The answers to Issues 1 and 2 should be considered in light of the issues raised in the Case Study II subpage of the Scanlan’s Rule page.
None of the approaches is correct or useful for distinguishing the sizes of disparities. The disparities are all the same. Each reflects the differences in various measures at a different cut points where two groups differ in mean scores by half a standard deviation. See generally the Measuring Health Disparities (MHD) and Scanlan’s Rule pages of this site and Table 1 of JSM 2008.
The ranking from largest to smallest disparity would be A, B, C. The three settings reflect, respectively, differences between means of .55, .50, and .45 standard deviations. See the Solutions and Solutions Database sub-pages of MHD.
The only measure one can derive from the information provided is the relative difference in selection rates. One can determine that DG’s chances of selection are 56% less than AG’s in Setting A and 67% less in setting B. But there is not enough information provided to enable one to determine which disparity is larger in a meaningful sense. In order to do that one must know the actual selection rates for the two groups.