Moving Average Updaters Sample Clauses

Moving Average Updaters. ‌ The Bayesian model is the standard in economics for its logical foundation and its normative beauty. Unfortunately, empirical failures of the model are numerous, and individuals frequently follow alternative modes of cognition (cf. Kahneman, Slovic, and Xxxxxxx 0000, Xxxxxxx 2012). In the context of sequential learning, Xxxxxxxxxx under a unanimous rule, always voting to acquit is an equilibrium strategy since a juror cannot affect the outcome by changing his vote. and Xxxxxx (1992) find a moving average model to be empirically preferable. In that model, the juror begins with an initial strength of belief J0 ∈ [0, 1]. The upper and lower thresholds correspond to full confidence in guilt and innocence, respectively. At each update the juror forms a new strength of belief that is a weighted average of the prior belief and the current signal, Jm = wJm−1 + (1 − w)sm, for w ∈ (0, 1), m ∈ Z+. The signal sm could equal λm if the juror perfectly tracks information, but for a fair comparison with the Bayesian model, assume the signal is either guilty or innocent, where a guilty (innocent) signal maps to one (zero) on the strength-of-belief scale. After the final update, the juror compares Jk to a threshold J¯. If Jk ≥ J¯, he prefers to convict; otherwise, he prefers to acquit. Mathematically, the primary difference between the moving average and Bayesian models is that in the former updates are additive while in the latter they are multiplicative. One advantage of the moving average model is that a result analogous to Proposi- tion 1 does not hold.10 A single additional update cannot lead to arbitrarily extreme beliefs because the weight on the initial belief constrains the update. Consider that J = J w2 + w(1 − w) g1 + (1 − w) g2 .