JD/XXX Dual Degree Programs for PI folks

[LogicalBaozi]

Should one mention one is applying to other departments of the same school? For example, if I am applying to CLS (LSAT willing), but also to their political science/econ PhD programs and their SIPA MIA program (all of which have dual degree programs with the law school), should I mention explicitly in the application/PS that I am applying to those schools and plan to do a dual degree if admitted? Especially for those interested in public interest, having another degree related to public policy might be useful. Anyone else know anything about applying dual degree?

With regards to informing both departments you are applying: would it increase your chances (s/he's dedicated, cares about PI, they can see two PSs, adcomms coordinate) or decrease you chances (if one of the two departments find a reason to reject you, they both do; your JD dies because the PhDs didn't want you)?