The public float sounds legit. I wouldn't argue with that, in fact, it's probably the technically accurate metric.
Where I was coming from was...
https://en.wikipedia.org/wiki/Dow_Jones_Industrial_Average
> The value of the Dow is not a weighted arithmetic mean[5] and does not represent its component companies' market capitalization, but rather the sum of the price of one share of stock for each component company. The sum is corrected by a factor which changes whenever one of the component stocks has a stock split or stock dividend, so as to generate a consistent value for the index.[6]. It is not an accurate representation of the US market or total market.[7][8][9]
It mentions "consistent value", but that's over time. You can be misrepresented in weightings but still consistent over time.
Basing the weightings on the stock price sounds royally stupid... if I'm even reading that correctly. But maybe this insanity is just the DOW?
It's also the first one I grab for, because it's the first one that media reports on.