What are the paradoxes in decision theory?

Decision theory models how rational agents should make choices under uncertainty using probability and expected utility. However, real-world choices and collective outcomes frequently reveal paradoxes that defy these theoretical models. Famous examples include the Ellsberg paradox, which demonstrates ambiguity aversion, and the Condorcet paradox, which shows that majority voting rules can lead to cyclic, self-contradictory preferences.

What we know

• Decision theory relies on expected utility and probability to prescribe optimal decisions for a rational agent under uncertainty. [3]
• The Ellsberg paradox illustrates that people often prefer choices with quantifiable risks over those with unknown, incalculable risks, violating subjective expected utility theory. [4]
• Condorcet's paradox demonstrates that majority rule can produce intransitive, rock-paper-scissors style preferences among three or more options. [5]
• Arrow's paradox implies that any social decision-making process must ultimately be either self-contradictory or a dictatorship. [5]

Where to go next

• a case in pointWhat is the Ellsberg paradox?
• how it workedHow does majority voting fail?
• the bigger pictureWhat is decision theory?
• what followedWhat does Arrow's theorem prove about voting?
• compared withHow do set theory paradoxes compare to mathematical decision puzzles?
• an unexpected connectionHow did set theory and decision theory both generate counter-intuitive paradoxes?Both mathematical set theory and prescriptive decision theory encounter foundational paradoxes that reveal surprising, counter-intuitive results rather than mere errors.

Sources

• [1]paradoxes of set theory (Wikidata Q4344872) · CC0 1.0
• [2]Paradoxes of set theory · CC BY-SA 4.0
• [3]Decision theory · CC BY-SA 4.0
• [4]Ellsberg paradox · CC BY-SA 4.0
• [5]Condorcet paradox · CC BY-SA 4.0