Dollar-Neutral in addition to Market-Neutral?

What is the point/benefit of using a dollar-neutral strategy in addition to a Beta-neutral strategy? What exactly does a dollar-neutral strategy buy the investor? What's useful about balancing long and short positions?

Using the notation in Qian et al.'s book, in the mean-variance optimization problem, why would an investor force:

$$w\cdot I = 0$$ in addition to $$w \cdot B = 0$$ ?

with

• $$w$$ being the portfolio weights
• $$B$$ being the exposure matrix
• Marketing wise, perhaps dollar neutral is easier for investors to understand and to check, while beta neutral is more obscure and subjective (different data services give different values for Beta). So "we give you both MN and BN" sounds like a good advertising line. – noob2 May 31 '16 at 18:02