Using the compensating and equivalent variations to define the Slutsky Equation under a discrete price change

In our experience, all textbook presentations of the Slutsky Equation under a discrete price change use a compensation scheme based on the compensating variation. Our students have sensed this convention is arbitrary in that they have asked, why consider this compensation scheme, and not one based on the equivalent variation? The present paper outlines how one might address this matter analytically, and then discusses how our findings provide a new insight into the Giffen Paradox.