Choices by one agent in which background conditions are independent of what other agents are doing. We usually represent these decisions with a decision matrix or decision table. Sometimes called evidential decision theory.

e.g. Pascal’s Wager

Components:

• Rows are possible acts
• Acts are functions that map states to outcomes
• Columns are possible states of the world
• Probabilities are sometimes included for decisions under risk.
• Should not depend on agent action
• States should be
• Mutually exclusive
• Exhaustive: no possibility is left out
• Relevant partition: distinctions that actually have impact on probability or utility of outcomes
• Independence: (optional) each state should be causally and probabilistically independent of the acts
• Dominance principle only holds if independent holds
• Cells are outcomes.
• Can be described using
• Verbal description
• Preference ranking on an ordinal scale
• Defines a partial ordering of outcomes
• is a weak preference
• is a strong preference
• is indifference between and
• Utility (numerical value) using an interval scale

Decision tables

1. Art: providing a good formalization of a decision into a table
2. providing a justified recommendation based off of the formalization

They can also be represented using decision trees

We can transform decision tables between each other using “reasonable transformations”

1. PIR: assign equal probabilities to all states (if we have no knowledge of probabilities, aka DUI)
2. Merger: if two states yield identical columns, then we can merge them into one state and add probabilities if we know them