8 Lecture 8 — More Information Equals Better Decisions
Informational cascades
8.1 Opening dissonance
In 1992 — the same year Elinor Ostrom, James Walker, and Roy Gardner published their canonical demonstration that face-to-face communication could sustain common-pool resources without external enforcement — Sushil Bikhchandani, David Hirshleifer, and Ivo Welch published a paper with a quieter title and an explosive implication. “A Theory of Fads, Fashion, Custom, and Cultural Change as Informational Cascades” (Bikhchandani et al. 1992) demonstrated that when rational agents make decisions sequentially and each can observe the choices (but not the private information) of those who went before, the agents can rationally converge on the wrong choice — and once they do, the cascade locks in. No one is irrational. No one is lying. Everyone is doing exactly what an expected-utility maximiser should do, given what they can observe. And the collective outcome is a mistake that persists indefinitely.
The mechanism is deceptively simple. Suppose two restaurants sit side by side, one excellent and one mediocre. Patrons arrive one at a time and must choose where to eat. Each patron receives a private signal — a noisy but informative hint about which restaurant is better — and can also see where the patrons who arrived earlier chose to sit. The first patron follows their private signal. The second patron, seeing the first’s choice, now has two pieces of information: their own private signal and the first patron’s revealed preference. If the signals agree, the second patron follows both. If they disagree, the second patron is indifferent and may flip a coin — and if the coin lands against their own signal, the visible choice now carries more weight than the private information for the third patron. The third patron sees two predecessors who both chose restaurant A. Even if the third patron’s private signal strongly favours restaurant B, the weight of two observed choices can overwhelm one private signal. The third patron rationally ignores their own information and follows the crowd. At that point, the cascade has begun. Every subsequent patron, regardless of their private signal, will choose restaurant A — because all they can see is a growing pile of patrons at A, and no amount of private information can overturn the accumulated visible evidence.
The patrons are rational. They are Bayesian updaters. They are doing everything the textbook says they should do. And they all end up at the wrong restaurant.
The same year, Abhijit Banerjee published an independent model with the same logic and a different label: herd behaviour (Banerjee 1992). Banerjee gave the result a second, purely informational derivation: agents who each hold a private signal but decide in sequence rationally imitate their predecessors once the public record of earlier choices outweighs any single signal. (A separate, reputational account — in which following the consensus is safer because a wrong call shared with everyone is less damaging than a wrong call made alone — reaches a similar conclusion by a different route, but herd behaviour is already rational on the information alone.)
These two papers — published within months of each other, in different journals, by authors who were unaware of each other’s work — launched a literature that would reshape how economists, political scientists, and eventually computer scientists thought about the relationship between information and decision quality. The good-will intuition — more information equals better decisions — was not refuted. But it was shown to be conditional on a structural feature that the intuition had not noticed: the distinction between private information and public information, and the way the latter can drown out the former when decisions are sequential and observable.
We have lived with this insight for three decades. Every financial bubble, every electoral surprise, every viral misinformation cascade has been partially explained by the BHW-Banerjee logic. The question this lecture asks is not whether the logic is correct — the laboratory and field evidence, which we will walk through in §3, confirms that it is. The question is whether the logic survives when the agents in the sequence are not human — when the private signals are processed by language-model agents, when the observable choices propagate at machine speed, and when the cascade locks in before any external corrective can arrive.
8.2 The classical setting
Before walking through the experimental record, we need to be precise about the formal structure of an informational cascade, because the structure — not the psychology, not the incentives, not the framing — is what makes the cascade possible.
8.2.1 The BHW model in formal terms
Bikhchandani, Hirshleifer, and Welch consider a sequence of agents \(i = 1, 2, \dots, N\) who must each choose between two actions, \(A\) (accept) and \(R\) (reject). One of the two actions is objectively correct, but the agents do not know which one. Before the sequence begins, nature draws the correct action with equal probability. Each agent receives a private signal \(s_i\) that is correct with probability \(p > 0.5\) and incorrect with probability \(1-p\). The signals are conditionally independent given the true state. Each agent observes the actions of all previous agents — but not their private signals — and then chooses their own action. The payoff is \(+1\) for a correct choice and \(-1\) for an incorrect choice.
The first agent has only their private signal. If \(s_1 = A\), they choose \(A\); if \(s_1 = R\), they choose \(R\). The second agent sees the first agent’s action (which reveals the first agent’s signal) and receives their own private signal \(s_2\). If the signals agree, the second agent follows both; if they disagree, the second agent is indifferent between \(A\) and \(R\), because the two signals cancel out. If the second agent breaks the tie by, say, following their own signal, then the third agent sees two predecessors who have chosen differently — one chose \(A\), one chose \(R\) — and the third agent’s private signal becomes decisive. The sequence continues without a cascade.
But if the second agent breaks the tie against their own signal — by flipping a coin, or by following a tie-breaking rule that does not favour the private signal — then the third agent sees two predecessors who chose the same action. Even if the third agent’s private signal points the other way, the Bayesian calculation says: the probability that both predecessors are wrong, given that they agreed, is \((1-p)^2\), while the probability that my own signal is right is \(p\). For \(p\) not too far above 0.5, \((1-p)^2\) can be smaller than \(1-p\) — meaning the weight of two agreeing predecessors outweighs the weight of one private signal. The third agent rationally ignores their own information and joins the consensus. The cascade has started.
Once a cascade starts, it is informationally efficient in a perverse sense: no subsequent agent’s private signal, no matter how strong, can overturn it. The public information — the sequence of identical choices — accumulates weight faster than any private signal can counter-balance. The cascade is rational, self-reinforcing, and fragile: a small amount of public information arriving after the cascade has formed (a restaurant review, an audit report, a whistleblower) can shatter it instantly, because the cascade was built on the absence of public information in the first place.
What makes the BHW model unsettling is not its prediction — that cascades can form — but its minimality. The model requires no irrationality, no conformity preference, no payoff externalities, and no deception. It requires only that agents are rational, that their choices are observable, and that their private information is not. Every assumption is individually innocuous. The conjunction is explosive.
8.2.2 Banerjee’s herd-behaviour extension
Banerjee’s model, published in the Quarterly Journal of Economics the same year, reaches the same conclusion as BHW by a slightly different route — and, importantly, on purely informational grounds, with no appeal to reputation (Banerjee 1992). In Banerjee’s setup, each decision-maker holds a private signal but chooses in sequence after observing what earlier movers did. Because each action reveals something about its mover’s signal, the accumulated public history of choices can rationally outweigh any single agent’s private information, so later agents imitate even when their own signal points elsewhere.
A separate strand of the herding literature reaches a similar conclusion through reputation rather than information. When decision-makers are judged by a principal or a future employer who can see their choice but not their private signal, following the herd is the safer bet: a wrong call shared with everyone is less damaging to one’s reputation than a wrong call made alone, and the premium for a lonely correct call is typically smaller than the penalty for a lonely wrong one. This reputational asymmetry can make cascades more likely and more persistent — but it is logically distinct from Banerjee’s informational mechanism, and his result does not depend on it.
Between them, the informational and reputational channels explain a range of phenomena the bare BHW model leaves puzzling: why fund managers herd into the same stocks, why analysts converge on the same forecasts, why academic disciplines develop orthodoxies that persist for decades despite accumulating contrary evidence. The mechanism is not that the agents are irrational. It is that the structure — informational, reputational, or both — penalises contrarianism and tilts a rational calculation toward the herd.
8.2.3 The key structural insight
The BHW-Banerjee literature delivers a precise structural insight that reorganises how we think about the relationship between information and decision quality. The insight has three components.
First, observational sequence is not the same as deliberation. When a committee deliberates — when members share their reasons, not just their votes — the group can aggregate private information. When a sequence observes only actions, the group cannot aggregate private information after the cascade starts. The distinction between deliberation and observation is the difference between a jury that discusses the evidence and a queue of customers who can only see where the people in front of them sat down.
Second, public information can be a curse, not a blessing. The good-will intuition holds that more information is better. The BHW model shows that the kind of information matters more than the amount. Public information — observable actions — can crowd out private information — unobservable signals — and the crowding-out is rational, not pathological. The agents are not ignoring their private signals out of laziness or conformity pressure. They are doing the Bayesian arithmetic, and the arithmetic tells them to discard what they alone know.
Third, cascades are fragile in a specific way. Because a cascade forms on the absence of public information — the early agents had only their private signals, and the later agents could not see those signals — the arrival of even a small amount of genuinely public information (a published audit, a credible news report, a regulator’s announcement) can shatter the cascade. The fragility is not a weakness of the model; it is a prediction. And it is a prediction that maps directly onto observable phenomena: the sudden collapse of asset bubbles after a disclosure, the rapid reversal of medical practices after a meta-analysis, the overnight disappearance of a fad after a credible exposé.
With this formal apparatus in hand, we can now ask: what happens when we move from the blackboard to the laboratory — and then to the computational platform?
8.3 The classical walk
The BHW and Banerjee models were theoretical contributions. They proved that informational cascades could happen — that the logic was internally consistent and that the conditions were minimal. The question the experimentalists picked up was: do they actually happen, in the laboratory, with real human subjects making real incentivised decisions? The answer, across three decades of careful experiments, is yes — with qualifications that matter for the BDPD angle.
8.3.1 The founding models (BHW 1992, Banerjee 1992)
The two founding papers share a core logic but differ in emphasis. BHW focus on the informational mechanism: agents rationally discard their private information when the accumulated weight of observed choices exceeds the weight of any individual signal (Bikhchandani et al. 1992). Banerjee gives a second, independent informational derivation: agents deciding in sequence rationally imitate their predecessors once the public history of observed choices outweighs their own private signal (Banerjee 1992).
Both papers make a prediction that cuts against the good-will intuition. The prediction is not that “people are irrational and follow the crowd.” It is that “rational people, under the right observational structure, should follow the crowd — and the crowd can be wrong.” The prediction is structural, not psychological. Change the structure — let agents observe each other’s signals, not just their actions — and the cascade disappears, because the private information is no longer private. Change the structure — let agents deliberate before choosing — and the cascade attenuates, because deliberation aggregates information that sequential observation discards. The structure is the binding variable.
What the two founding papers did not do — because the question would have been anachronistic in 1992 — is to ask: what if the agents in the sequence are not human Bayesian updaters with natural-language private signals, but computational agents with prompt-induced signals and machine-speed decision cycles? The BHW model assumes agents who compute posterior probabilities over the set {Correct, Incorrect} given their private signal and the observed action history. An LLM agent receiving a structured state vector can perform that computation — but it can also perform computations that human subjects, constrained by working memory and arithmetic capacity, cannot. The cascade mechanism may be strengthened, weakened, or transformed when the Bayesian updater is an LLM. The founding papers give us the logic; the BDPD platform gives us the experimental apparatus to test it.
What if the agents in the sequence were LLMs — capable of computing the exact Bayesian posterior at each step, with no rounding error, no fatigue, and no reputational anxiety? The cascade logic should hold more tightly, because the agents are closer to the ideal Bayesian reasoners the model assumes. But if the cascade logic holds more tightly, the cascade is harder to break — and the fragility that the BHW model identifies as a feature of cascades among humans may not be present among LLM cascades, because the LLM computes the Bayesian update correctly and the cascade never forms on a mistake.
8.3.2 The laboratory confirmation (Anderson & Holt 1997)
Three years after the theoretical papers, Lisa Anderson and Charles Holt brought the cascade logic into the laboratory and tested it with real human subjects making real incentivised decisions (Anderson and Holt 1997). The design was elegant in its simplicity. Subjects were arranged in a sequence and asked to guess which of two urns — one containing two-thirds red balls and one-third blue, the other with the proportions reversed — was the “red-majority” urn. Before guessing, each subject drew a ball from the urn (their private signal), observed its colour, and then saw the guesses (but not the draws) of all previous subjects. The decision was incentivised: a correct guess earned a cash payment; an incorrect guess earned nothing.
The result was clear. In 87 of 122 sequences (71%), an informational cascade formed — meaning that after some point, all subsequent subjects made the same guess regardless of their private draw. Of those 87 cascades, 57 (66%) were correct — the cascade converged on the true urn — but 30 (34%) were incorrect. Subjects who drew a signal contradicting the cascade faced a choice: follow their private information (which had been, on average, informative two-thirds of the time) or follow the observed consensus (which represented the aggregated information of multiple predecessors). The Bayesian arithmetic favoured the consensus when two or more predecessors had agreed. Subjects performed the arithmetic, approximately: when two predecessors agreed on a guess, the third subject followed the consensus 79% of the time regardless of their own draw.
The Anderson-Holt experiment confirmed the BHW prediction with laboratory precision. Cascades form. They form frequently. They are sometimes wrong. And they are caused by rational inference, not by conformity pressure or social desirability — the design was anonymous, the stakes were real, and the Bayesian arithmetic was available to any subject who could perform it.
But the experiment also documented something the BHW model did not predict: subjects were more likely to follow their private signal than the Bayesian model would prescribe. The model predicts that, after two agreeing predecessors, the third agent should always ignore their private signal and join the cascade. The data showed that 21% of subjects in that position deviated — they went against the cascade, following their private draw. The deviation is not large enough to prevent cascades from forming, but it is large enough to suggest that human subjects bring something to the cascade decision that the Bayesian model does not capture: a reluctance to discard their own information entirely, a preference for independence, or a simple failure to compute the posterior probabilities correctly.
What if the subjects in the Anderson-Holt design were LLM agents rather than undergraduates? An LLM receiving a prompt that describes the urn problem, the draw, and the observed guesses should compute the Bayesian posterior correctly — no 21% deviation, no reluctance to discard private information, no computational error. The cascade should form more quickly (the second agent, not the third, should trigger it, if the tie is broken in the cascade direction) and more rigidly (no subject should deviate once the cascade is in place). The LLM cascade would be, in a precise sense, more faithful to the BHW model than the human cascade — but also more dangerous, because the deviations that human subjects introduce are the only mechanism for breaking a cascade from within.
8.3.3 Distinguishing cascades from herd behaviour (Çelen & Kariv 2004)
Bogaçhan Çelen and Shachar Kariv addressed a question that the Anderson-Holt experiment could not answer because its design did not permit the distinction: when subjects follow the crowd, are they engaging in an informational cascade (rationally inferring that the crowd knows something they do not) or in herd behaviour (following the crowd because deviation is costly, regardless of what they privately believe)? The distinction matters because the two mechanisms imply different policies. If the problem is informational, the solution is to reveal private information. If the problem is reputational, the solution is to change the incentives (Çelen and Kariv 2004).
Çelen and Kariv designed an experiment in which subjects received a continuous private signal — not a binary draw from an urn, but a real number drawn from a distribution centred on the true value — and observed the actions of their predecessors. The continuous signal space meant that the Bayesian updating problem was more demanding (subjects had to compute a posterior distribution rather than a simple probability comparison), but it also meant that the experimenter could distinguish informational from reputational cascades: in a pure informational cascade, the subject’s belief about the true value should converge to the cascade value; in a reputational cascade, the subject’s belief and action should diverge.
The results were nuanced. Subjects did update their beliefs in the direction of the cascade, confirming the informational mechanism. But they did not update as strongly as the Bayesian model predicted, and their actions were more variable than their beliefs — suggesting that the simple Bayesian model captures the direction of the effect but not its magnitude. The cascade mechanism is real, but the human implementation of it is approximate.
The distinction Çelen and Kariv introduced — between what an agent believes and what an agent does — is central to the BDPD angle. Human subjects in cascade experiments cannot report their beliefs with precision; the experimenter infers beliefs from actions, and the inference is noisy. LLM agents, by contrast, can be prompted to report their belief at each step of the sequence — a direct introspectable measure of the Bayesian posterior, separable from the action they choose. The Çelen-Kariv distinction, which among humans requires indirect inference, becomes direct observation among LLMs. This is not a minor methodological upgrade. It changes what kind of cascade experiment is possible.
What if the Çelen-Kariv design were run with LLM agents instead of human subjects? The LLM could report, at each step, its posterior belief about the true value — and the experimenter could compare the reported belief with the action the LLM chooses. If the two diverge — if the LLM reports a belief contrary to the cascade but joins the cascade anyway — the divergence tells us something about LLM decision-making that the human data cannot reveal, because humans in the Çelen-Kariv design could not report beliefs with that precision. If the two converge — the LLM’s belief tracks its action exactly — we have a clean demonstration of a pure informational cascade, unconfounded by reputation, computational error, or conformity preference.
8.3.5 The filter bubble and epistemic bubble (2010s)
In 2011, Eli Pariser published The Filter Bubble and gave a name to a phenomenon that the cascade literature had anticipated but not operationalised: the algorithmic curation of information, by search engines and social-media platforms, creates personalised information environments in which users see only what the algorithm predicts they will engage with (Pariser 2011). The filter bubble is not an informational cascade in the BHW sense — the agents are not observing each other’s choices and discarding their private signals. But the mechanism is related: both involve a structure in which the information an agent receives is determined by the choices of others (in a cascade) or by the automated extrapolation of past choices (in a filter bubble). In both cases, the agent does not know what they are not seeing — and the invisibility of the unseen information makes the outcome self-reinforcing.
Cass Sunstein, writing across several books and articles in the 2010s, extended the argument to epistemic bubbles and echo chambers (Sunstein 2017). An epistemic bubble forms when relevant information is excluded from an agent’s view — not by active curation but by the structure of the information environment. An echo chamber forms when the excluded information is actively discredited by sources the agent trusts. The distinction matters: popping an epistemic bubble requires only exposing the agent to the missing information; breaking an echo chamber requires overcoming the agent’s distrust of the information source. Both mechanisms, like informational cascades, produce outcomes in which more information — more of the same kind of information — makes the decision worse, not better.
The filter-bubble and echo-chamber literature matters for the BDPD angle because it identifies a variable that the BHW-Anderson tradition does not: the curation algorithm. In a BHW cascade, the curation algorithm is the sequence itself — agents observe the choices of all predecessors, unfiltered. In a filter bubble, the curation algorithm is personalised and opaque. In a BDPD scenario with LLM agents, the experimenter controls the curation algorithm — which predecessors’ choices are visible to which subsequent agents, under what aggregation rule, with what latency. The variable that Pariser and Sunstein identified as a structural feature of the information environment becomes an experimental parameter on the BDPD platform.
What if the agents in a cascade scenario could only observe a curated subset of their predecessors’ choices — the subset selected by an algorithm that maximises engagement, or confirms prior beliefs, or minimises cognitive dissonance? The cascade might form faster (if the curation reinforces the emerging consensus) or might be prevented from forming (if the curation exposes agents to dissenting choices). The curation algorithm, which among humans is an exogenous feature of the platform, becomes an endogenous experimental variable in the BDPD cascade scenario.
8.3.6 LLM conformity: the direct evidence (Bito et al. 2026)
The most recent and most directly relevant empirical finding comes from outside the cascade literature proper. Mikako Bito and colleagues, in a 2026 preprint, tested six large language models on tasks designed to distinguish informational conformity (changing one’s judgment because others’ answers contain useful information) from normative conformity (changing one’s judgment to avoid conflict or gain acceptance) (Bito et al. 2026). The experimental design is directly relevant to the cascade question because informational conformity is precisely the mechanism the BHW model describes: an agent observes the choices of others, infers that those choices contain information, and updates their own judgment accordingly.
Bito et al. found that five of the six LLMs tested exhibited significant informational conformity — they changed their answers after observing the answers of others, even when those answers were wrong. Four of the six also exhibited normative conformity — they changed their answers when the social context made conformity desirable, even when no new information was provided. The finding is a direct empirical bridge between the classical cascade literature and the LLM-agent question. If LLMs exhibit informational conformity in a simple judgment task, they are likely to form informational cascades in the sequential-choice tasks that the BHW-Anderson tradition studies — possibly more strongly, because the Bayesian computation that drives the cascade is one that LLMs, as language models trained on vast corpora of human text, may be particularly well equipped to perform.
The Bito finding also introduces a variable the classical cascade literature did not measure: the magnitude of the conformity effect varies across models. Some LLMs conformed more than others; some conformed under conditions where others did not. The implication for the BDPD cascade scenario is that the cascade propensity is not a fixed feature of “LLM agents” but a parameter that varies with the model architecture, the prompt design, and the persona assignment. The BDPD platform, by making the agent’s model and persona experimental variables, can measure this variation directly.
What if the BHW cascade experiment were run with six different LLM architectures, parallel to the six models Bito et al. tested for conformity? The cascade propensity — the probability that a cascade forms, the speed at which it locks in, the fragility with which it breaks — should vary across architectures in ways that map onto the conformity scores Bito et al. report. An LLM that exhibits high informational conformity in the Bito design should form cascades more readily in the BHW design. An LLM that exhibits low conformity should resist cascades. The mapping is a testable hypothesis, and the BDPD platform — by running the same cascade scenario across multiple LLM backends — is, to our knowledge, among the first experimental apparatuses positioned to test it.
8.4 What survives of the good-will intuition
The record we have walked through does not refute the good-will intuition that more information produces better decisions. It bounds it — and, in bounding it, it identifies the structural conditions under which the intuition holds and the conditions under which it reverses.
Transparency and information abundance improve decisions — but only when the kind of information and the structure of observation respect the distinction between private signals and public actions. When the structure collapses that distinction, more information can make decisions worse.
The cascade is rational, not pathological. The BHW model and the Anderson-Holt experiment converge on the same finding: agents who follow the crowd in a sequential decision are not irrational, lazy, or conformist. They are performing the Bayesian calculation that any expected-utility maximiser should perform, given the information they can observe. The cascade is an equilibrium phenomenon, not a behavioural anomaly. This means that transparency — making everyone’s choices observable — is not sufficient to prevent bad collective decisions. It can be the cause of bad collective decisions, if the observable choices are uncoupled from the private information that justified them.
The cascade is fragile — but only to new public information. Because a cascade forms on the absence of public information — the early agents had only private signals, and the later agents could not see them — the arrival of genuinely public information (an audit, a disclosure, a regulator’s announcement) can shatter the cascade. But the fragility is specific: private information, arriving through additional agents whose private signals contradict the cascade, does not shatter it, because the cascade mechanism precisely discards private signals that contradict the accumulated public consensus. The policy implication is direct: if you want to break a cascade, do not add more decision-makers with private information; add a mechanism that publishes the private information.
The observational structure is the binding variable — not the number of agents, not their incentives, not their cognitive biases. Whether a cascade forms depends on whether agents observe actions or signals. If they observe signals, they aggregate information; if they observe only actions, they potentially cascade. The Centola et al. experiment adds that the network topology of observation — who can see whom — determines the cascade threshold. The filter-bubble literature adds that the curation algorithm — which observations are shown to which agents — determines whether the observational structure amplifies or dampens the cascade. The binding variable is not “how much information” but “what kind of information, visible to whom, in what order.”
Conformity is not uniform — it varies with the agent’s architecture. The classical experiments (Anderson-Holt, Çelen-Kariv) document that human subjects deviate from the Bayesian prescription — they follow their private signal more often than the model predicts, and their cascade propensity varies across individuals. Bito et al. document that LLMs exhibit informational conformity that varies across model architectures. The cascade propensity is a parameter, not a constant — and the parameter depends on the cognitive architecture of the agent. The classical literature could measure this parameter for humans; the BDPD platform can measure it for LLMs — and the comparison is the empirical object that neither literature, alone, can deliver.
Taken together, these four findings reorganise the question. The interesting question is no longer does more information produce better decisions? — the record says sometimes yes, sometimes no, depending on the structure. The interesting question is under what observational structure does more information improve decisions, and does the answer change when the agents processing the information are not human?
8.5 The BDPD angle — speculative: cascades at machine speed
The good-will intuition — more information equals better decisions — rests on a silent assumption that the cascade literature did not notice because the question was not on its agenda: the agents who observe each other’s choices share a cognitive architecture that processes observable actions and private signals in broadly similar ways. The cascade mechanism — the Bayesian updating, the discarding of private signals, the convergence on a public consensus — requires agents who can compute posterior probabilities, who treat the observable actions of predecessors as informative, and who agree on what constitutes a signal. All of these requirements were satisfied, approximately, by the human subjects in the Anderson-Holt and Çelen-Kariv laboratories. They may not be satisfied — or may be satisfied differently, or may be satisfied more precisely — when the agents are LLMs.
8.5.1 Direction 1: The structural prediction from BDPD1
The BDPD1 paper found that cheap talk — the same pre-play communication intervention that produces a Cohen’s \(d \approx 1.01\) among human subjects in social dilemmas — produces a \(d \approx 0.17\) among LLM agents in the same dilemma (Brunelli 2026). The cheap-talk effect, one of the most robust findings in behavioural social science, nearly vanishes when the agents around the table are not human. The BDPD1 finding is not about cascades — it is about communication in a simultaneous-move commons dilemma, not sequential observation of choices. But the structural parallel is precise.
An informational cascade, in the BHW-Anderson sense, is a specific kind of cheap-talk channel: the agents communicate not through words but through actions, and the communication is unidirectional (earlier agents talk, later agents listen). If LLM agents do not metabolise cheap talk in a simultaneous-move dilemma — if they do not treat the messages of others as credible commitments, as Farrell and Rabin’s theory predicts humans do — then they may also fail to treat the observable actions of predecessors as informative signals in the way the BHW model requires. The cascade logic requires that the observing agent treat the predecessor’s action as a signal about the predecessor’s private information. If LLM agents are insensitive to that kind of signal — if they treat the predecessor’s action as just another data point in the state vector, to be weighted by an opaque attention mechanism rather than by a transparent Bayesian calculus — then the cascade may not form, or may form under different conditions than among humans, or may form more slowly and break more easily.
The BDPD1 result points in a specific direction: LLM agents are less sensitive to the informational content of others’ choices than Bayesian decision theory predicts. The cheap-talk null suggests that LLMs do not invest natural-language messages with the commitment weight that human agents do. The cascade null — if it materialises — would suggest that LLMs do not invest observable actions with the signal weight that human agents do. Both nulls share the same architectural root: LLM agents process the state vector through a transformer architecture that does not, by default, distinguish between private signal and public action in the way the cascade model requires. The distinction is not built into the architecture; it must be engineered into the prompt.
The prediction: an LLM-agent version of the Anderson-Holt cascade experiment should produce fewer cascades than the human version, because LLM agents are less prone to discard their private signals in response to observed actions. But the structure of the cascade — once it forms, does it persist? — may be different: if the LLM cascade forms despite the BDPD1 null, it may be more rigid than the human cascade, because the LLM, having computed the Bayesian posterior correctly at the point of cascade formation, will not introduce the 21% deviation rate that Anderson and Holt observed among human subjects. The cascade, once locked in, stays locked in.
8.5.2 Direction 2: Speed — the cascade locks in before correction arrives
The classical cascade literature operates on human timescales. In the Anderson-Holt experiment, subjects took several seconds to examine their private draw, observe the predecessors’ guesses, and record their own guess. The sequence of 6–8 subjects filled a laboratory session. In the world outside the laboratory — financial markets, social media, electoral dynamics — cascades unfold over hours, days, or weeks. There is time for an external corrective — a news report, an audit, a whistleblower — to arrive and shatter the cascade before it causes irreversible damage.
Among LLM agents, the timescale collapses. A cascade of twenty LLM agents, each receiving a private signal and observing the actions of predecessors, can propagate at API latency — milliseconds per agent, a fraction of a second for the entire sequence. The cascade forms, locks in, and produces its outcome before any external information can arrive. The fragility that the BHW model identifies as a feature of cascades — their vulnerability to new public information — is neutralised not by design but by speed. The cascade completes before the corrective can be deployed.
The speed asymmetry has a structural implication that the classical cascade literature did not consider. In the BHW model, the cascade forms because the early agents’ private signals are lost — observable only through their actions, which are coarser than the signals themselves. Among LLM agents, the speed of cascade formation means that all private signals are lost, not just those of the early agents — because no external observer, human or algorithmic, can inspect the agents’ internal states at millisecond resolution. The cascade among LLMs is not just faster; it is more opaque, because the speed at which it propagates exceeds the sampling rate of any monitoring system a human regulator could deploy.
The prediction: LLM cascades should exhibit qualitatively different fragility dynamics than human cascades. Among humans, a cascade can be broken by a well-timed disclosure — a public signal arriving after the cascade has formed but before it has produced irreversible consequences. Among LLMs, the window between cascade formation and cascade completion may be too short for any disclosure to intervene. The fragility of the cascade — a feature that the BHW model treats as a saving grace — may be eliminated by the speed of the agents. The cascade among LLMs is not just an information cascade; it is a latency cascade, locked in before the monitoring system can detect it.
8.5.3 Direction 3: Introspectable belief state
The Çelen-Kariv distinction — between what an agent believes and what an agent does — is central to cascade diagnosis. If an agent’s belief and action diverge, the cascade is not purely informational; something else — reputation, conformity pressure, strategic calculation — is at work. If they converge, the cascade is informational in the strict BHW sense.
Among human subjects, belief-action divergence is difficult to measure. The experimenter infers the belief from the action, or from post-experiment questionnaires whose reliability is limited. Çelen and Kariv could only infer beliefs indirectly, from the continuous-action data in their design. The inference is noisy, and the distinction between informational and reputational cascades among humans remains partially conjectural.
Among LLM agents, the belief is introspectable. An LLM receiving a cascade prompt can be asked, at each step of the sequence, to report its posterior belief about the correct action — not just what action it chooses, but what probability it assigns to each action being correct. The report is not an inference from behaviour; it is a direct output of the model’s generation process. The experimenter can compare the reported belief with the chosen action and measure the divergence directly.
This capability changes the type of cascade experiment that is possible. A BDPD cascade scenario can cross two factors: the observational structure (standard BHW sequential observation vs. Çelen-Kariv continuous-signal observation) and the belief-reporting requirement (silent action choice vs. action choice plus introspective belief report). The design can answer questions that the classical literature could only speculate about: do LLM agents who know they must report their beliefs behave differently from those who only choose actions? Does the introspective-reporting requirement — which makes the private signal observable after the fact, though not during the decision — attenuate the cascade, because agents anticipate that their beliefs will be scrutinised? Does the cascade form at all when the belief-reporting channel is open, or does the mere existence of an introspective outlet prevent the cascade from locking in?
The prediction: LLM agents that are required to report beliefs alongside actions should exhibit fewer cascades than agents that only choose actions, because the belief-reporting requirement forces the agent to separately encode its private signal and its public action — and the separation makes the private signal salient in a way that the standard BHW design does not. The belief-reporting channel functions as a cascade inhibitor — a structural feature of the experimental design that breaks the observational closure on which the cascade depends.
8.5.4 Direction 4: The missing experiment — a BDPD cascade scenario
The BDPD platform’s architecture makes it possible to specify a cascade scenario that operationalises the BHW-Anderson-Çelen comparison with the same parameterised rigour that the D-series pilots brought to the graduated-sanctions comparison and that the BDPD1 factorial brought to the cheap-talk question. The scenario has not been built, but its specification follows directly from the platform’s existing capabilities.
Scenario design. \(N\) LLM agents are arranged in a sequence, with \(N \in \{6, 12, 24\}\). At the start of the run, nature selects a binary state: the “correct” action is \(A\) or \(B\), with equal probability. Each agent receives a private signal — a structured prompt that reports a noisy observation favouring the correct action with probability \(p \in \{0.55, 0.65, 0.75\}\), varied as a between-runs parameter. Each agent, in sequence, observes the actions (but not the private signals) of all predecessors and chooses an action \(A\) or \(B\). The payoff is \(+1\) for a correct choice, \(0\) otherwise. At each step, the agent is prompted to report its posterior belief — a probability between 0 and 1 that \(A\) is correct — alongside its action.
The design crosses four factors, producing a \(3 \times 3 \times 2 \times 2\) factorial:
- Sequence length \(N \in \{6, 12, 24\}\)
- Signal precision \(p \in \{0.55, 0.65, 0.75\}\)
- Agent architecture: LLM vs. rule-based Bayesian updater (a deterministic agent that computes the exact BHW posterior and chooses the action with the higher posterior probability)
- Belief-reporting requirement: silent action only vs. action plus belief report
Each cell is run at \(S = 10\) different seeds (different random draws of the true state and private signals). The primary outcome metric is the cascade formation rate — the proportion of runs in which, after some agent \(k\), all subsequent agents choose the same action regardless of their private signal. Secondary metrics include the cascade correctness rate (proportion of cascades that are correct), the cascade onset point (the index \(k\) at which the cascade locks in), and the belief-action divergence (the mean absolute difference between reported belief and chosen action, for cells with the belief-reporting requirement).
The scenario as specified is within the platform’s existing capabilities: the sequential scheduler exists (BDPD scenarios can specify turn-by-turn agent activation), the LLM agent infrastructure exists, the structured state vector can deliver per-agent observation histories, and the prompt schema can include the belief-reporting instruction. The missing pieces are the cascade-specific agent decision module (which simulates the private-signal draw and formats the observation history) and the cascade outcome metrics (which detect lock-in and compute correctness rates). Both are incremental extensions, not architectural changes. The scenario has been designed but not implemented.
8.6 Synthesis
The good-will intuition — more information equals better decisions — emerges from this lecture confirmed in structure, bounded by observational architecture, and predictive of a new failure mode when the agents are not human.
Confirmed — conditionally. The classical literature confirms that more information can produce better decisions — when the information includes private signals, when the observational structure allows those signals to be aggregated, and when the sequence is not constrained to observe only actions. The BHW model, Banerjee’s herd-behaviour extension, and the Anderson-Holt laboratory results all confirm that the conditions under which more information helps are narrower than the good-will intuition assumes. The intuition is not wrong; it is incomplete in a specific, structural way.
Bounded by observational architecture. The binding variable is not the amount of information but the kind — specifically, whether the information is private (a signal that only the agent observes) or public (an action that all subsequent agents can see). When the structure makes only actions observable, information cascades can form, and they can be wrong. When the structure makes signals observable as well, cascades are prevented. The Centola et al. experiment adds that the network topology of observation determines the cascade threshold. The filter-bubble literature adds that the curation algorithm determines whether the observational structure amplifies or dampens the cascade. All three bounds are structural, not psychological.
Predictive of LLM-specific dynamics. The four BDPD directions identify ways in which the cascade mechanism changes when the agents are LLMs rather than humans. The BDPD1 cheap-talk null predicts that LLM agents may be less prone to cascade — because they are less sensitive to the signal content of observable actions. The speed asymmetry predicts that LLM cascades, when they do form, will be harder to break — because they propagate at machine speed, closing the window for corrective intervention. The introspectable-belief capability predicts that requiring belief reports will inhibit cascade formation — because the reporting requirement breaks the observational closure on which the cascade depends. And the missing experiment operationalises all three predictions in a factorial design that isolates the cascade mechanism from confounds.
The cultural payoff of the lecture is not “transparency is bad” or “information doesn’t help.” It is the more careful claim that information helps when it is structured to preserve the distinction between private signals and public actions, and the structure that preserves that distinction for human agents may not preserve it for LLM agents. The BDPD platform, by making the agents’ architecture an experimental variable rather than an implicit constant, can ask which observational structures survive the transition — and the answer matters because the transition is already under way.
8.7 Open questions and the bridge to Lecture 9
8.7.1 What does the existing BDPD data not tell us about cascades?
None of the three published BDPD papers operationalises a cascade experiment. The BDPD1 cheap-talk paper provides a structural bridge — the near-null cheap-talk effect among LLMs predicts a near-null cascade effect — but the prediction has not been tested. The BDPD3 polycentric-cascade experiment studies cascading externalities across governance arenas, not informational cascades among sequential decision-makers. The conceptual parallel between the two kinds of cascade — both involve agents whose decisions propagate effects that subsequent agents cannot fully observe — is suggestive but not probative. The empirical ground under the BDPD-cascade reframe is thin.
8.7.2 Can LLM agents be designed to resist cascades?
The Bito et al. finding that informational conformity varies across LLM architectures suggests that the cascade propensity is not a fixed feature of “LLM agents” but a parameter that can be tuned — through model selection, prompt engineering, persona assignment, or fine-tuning. If the cascade propensity can be reduced below the human baseline, then the LLM cascade problem identified in Direction 1 (too few cascades) and Direction 2 (too fast to break) may be solvable through architectural engineering rather than institutional design. The question — can LLM agents be designed to resist informational cascades? — is the mirror image of the classical question — can institutional rules prevent cascades among humans? — and the BDPD platform is the tool for asking both.
8.7.3 What about cascades in mixed human-LLM populations?
The missing experiment described in §5 assumes homogeneous populations within each cell (all LLM or all rule-based). A more demanding experiment — and one that maps onto the mixed human-AI decision environments that are already emerging (algorithmic trading alongside human traders, LLM-assisted medical diagnosis alongside human clinicians, automated content moderation alongside human moderators) — would cross agent architecture with position in the sequence. What happens when the first two agents are LLMs and the subsequent agents are humans? What happens when the sequence is LLM-human-LLM-human, alternating? The classical cascade literature found that the early agents in a sequence are disproportionately influential — their choices, being the first, carry the most weight for those who follow. If the early agents in a mixed sequence are LLMs, their cascade propensity — whatever it turns out to be — will disproportionately shape the outcome for the humans who come after.
8.7.4 The bridge to Lecture 9
The thread connecting Lecture 8 to Lecture 9 is the question of repetition. Informational cascades, in the BHW-Anderson sense, are a one-shot phenomenon: the sequence runs once, the cascade forms or does not form, and the outcome is final. But many real-world cascade-like phenomena — fads, fashions, technological standards, political movements — involve repeated interactions among the same agents over time. The folk theorem of repeated games, the subject of Lecture 9, says that under repetition, almost any outcome — including full cooperation and full mutual exploitation — can be sustained as an equilibrium. The cascade mechanism of Lecture 8 and the folk-theorem mechanism of Lecture 9 share a core structural feature: both depend on the observability of others’ past actions. In a cascade, the observability produces lock-in on a wrong answer. In a repeated game, the observability can produce cooperation — or can produce the opposite, depending on the equilibrium the agents coordinate on. The bridge between the two lectures is the question: does the introduction of repetition break the cascade or reinforce it? The answer depends on what the agents do with the repeated observations — and the BDPD platform, by making repetition an experimental parameter, can deliver it.