Decision Tables

A decision table is a simple format used in classical decision theory to present simple decision-making problems under uncertainty. The rows of such a table represent the decisions (actions) available to the decision maker (DM) and the columns represent the states of the world, that is states of Nature associated with the with the problem. The entries of such a table represent the outcomes/consequences associated with the respective (decision,state) pairs.

The following decision table, due to Leonard Savage (1917-1971), is the most famous decision table in this Universe:

Decision State of Nature
Good Rotten
Break into bowl Six-egg omelet No omelet and five good eggs destroyed
Break into saucer Six-egg omelet and a saucer to wash Five-egg omelet and a saucer to wash
Throw away Five-egg omelet and one good egg destroyed Five-egg omelet

The short story behind it is as follows:

A senior decision theorist has to decide whether to break the sixth egg into a ball of five eggs before making an omelet; or to throw it away; or to break it into a saucer.

There are two states regarding the sixth egg: it can be either “good” or “rotten”. The DM has three possible decisions and She must decide which one is best (without knowing the state of the sixth egg).

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