Evaluating Approval Voting Against Arrow's Impossibility Theorem Using Binary Matrices and Primary Preference Data

This investigation explores the extent to which approval voting satisfies the fairness conditions of Arrow's Impossibility Theorem using primary preference data. The author collects cuisine preferences from students and models the results using a binary approval matrix and vector summation to establish social rankings.

The analysis tests the dataset against five fairness principles: nondictatorship, Pareto efficiency, independence of irrelevant alternatives (IIA), unrestricted domain, and social ordering. Findings indicate that most conditions were satisfied, though Pareto efficiency remained inconclusive. The exemplar is valuable for its systematic application of matrix algebra to social choice theory and its critical evaluation of the limitations of empirical voting data.