Before revision:  A choice p\in X is called a \beta-plurality point for V, if for any other choice q\in X it holds that  \{v\in V\mid \beta\cdot d(p,v)\le d(q,v)\}  \ge|V|{2}.
After revision:  A choice p\in X is called a \beta-plurality point for V, if for any other choice q\in X it holds that | \{v\in V\mid \beta\cdot d(p,v)\le d(q,v)\} \ge|V|{2}.