Pignistic probability
Encyclopedia
Pignistic probability, in decision theory
, is a probability
that a rational person will assign to an option when required to make a decision.
A person may have, at one level certain beliefs or a lack of knowledge, or uncertainty, about the options and their actual likelihoods. However, when it is necessary to make a decision (such as deciding whether to place a bet
), the behaviour of the rational person would suggest that the person has assigned a set of regular probabilities to the options. These are the pignistic probabilities.
The term was coined by Philippe Smets, and stems from the Latin pignus, a bet. He contrasts the pignistic level, where one might take action, with the credal level, where one interprets the state of the world:
A pignistic probability transform will calculate these pignistic probabilities from a structure that describes belief structures.
Decision theory
Decision theory in economics, psychology, philosophy, mathematics, and statistics is concerned with identifying the values, uncertainties and other issues relevant in a given decision, its rationality, and the resulting optimal decision...
, is a probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
that a rational person will assign to an option when required to make a decision.
A person may have, at one level certain beliefs or a lack of knowledge, or uncertainty, about the options and their actual likelihoods. However, when it is necessary to make a decision (such as deciding whether to place a bet
Gambling
Gambling is the wagering of money or something of material value on an event with an uncertain outcome with the primary intent of winning additional money and/or material goods...
), the behaviour of the rational person would suggest that the person has assigned a set of regular probabilities to the options. These are the pignistic probabilities.
The term was coined by Philippe Smets, and stems from the Latin pignus, a bet. He contrasts the pignistic level, where one might take action, with the credal level, where one interprets the state of the world:
- The transferable belief modelTransferable belief modelThe transferable belief model is an elaboration on the Dempster-Shafer theory of evidence.-Context:Consider the following classical problem of information fusion. A patient has an illness that can be caused by three different factors A, B and C...
is based on the assumption that beliefs manifest themselves at two mental levels: the ‘credal’ level where beliefs are entertained and the ‘pignistic’ level where beliefs are used to make decisions (from ‘credo’ I believe and ‘pignus’ a bet, both in Latin). Usually these two levels are not distinguished and probability functions are used to quantify beliefs at both levels. The justification for the use of probability functions is usually linked to ”rational” behavior to be held by an ideal agent involved in some decision contexts.
A pignistic probability transform will calculate these pignistic probabilities from a structure that describes belief structures.
Further reading
- P. Smets and R. Kennes, “The Transferable Belief Model", Artificial Intelligence (v.66, 1994) pp. 191-243