Savage's Concept of Probability

Starting with personal preference, Savage [3] constructs a foundation theory for probability from the qualitative probability to the quantitative probability and to utility. There are some profound logic connections between three steps in Savage's theory; that is, quantitative concepts properly represent qualitative concepts. Moreover, Savage's definition of subjective probability is in accordance with probability theory, and the theory gives us a rational decision model only if we assume that the weak ...

Understanding Expected Utility for Decision Making

In this paper,we present a brief version of de Finetti-Ramsey’s subjective probability theory and provide a rigorous yet intuitively plausible explanation of expected utility using elementary mathematics.In a final section,we take up the case of some“Paradoxes in Expected Utility Theory”and try to reconcile them with the help of subjective probabilities.

Certainty-based Preference Completion

As from time to time it is impractical to ask agents to provide linear orders over all alternatives,for these partial rankings it is necessary to conduct preference completion.Specifically,the personalized preference of each agent over all the alternatives can be estimated with partial rankings from neighboring agents over subsets of alternatives.However,since the agents’rankings are nondeterministic,where they may provide rankings with noise,it is necessary and important to conduct the certainty-based preference completion.Hence,in this paper firstly,for alternative pairs with the obtained ranking set,a bijection has been built from the ranking space to the preference space,and the certainty and conflict of alternative pairs have been evaluated with a well-built statistical measurement Probability-Certainty Density Function on subjective probability,respectively.Then,a certainty-based voting algorithm based on certainty and conflict has been taken to conduct the certainty-based preference completion.Moreover,the properties of the proposed certainty and conflict have been studied empirically,and the proposed approach on certainty-based preference completion for partial rankings has been experimentally validated compared to state-of-arts approaches with several datasets.

The Role of the Subjectivist Position in the Probabilization of Forensic Science

This paper is concerned with the contribution of forensic science to the legal process by helping reduce uncertainty.Although it is now widely accepted that uncertainty should be handled by probability because it is a safeguard against incoherent proceedings,there remain diverging and conflicting views on how probability ought to be interpreted.This is exemplified by the proposals in scientific literature that call for procedures of probability computation that are referred to as"objective,"suggesting that scientists ought to use them in their reporting to recipients of expert information.I find such proposals objectionable.They need to be viewed cautiously,essentially because ensuing probabilistic statements can be perceived as making forensic science prescriptive.A motivating example from the context of forensic DNA analysis will be chosen to illustrate this.As a main point,it shall be argued that such constraining suggestions can be avoided by interpreting probability as a measure of personal belief,that is,subjective probability.Invoking references to foundational literature from mathematical statistics and philosophy of science,the discussion will explore the consequences of this interdisciplinary viewpoint for the practice of forensic expert reporting.It will be emphasized that-as an operational interpretation of probability_the subjectivist perspective enables forensic science to add value to the legal process,in particular by avoiding inferential impasses to which other interpretations of probability may lead.Moreover,understanding probability from a subjective perspective can encourage participants in the legal process to take on more responsibility in matters regarding the coherent handling of uncertainty.This would assure more balanced interactions at the interface between science and the law.This,in turn,provides support for ongoing developments that can be called the"probabilization"of forensic science.