A more accurate measure would be used to calculate cost-of-living increases for Social Security and other programs and to adjust tax brackets.
The idea of a switch to a "chained" CPI, according to a commonly cited example, is that if consumers switch from expensive apples to cheap pears their cost of living may have actually gone down instead of up.
Those who have read the Pearl Buck historically based novel, "The Good Earth", may recall that desperately poor Chinese peasants ate dirt out of unsatisfied hunger. Under a "chained" CPI calculation, if one had been made in those times, "food" in China would have been literally dirt cheap.
Some adjustments to the CPI "market basket" need to be and have been made to reflect the changing composition and quality characteristics of goods offered. The current proposal, however, achieves savings by purposely not accounting for forced reductions in the consumer's quality of life.
I would suggest to our right of center advocates of free markets in particular that "savings" achieved by the sacrifice and enterprise of careful shoppers are no less deserved than the rewards earned by investors though their business acumen and deferred gratification and should not be made to count against them.