From the summary:
Cost-of-living adjustments can help ensure that federal benefits keep pace with inflation. Using a consumer price index to adjust benefits can help ensure that recipients have enough purchasing power to get what they need.
Social Security and other federal retirement programs generally use one of the four consumer price indexes maintained by the Bureau of Labor Statistics.
We looked at what switching indexes would mean for people’s benefits and federal spending. For example, people who retire earlier or have lower incomes would feel the largest effects of any change.