Let's take a grocery basket. In it is a box of Craft Mac and Cheese selling for $1. Over the course of a year that box of Craft Mac and Cheese increases to $1.49. Under any sane and objective measure of inflation you would conclude that the price of Kraft Mac and cheese has increased by 50% -- a massive increase. Enter the magic of chained CPI.
They simply find a box of mac and cheese, in this case Fukushima Select brand "Mak and Cheez" that's still selling for a buck and voila, there was no inflation.
When the Economic Assistant (EA) first goes to an outlet, s/he has a list for that outlet of specific items...in this case "macaroni and cheese." The EA notes what different varieties (brand, size) and asks the manager about proportion of sales. The EA then weights the different types proportional to sales and uses random selection with greater probability assigned to those brands/sizes that sell more. Once that's done, each month the EA will collect the price of the exact same item (Kraft Mac and Cheese, single box, 3 packets or Fkushima Mak and Cheez 6 pack etc) every time. There is no ability to change that selection and any attempt to do so will be flagged in Washington and reviewed by an analyst. If the item is not available (sold out) during the visit, the EA has a choice to just not collect or replace the item with a close substitute. Either way the decision will be reviewed and corrected if the EA made the wrong decision.
Chained CPI deals with overall weights, not individual item selections. If Mac and cheese made up 0.01% of spending in month 1 and 0.015% the next month, current measures would weight the price change of mac and cheese as 0.01%. The chained CPI would weight it as 0.018% And vice-versa if the % of spending went down.