Response to a review of voting theory for democracy, in the light of the economic crisis and the role of mathematicians

Economic theory needs a stronger defence against unwise application of mathematics. Mathematicians are trained for abstract thought and not for empirical science. Their contribution can wreak havoc, for example in education with real life pupils and students, in finance by neglecting real world risks that contribute to a world crisis, or in voting theory where they don’t understand democracy. In 1951 the mathematician Kenneth Arrow formulated his Impossibility Theorem in social welfare theory and since then mathematicians have been damaging democracy. My book Voting Theory for Democracy (VTFD) tries to save democracy and social welfare from such destruction. VTFD applies deontic logic to Arrow’s Theorem and shows that Arrow’s interpretation cannot hold. The editor of a journal in voting matters has VTFD reviewed by a mathematician instead of a researcher who is sensitive to economics, democracy and empirical issues. Guess what happens. The review neglects economics, democracy and empirical issues. Curiously it also neglects the argument in deontic logic, perhaps given the distinction between mathematics and logic. Given the importance of democracy it is advisable that economists study the situation and rethink how economics and mathematics interact in practice.