Originally posted on Combinatorics and more:
I took part in a workshop celebrating the publication of a new book on Social Choice by Shmuel Nitzan which took place at the Open University. (The book is in Hebrew, and an English version is forthcoming from Cambridge University Press.) It was a very interesting event and all the lectures were excellent. I thought of blogging about my lecture.
The main part of the lecture was about the four old theorems in the table above and about what should replace the two question marks. The left side of the table deals with properties of the majority voting rule for binary preferences. The right side of the table is about general voting rules. On the top tight is the famous Arrow Impossibility Theorem. The table is filled by two theorems I proved in 2002 (in this paper) and it now looks like this: