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Diversity isn't just a Democratic value. It actually grants an advantage in appealing to groups who feel excluded from the political process. As an active grassroots Democrat, the process I see is we try to figure out the agenda of the excluded group, and ask how to incorporate it into ours. That's how the agendas of racial minorities, organized labor, religious minorities etc. came to be so ingrained in Democratic thinking.
Republicans, by contrast, with the admission this is just how it looks from outside, don't ask how to incorporate someone else's agenda in theirs, or ask how they can help an excluded group. Instead, Republicans pick some part of the Republican agenda think think will have some appeal and push that, like promoting school vouchers to inner city blacks, or opposition to gay marriage to socially conservative Hispanics.