Description and the Problem of Priors

Abstract

Abstract. Belief-revision models of knowledge describe how to update one's degrees of belief associated with hypotheses as one considers new evidence, but they typically do not say how probabilities become associated with meaningful hypotheses in the first place. Here we consider a variety of Skyrms-Lewis signaling game [Lewis (1969)] [Skyrms (2010)] where simple descriptive language and predictive practice and associated basic expectations coevolve. Rather than assigning prior probabilities to hypotheses in a fixed language then conditioning on new evidence, the agents begin with no meaningful language or expectations then evolve to have expectations conditional on their descriptions as they evolve to have meaningful descriptions for the purpose of successful prediction. The model, then, provides a simple but concrete example of how the process of evolving a descriptive language suitable for inquiry might also provide agents with conditional expectations that reflect the type and degree of predictive success in fact afforded by their evolved predictive practice. This illustrates one way in which the traditional problem priors may simply fail to apply to one's model of evolving inquiry. Description, Prediction, and ExpectationBelief-revision models of knowledge describe how to update one's degrees of belief as one considers new evidence. On a Bayesian model, for example, one fixes a descriptive language, sets coherent prior probabilities over a set of hypotheses expressed in the language, then updates one's degrees of belief as one conditions on new evidence. While such an account of reflective inquiry has many virtues, it has nothing to say concerning how to assign prior probabilities to meaningful hypotheses. This is the problem of priors.On reflection, one might, however, find the problem of priors itself puzzling.While it is indeed unclear what procedure one should adopt in assigning prior expectations to hypotheses expressed in a fixed descriptive language, it is similarly unclear how one might ever come to use such a language without already having a rich set of expectations. The symmetry of these reflections suggests a strategy.We will consider how it might be possible for basic expectations to coevolve with a simple descriptive language. More specifically, we will consider how simple for coordinated prediction might also also provide a core set of well-tuned posterior expectations that might then be available to constrain subjective degrees of belief should the agent turn to reflective inquiry.We will consider the story in three parts. Part I: The Coevolution of Description and PredictionA sender-predictor game is a variety of Skyrms-Lewis signaling game.2 In a sender-predictor game, however, the agents coevolve both descriptive and predictive dispositions. We will refer to these are the agents' first-order dispositions. Their second-order dispositions determine how they update their first-order dispositions as they learn from experience.

Evolving to Generalize: Trading Precision for Speed

“…An ESS is a strategy in a game that is robust against invasion by other strategies because it garners high payoffs for those using it. 3 The arguments Maynard Smith and Harley give are intuitively straightforward. Suppose that some learning rule does not lead to play of ESSes in games.…”

“…6 But, if learning is most effective in a variable environment, to the extent that it should not be expected to evolve otherwise, this assumption is suspect. In a vari- 3 To be specific, an evolutionary stable strategy x i is one such that if u(x i , x j ) is the payoff of strategy x i played against [28], and Maynard-Smith [21]. 6 There are some exceptions.…”

“…27 The results of simulations for these rules were highly similar to those presented in the last section. I also explored a learning rule outlined by Barrett [3], which I call Barrett Learning. This rule is in some ways similar to Adjustable Reference Point with Truncation learning introduced by Bereby and Erev [5].…”

Typical worlds

“…Why we should be able to assume our own world to be typical is, of course, itself an interesting question, but one that is beyond the scope of the present paper. (1973,252) 23 See Barrett (2014) for a signaling-game account of how a descriptive partition and an assignment of effective priors might coevolve. The model illustrates how a rich set of effective priors might evolve by means of precisely the same process by which one comes to have a reliable descriptive language.…”