Degrees of belief are usually expressed using real numbers ranging from 0 to 1, where 0 means that the person thinks the proposition is certainly false, 1 means that they think the proposition is certainly true, and 0.5 means that they think that it is just as likely to be true as it is to be false (Hájek ~~2011)~~2002). For example, if all of the evidence a person has suggests that there's a 73% chance of rain tomorrow, then their credence that it will rain tomorrow should be 0.73.

Rational credences follow the probability axioms. For example: it is irrational to think that "the sky is blue and it is raining" is more likely than "it is raining" (Wikipedia ~~2016a)~~2001). Credences are deemed more accurate the closer that they are to the truth (see Wikipedia ~~2016b)~~2006): if the sky is blue, a credence of 0.3 that the sky is blue is more accurate than a credence of 0.2 that the sky is blue, even if neither is particularly good.

Bradley, ~~Seamus. 2014.~~Seamus (2014) Imprecise ~~credences~~probabilities~~. In Edward Zalta (ed.)~~, * The Stanford Encyclopedia of Philosophy*, December 20 (updated 19 February 2019).

Hájek, ~~Alan. 2011.~~Alan (2002) Interpretations of probability~~. In Edward Zalta (ed.)~~, * The sect. 3.3, Stanford Encyclopedia of Philosophy*,

~~Wikipedia. 2016a.~~Wikipedia (2001) Probability axioms, *Wikipedia*, September 13 (updated 11 April 2021).

~~Wikipedia. 2016b.~~Wikipedia (2006) Scoring rule, *Wikipedia*, February 15 (updated 13 February 2021).

credal resilience | decision theory | expected value | forecasting | model uncertainty | value of information

The **credence** a person has in a proposition is the degree of belief that they have in that proposition: how probable they think it is, given their evidence.

Degrees of belief are usually expressed using real numbers ranging from 0 to 1, where 0 means that the person thinks the proposition is certainly false, 1 means that they think the proposition is certainly true, and 0.5 means that they think that it is just as likely to be true as it is to be false (Hájek 2011). For example, if all of the evidence a person has suggests that there's a 73% chance of rain tomorrow, then their credence that it will rain tomorrow should be 0.73.

Rational credences follow the probability axioms. For example: it is irrational to think that "the sky is blue and it is raining" is more likely than "it is raining" (Wikipedia 2016a). Credences are deemed more accurate the closer that they are to the truth (see Wikipedia 2016b): if the sky is blue, a credence of 0.3 that the sky is blue is more accurate than a credence of 0.2 that the sky is blue, even if neither is particularly good.

Because credences can be represented by real numbers, they admit of arbitrarily high degrees of precision: the credence a person should have that their candidate will win the election could be 0.6172935479 … . However it seems that sometimes, especially when people are ignorant about the probability that a given event will occur, their credences should be imprecise. Imprecise credences can be represented as an interval. So a person’s credence that their candidate will win the election could be the interval [0.6, 0.65] instead of a precise credence within that interval (Bradley 2014).

Bradley, Seamus. 2014. Imprecise credences. In Edward Zalta (ed.), *The Stanford Encyclopedia of Philosophy*.

Hájek, Alan. 2011. Interpretations of probability. In Edward Zalta (ed.), *The Stanford Encyclopedia of Philosophy*, sect. 3.3.*Discusses probabilities as degrees of belief in a proposition.*

Wikipedia. 2016a. Probability axioms.

Wikipedia. 2016b. Scoring rule.

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Because credences can be represented by real numbers, they admit of arbitrarily high degrees of precision: the credence a person should have that their candidate will win the election could be 0.6172935479 … . However it seems that sometimes, especially when people are ignorant about the probability that a given event will occur, their credences should be

~~imprecise.~~imprecise. Imprecise credences can be represented as an interval. So a person’s credence that their candidate will win the election could be the interval [0.6, 0.65] instead of a precise credence within that interval (Bradley 2014).