The chained CPI is a twist on that: It measures living costs differently because it assumes that when prices for one thing go up, people sometimes settle for cheaper substitutes (if beef prices go up, for example, they’ll buy more chicken and less beef).

Bottom line: Cost-of-living adjustments would be lower with the chained CPI than with the plain old CPI. So depending on which formula is used, the amount of your Social Security payments could change over time.
AARP – Bottom line: Cost-of-living adjustments for Social Security would be lower with the chained CPI than with the “plain” CPI

Congressional Budget Office – Differences Between the Traditional CPI and the Chained CPI

Chain Weighted CPI Wrong for Social Security Benefits

Cutting the Social Security COLA by Changing the way inflation is Calculated Would Especially hurt Women

The Chained Consumer Price Index Would Hurt People With Disabilities