2. Preference and Choice

Foundations of rational choice — from the axioms of preference relations to choice rules and WARP.

• Preference Relations and Axioms — This scene draws your preferences on the two-good plane. A ranking is rational when nothing is left unranked. It also never loops back on itself. Such a ranking can be written as utility numbers, as in the formula below. Change the utility family and the whole curve map changes. You also see what breaks when an axiom fails. For example, suppose a 🍎 apple bundle beats a 🍌 banana bundle. And the banana bundle beats a 🍞 bread bundle. Then the apple bundle must beat the bread bundle too.
• Choice Rules and WARP — In this scene you pick bundles yourself under two different budgets. A chosen bundle reveals what you like. A bundle you could afford but skipped counts as worse. If two situations flip each other's picks, that is a contradiction. The formula below, WARP, is the rule that catches it. For example, you have 💰 1,000 won and pick 🍎 apples, though 🍌 bananas cost no more. The next day you pick bananas, though apples cost no more. Your two picks now contradict each other.