My views on the chained-CPI—a benefit cut—are here. I support the change—it’s a more accurate measure of price growth (though a chained index for the elderly would be better), and I’m sure it’s coming, so I want to get something for it. That ‘something’ is an offset from the benefit cut for poor, old elderly. But I agree, and stress in the post, that there are reasons to be nervous about the change.
It's possible chained-CPI is a better measure of the "true" CPI. But that has nothing to do with a the hypothetical elderly CPI-E. If the true CPI-E increases faster than CPI, then chained-CPI is worse, not better.