The Borda count illustrates Arrow’s impossibility theorem by showing that majority voting:
is inconsistent with the principle of unanimity
leads to social preferences that are not transitive
violates the independence of irrelevant alternatives
makes one person in effect a dictator
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The Condorcet paradox shows Arrow’s impossibility theorem by showing that pairwise majority voting
There are two politicians running for office. A key issue is how much to spend on environment protection programs. Among the 1000 voters, 400 want to spend $80 million, 300 want to spend $20 million, and 300 want to spend nothing. What is the winning position on this issue?