As long as the idea of switching to the use of the Chained CPI is in the news it’s worth emphasizing that though the scale of the cut to Social Security benefits implied by doing this is very small, it falls quite heavily on people who are very old since it compounds over time. Social Security Works has a table (PDF):
CAP’s Social Security proposal pairs a switch to Chained CPI with more generous benefits for the poorest retirees and with more generous benefits for the very elderly. On net, our proposal would reduce poverty among senior citizens. But if you simply do the C-CPI-U switch without changing anything else, you end up making Social Security’s adequacy problem worse.