Let X=\Gamma \backslash D be a Mumford-Tate variety, i.e., a quotient of a Mumford-Tate domain D=G(\mathcal{R})/V by a discrete subgroup \Gamma . Mumford-Tate varieties are generalizations of Shimura varieties. We define the notion of a special subvariety Y \subset X (of Shimura type), and formulate necessary criteria for Y to be special. Our method consists in looking at finitely many compactified special curves C_i in Y , and testing whether the inclusion \bigcup_i C_i \subset Y satisfies certain properties. One of them is the so-called relative proportionality condition. In this paper, we give a new formulation of this numerical criterion in the case of Mumford-Tate varieties X . In this way, we give necessary and sufficient criteria for a subvariety Y of X to be a special subvariety of Shimura type in the sense of the André-Oort conjecture. We discuss in detail the important case where X=A_g , the moduli space of principally polarized abelian varieties.