Choice sets.md

#flashcards/micro

Choice sets

Choice sets are determined by preferences and choices

Preferences

Preferences are indicated by the symbol $\succsim$. Implies that item 1 is at least indifferent to item b.

$a\succsim b$	$b\succsim a$	Result
true	false	$a\succ b$. (Strict preference)
true	true	$a\ \mathtt{\sim} \ b$ (Indifference)
false	false	incomplete set

Comprehensible preference sets are Transitive and complete

Transitivity

A preference set is Transitive if :: $a\succsim b$ and $b\succsim c$ then $a\succsim c$ or $a\succ b$ and $b\succ c$ then $a\succ c$

A Transitive set requires at least 3 elements

Completeness

A set where $a\succsim b$ and $b\succsim a$ or adequate information is not present is an incomplete set

Choices

a is a maximal element in the Choice set X if :: $a\succsim b$ for all $b \in X$

If there is a maximal element in the choice set, it will be chosen. Else indifferent elements will have equal chance to be chosen. There can be a subset of more preffered elements that are all indifferent to each other.