By Michael D. Resnik
An advent to what's known as "Choice Theory" in Economics.
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Additional resources for Choices: An Introduction to Decision Theory
Decision theorists call the various ways of numbering the items in a preference ordering utility functions or utility scales. (More precisely, the functions are the various ways of associating numbers with preference orderings and the scales are the sequences of numbers used. ) Utility functions (scales) that satisfy conditions (a) and (b) are called ordinal utility functions (scales) because they represent only the ordering of an agent's preferences. Any change or transformation of an ordinal scale that preserves this representation gives rise to an equally acceptable ordinal scale for the agent's preferences.
Explain your reasoning. 3. My criticism of the maximin rule based on table 2-4 tacitly presupposes that we know more than the fact that the agent prefers more money to less. What more must we know for my criticism to work? 4. Present decision tables that show that neither the maximin nor the lexical maximin rule always excludes a dominated act. 2-3. 50, suggest that in some situations it may be relevant to focus on missed opportunities rather than on the worst possibilities. 50 if he does AI when the true state is S\.
Both times we transformed the decision tables using an ordinal transformation, but the second time we operated in accordance with a special type of ordinal transformation. For notice that the conversion of 1 to 3, 3 to 7, 5 to 11, and 7 to 15 takes place according to the formula 29 DECISIONS UNDER IGNORANCE This is a special case of the formula which is known as a linear transformation because the graph of u' against u is a line. When a > 0, as happens above, the transformation is called a positive linear transformation.