  The traditional Arrow--Sen Social Choice Theory $\bf{TSCT}$ is a mathematical
theory built apparently on higher--order formal language. In this paper, we
propose a reformulation and reclassification of the $\bf{TSCT}$ axioms in order
to obtain a simpler theory based on the first--order language axioms, keeping
the spirit of original ideas. This new theory, called Simplified Social Choice
Theory, denoted by $\bf{SSCT}$, presents a sub--theory of $\bf{TSCT}$. Roughly
speaking, we extract all quatifications over $n$--tuples of binary relations
from the axioms of $\bf{TSCT}$ and move them to the meta--level obtaining a
sub--theory $\bf{SSCT}$ of $\bf{TSCT}$. More accurately, we assign to each
traditional higher--order axiom $\bf{TA}$ its simplified first--order version
$\bf{SA}$ such that $\bf{TA}\vdash\bf{SA}$, i.e. $\bf{SA}$ can be logically
derived from $\bf{TA}$. In this way we define a simpler and more accessible set
of principles that provide a context in which we can prove many propositions
analogous to well--known theorems including the Arrow's impossibility of
Paretian non--dictatorship and Sen's impossibility of Paretian liberal. These
simplifications are the result of decades of lecturing by the author with the
aim of bridging the barriers between this beautiful complex theory and his
students.
