Edited by Richard Pettigrew (Bristol University)
|Summary||Scoring rules play an important role in statistics, decision theory, and formal epistemology. They underpin techniques for eliciting a person's credences in statistics. And they have been exploited in epistemology to give arguments for various norms that are thought to govern credences, such as Probabilism, Conditionalization, the Reflection Principle, the Principal Principle, and Principles of Indifference, as well as accounts of peer disagreement and the Sleeping Beauty puzzle. A scoring rule is a function that assigns a penalty to an agent's credence (or partial belief or degree of belief) in a given proposition. The penalty depends on whether the proposition is true or false. Typically, if the proposition is true then the penalty increases as the credence decreases (the less confident you are in a true proposition, the more you will be penalised); and if the proposition is false then the penalty increases as the credence increases (the more confident you are in a false proposition, the more you will be penalised). In statistics and the theory of eliciting credences, we usually interpret the penalty assigned to a credence by a scoring rule as the monetary loss incurred by an agent with that credence. In epistemology, we sometimes interpret it as the so-called 'gradational inaccuracy' of the agent's credence: just as a full belief in a true proposition is more accurate than a full disbelief in that proposition, a higher credence in a true proposition is more accurate than a lower one; and just as a full disbelief in a false proposition is more accurate than a full belief, a lower credence in a false proposition is more accurate than a higher one. Sometimes, in epistemology, we interpret the penalty given by a scoring rule more generally: we take it to be the loss in so-called 'cognitive utility' incurred by an agent with that credence, where this is intended to incorporate a measure of the accuracy of the credence, but also measures of all other doxastic virtues it might have as well. Scoring rules assign losses or penalties to individual credences. But we can use them to define loss or penalty functions for credence functions as well. The loss assigned to a credence function is just the sum of the losses assigned to the individual credences it gives. Using this, we can argue for such doxastic norms as Probabilism, Conditionalization, the Principal Principle, the Principle of Indifference, the Reflection Principle, norms for resolving peer disagreement, norms for responding to higher-order evidence, and so on. For instance, for a large collection of scoring rules, the following holds: If a credence function violates Probabilism, then there is a credence function that satisfies Probabilism that incurs a lower penalty regardless of how the world turns out. That is, any non-probabilistic credence function is dominated by a probabilistic one. Also, for the same large collection of scoring rules, the following holds: If one's current credence function is a probability function, one will expect updating by conditionalization to incur a lower penalty than updating by any other rule. There is a substantial and growing body of work on how scoring rules can be used to establish other doxastic norms.|
|Key works||Leonard Savage (Savage 1971) and Bruno de Finetti (de Finetti 1970) introduced the notion of a scoring rule independently. The notion was introduced into epistemology by Jim Joyce (Joyce 1998) and Graham Oddie (Oddie 1997). Joyce used it to justify Probabilism; Oddie used it to justify Conditionalization. Since then, authors have improved and generalized both arguments. Improved arguments for Probabilism can be found in (Joyce 2009), (Leitgeb & Pettigrew 2010), (Leitgeb & Pettigrew 2010), (Predd et al 2009), (Schervish et al manuscript), (Pettigrew 2016). Improved arguments for Conditionalization can be found in (Greaves & Wallace 2005), (Easwaran 2013), (Schoenfield 2017), (Pettigrew 2016). Furthermore, other norms have been considered, such as the Principal Principle (Pettigrew 2012), (Pettigrew 2013), the Principle of Indifference (Pettigrew 2016), the Reflection Principle (Huttegger 2013), norms for resolving peer disagreement (Moss 2011), (Levinstein 2015), (Levinstein 2017), and norms for responding to higher-order evidence (Schoenfield 2018).|
|Introductions||Pettigrew, Richard (2011) 'Epistemic Utility Arguments for Probabilism', Stanford Encyclopedia of Philosophy (Pettigrew 2011)|
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