Before revision:  We prove that \beta^*_2 = 3/2, and that 1/d \leq \beta^*_d \leq 3/2 for all d\geq 3. \}.
After revision:  We prove that \beta^*_2 = 3/2, and that 1/d \leq \beta^*_d \leq 3/2 for all d\geq 3. * Define \beta(p, V) := \sup \{ \beta : \text{p is a \beta-plurality point for V\}.