You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
It is well known that sequential decision making may lead to information cascades. That is, when agents make decisions based on their private information, as well as observing the actions of those before them, then it might be rational to ignore their private signal and imitate the action of previous individuals. If the individuals are choosing between a right and a wrong state, and the initial actions are wrong, then the whole cascade will be wrong. This issue is due to the fact that cascades can be based on very little information. We show that if agents occasionally disregard the actions of others and base their action only on their private information, then wrong cascades can be avoided. Moreover, we study the optimal asymptotic rate at which the error probability at time @math can go to zero. The optimal policy is for the player at time @math to follow their private information with probability @math , leading to a learning rate of @math , where the constants @math and @math are explicit.

Cited Abstract(s):
[1]: In this paper, we explore the rules that determine intuitive predictions and judgments of confidence and contrast these rules to the normative principles of statistical prediction. Two classes of prediction are discussed: category prediction and numerical prediction. In a categorical case, the prediction is given in nominal form, for example, the winner in an election, the diagnosis of a patient, or a person's future occupation. In a numerical case, the prediction is given in numerical form, for example, the future value of a particular stock or of a student's grade point average. In making predictions and judgments under uncertainty, people do not appear to follow the calculus of chance or the statistical theory of prediction. Instead, they rely on a limited number of heuristics which sometimes yield reasonable judgments and sometimes lead to severe and systematic errors (Kahneman & Tversky, 1972b, 3; Tversky & Kahneman, 1971, 2; 1973, 11). The present paper is concerned with the role of one of these heuristics – representativeness – in intuitive predictions. Given specific evidence (e.g., a personality sketch), the outcomes under consideration (e.g., occupations or levels of achievement) can be ordered by the degree to which they are representative of that evidence. The thesis of this paper is that people predict by representativeness, that is, they select or order outcomes by the degree to which the outcomes represent the essential features of the evidence.

[2]: When a series of individuals with private information announce public predictions, initial conformity can create an 'information cascade' in which later predictions match the early announcements. This paper reports an experiment in which private signals are draws from an unobserved urn. Subjects make predictions in sequence and are paid if they correctly guess which of two urns was used for the draws. If initial decisions coincide, then it is rational for subsequent decisionmakers to follow the established pattern, regardless of their private information. Rational cascades formed in most periods in which such an imbalance occurred. Copyright 1997 by American Economic Association.

[3]: This paper reports an experimental test of how individuals learn from the behavior of others. By using techniques only available in the laboratory, we elicit subjects' beliefs. This allows us to distinguish informational cascades from herd behavior. By adding a setup with continuous signal and discrete action, we enrich the ball-andurn observational learning experiments paradigm of Lisa R. Anderson and Charles Holt (1997). We attempt to understand subjects' behavior by estimating a model that allows for the possibility of errors in earlier decisions.
One possible source of additional information comes from people not acting in a rational, Bayesian manner. It is well documented that human behavior is often irrational (see, e.g., [1] ). In the information cascades setting, laboratory experiments by Anderson and Holt [2] show that while most participants act rationally, many do not. When deviations from rational behavior occur, participants often act mainly or solely based on their private information, disregarding the information in the actions of those before them. See also related experiments and results by C elen and Kariv [3] for a setting with continuous signals. Such individuals effectively reveal their private signal, which is valuable information for those coming after them. The model described in , which contains and , captures this empirically observed behavioral phenomenon.