For years this has been the fundamental fraud behind "chained CPI," that it was a more accurate measure of changes in cost of living. Maybe it is overall (not saying it is, just not bothering to argue here), but its proponents were oddly uninterested in embracing a genuine CPI for Social Security recipients. Because, you know, the elderly don't buy the same stuff as the rest of the population.
CPI-E would give Social Security beneficiaries a small raise. It's a start.