Abstract:
In social choice theory, Arrow’s impossibility theorem states that, when
voters have three or more distinct alternatives (options), no rank order
voting system can convert the ranked preferences of individuals into a
community-wide (complete and transitive) ranking while also meeting a
specific set of criteria. These criteria are called unrestricted domain,
non-dictatorship, Pareto efficiency, and independence of irrelevant
alternatives.
In short, the theorem states that no rank-order voting system can be
designed that satisfies these three "fairness" criteria:
- If every voter prefers alternative X over alternative Y, then the
group prefers X over Y.
- If every voter's preference between X and Y remains unchanged, then
the group's preference between X and Y will also remain unchanged
(even if voters' preferences between other pairs like X and Z, Y and
Z, or Z and W change).
- There is no "dictator": no single voter possesses the power to always
determine the group's preference.
We will examine whether Arrow's Theorem is a contribution to the
Calculus of Relations.
Short Bio:
Prof. Roger Maddux is an American mathematician specializing in
algebraic logic.
He completed his B.A. at Pomona College in 1969, and his Ph.D. in
mathematics at the University of California in 1978, where he was one of
Alfred Tarski's last students. His career has been at Iowa State
University, where he fills a joint appointment in computer science and
mathematics.
Prof. Maddux is primarily known for his work in relation algebras and
cylindric algebras, and as the inventor of relational bases.
His Erdős number is 2.
