Why rational choices can change faster than the world they track

Choosing a university major involves both personal research and clues from what recent graduates have chosen. But the labor-market conditions those choices reflect may already be changing. Wanying Huang uses this kind of problem to motivate Action Volatility in a Changing World, a theoretical paper about how frequently decisions shift when people learn from one another in an evolving environment.

The preprint, first submitted in 2022 and revised in November 2026, establishes a precise ordering within its model: underlying conditions change least frequently, private signals change most frequently, and actions fall strictly between them over the long run. Temporary herding smooths noisy information, but not enough to make behavior as stable as the conditions being tracked.

Different people, successive decisions

The model has two possible states of the world and two possible actions. Each period brings a new agent who acts only once, earning a payoff if her choice matches the current state. Action switching therefore means a difference between successive agents’ choices—not a single person repeatedly changing her mind.

Before choosing, each agent observes every previous action and receives a private signal about the current state. Signals are informative but imperfect. Agents make rational decisions using the information available to them; the result does not require imitation as a behavioral shortcut or rewards for conforming.

The state has the same probability of switching in either direction. Huang focuses on a relatively stable environment: the switching probability must be positive but smaller than signal accuracy multiplied by its error probability. This restriction allows past actions to remain informative enough for temporary information cascades to arise.

When both actions are equally attractive, the agent follows her immediate predecessor. The paper uses this rule so that switches reflect strict preferences rather than arbitrary tie-breaking.

Herding has an expiration date

An information cascade begins when evidence inferred from past choices outweighs either possible private signal. An agent then chooses the same action regardless of what her own signal says.

That makes successive actions look stable. However, a cascade also prevents those actions from revealing fresh private information. Meanwhile, the possibility of a state change gradually makes older evidence less relevant. Public beliefs move toward uncertainty until a new agent’s private signal can influence her choice again.

This is why cascades cannot persist indefinitely in the model. They alternate with periods in which agents follow—and thereby reveal—their private signals.

These recurring learning periods create opportunities for action switches even when the state has not changed. Conversely, a cascade can keep actions unchanged when the state does change. Huang’s theorem establishes that, over the long run, the resulting action-switching frequency remains strictly above the state-switching frequency and strictly below the signal-switching frequency.

For illustration, the paper considers signals that are correct 80% of the time and a state that switches with a 1% probability each period. State changes occur once every 100 periods on average, while signals switch roughly once every three periods. Huang derives an upper bound of about 44 periods on the expected interval between action switches. That is a bound, not an exact prediction of how long each action persists.

More information can push either way

The paper also considers agents who observe all previous signals rather than only previous actions. This removes the information loss associated with observing choices that conceal private signals during cascades.

Yet the extra information does not always reduce switching. Huang identifies a regime with very weak signals and a sufficiently stable state in which observing signals produces more action changes. Long cascades stabilize behavior when only actions are visible; agents with access to signals instead keep incorporating noisy evidence.

In another regime, with highly accurate signals and a particular relationship between state changes and signal errors, the ordering reverses. Access to accumulated signals helps agents resist an isolated misleading observation, reducing switching relative to the public-action setting.

These are results about a specified theoretical environment, not measurements of actual students or financial traders. The paper leaves a complete characterization of the information regimes—and comparisons of their long-run mistake probabilities—for future research. Its central distinction is therefore between how often choices change and how often reality changes, not a claim that fewer switches necessarily mean better decisions.