A full formal representation of Arrow's impossibility theorem.

Area of Science:

• Economics
• Political Science
• Philosophy
• Formal Logic

Background:

• Kenneth Arrow's impossibility theorem is a cornerstone in social choice theory, economics, and political science.
• Existing proofs often prioritize intuitive accessibility over mathematical rigor.
• The theorem has profound implications for understanding collective decision-making and social welfare functions.

Purpose of the Study:

• To develop a new, mathematically rigorous proof of Kenneth Arrow's impossibility theorem using formal logic.
• To reveal the global structure of the social welfare function central to the theorem.
• To extend the theorem's applicability to a wider range of preference relations.

Main Methods:

• Construction of a proof using a formal logic proof calculus.
• Development of a full mathematical representation of the theorem.
• Systematic application of formal logic techniques to theorem proving.

Main Results:

• A novel proof of Arrow's impossibility theorem with enhanced mathematical detail.
• Identification of the global structure of the social welfare function.
• Accommodation of a broader spectrum of preference relations beyond standard rationality assumptions.

Conclusions:

• Formal logic offers a powerful methodological contribution to the study of Arrow's impossibility theorem.
• The new proof enhances understanding of the theorem's structure and implications.
• The framework supports the integration of diverse human behavior patterns into social choice theory.