Calculate and compare selected member to non-selected members

It's not pretty, but you could do a CASE statement if the list of countries isn't changing too much...

CASE
WHEN [Total of Something] = ( [Total of Something] , [Country = India] )
THEN ( [Total of Something] , [Country <> India] )
WHEN [Total of Something] = ( [Total of Something] , [Country = US] )
THEN ( [Total of Something] , [Country <> US] )
ETC. END

Or if you have both a Country field and a Country ID field, and the Country description is on Categories, then you can get more exacting (the above could throw bad results if 2 countries have the same [Total of Something].

CASE WHEN [Max Country ID] = {hard-coded Country ID of India}
THEN ( [Total of Something] , [Country <> India] )
ETC. END

Otherwise, I'd be eager to hear of others' tricks for getting a formula filter to more dynamically adjust in response to the category grouping or higher-level filter changes.

If it's totals or counts you're calculating (this doesn't work with averages unless you calculate them yourself from counts/sums), I wonder if you can't have two formulas, one of which is 
Formula 1: [Total of Something] 
Formula 2: ([Total of Something], ALL(Country)) - [Total of Something]


You can still combine this with filters on region/country on the dashboard itself by duplicating the 'Country' column and using one column in the dashboard filter and one in the widget
If you have no filter on Country, Formula 2 will be 0, but if there *is* a filter on Country, you should see values for Formula 1 *and* Formula 2