depends on the prevailing belief. When the shared model is “inflation is controlled, the main risk is growth,” bonds hedge equities and the correlation is negative. When inflation or policy credibility becomes the dominant risk instead, equity selloffs are more likely to coincide with rising yields, so bonds can stop hedging equities and the correlation can turn positive. The sign is one expression of the regime the population believes it is in: regime-dependent because macro shocks, policy expectations and beliefs interact.
The opinion-dynamics framework reframes how you watch for that change. Waiting for the realised correlation to flip is a price summary, and a slow one. This framework points instead to the belief structure those prices express, which can shift before the correlation does. Two observables follow from the model.
The first is dispersion. As a consensus loses its hold, the cross-section of forecasts may widen, become more persistent, or turn multimodal before the average or realised correlation clearly moves. Forecast disagreement is measured continuously, and the work of Gregory Mankiw, Ricardo Reis and Justin Wolfers established that it varies over time, tending to be higher when inflation is high, changing rapidly, or relative prices are more variable.
The second observable is not the confidence bound itself, which is latent, but the behavioural proxies for it: the tone and connectedness of the conversation. When the discourse hardens into camps that stop citing each other, when forecasts turn bimodal rather than merely spread, and when previously marginal narratives migrate into the core, those are signs consistent with a narrowing confidence bound. This is the soft signal that Robert Shiller’s work on narrative economics points to: narrative tracking may register changes in the belief environment that the aggregate data have not yet stabilised into.
The transfer here is specific. Opinion dynamics has been applied to markets before, but the use is not to price an asset directly; it is to watch the stability of the belief structure that makes a regime possible, something readable before it resolves into a slow price summary.
The same reading applies wherever a shared view is held by a population that talks to itself. In an organisation, a settled strategy holds while its supporters still engage the colleagues who doubt it, and fractures when the two sides stop finding each other worth answering. In a scientific field, a dominant position can look secure while the dispersion of published views widens and rival camps stop citing one another. In a profession, an agreed standard survives on the bridgeability of disagreement, not merely on the original case for it.
Two cautions keep this honest. The first is that dispersion is only a proxy for fragmentation, not the thing itself, and treating it as an alarm is a problem in signal detection of the kind set out in When Right Still Looks Wrong. Disagreement also rises in ordinary times that resolve without any regime change, so a low threshold for concern produces false alarms, and a high one misses real transitions. Forecaster disagreement has widened many times without a regime turning.
The second caution is sharper, because it turns the framework on its user. Once participants begin watching dispersion as a regime indicator, the indicator becomes part of the dynamics it was meant to observe. A widely shared narrative that the consensus is fragmenting can itself narrow the confidence bound, as participants brace, harden and stop listening across the divide, the very condition that produces the fragmentation the narrative predicted. Understanding how a crowd comes apart does not place you outside the crowd; it can make you a faster contributor to the process you were trying to anticipate.
The discipline is in asking: not where the consensus has settled, but how wide it is, where its gaps are, and how far it still listens across its own disagreement?
References & Further Reading
Reaching a Consensus: Morris H. DeGroot
Opinion Dynamics and Bounded Confidence: Models, Analysis and Simulation: Rainer Hegselmann & Ulrich Krause
Mixing Beliefs Among Interacting Agents: Guillaume Deffuant, David Neau, Frédéric Amblard & Gérard Weisbuch
Statistical Physics of Social Dynamics: Claudio Castellano, Santo Fortunato & Vittorio Loreto
Disagreement about Inflation Expectations: N. Gregory Mankiw, Ricardo Reis & Justin Wolfers
The Great Inflation and Its Aftermath: The Past and Future of American Affluence: Robert J. Samuelson
Narrative Economics: How Stories Go Viral and Drive Major Economic Events: Robert J. Shiller
Making Sense of Chaos: A Better Economics for a Better World: J. Doyne Farmer
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