A possible solution would be to pay each member of Congress 100% of the average income of his constituents plus free rent in a Congressional apartment building. Even here, though, we'd have to be careful that the apartments not get turned into miniature mansions by the ever-scheming members of Congress.
Let’s agree to a DC housing allowance to be determined statistically. They should be able to afford a one bedroom apartment with a minimum of amenities.
nacl