Here's a couple articles that are talking about blind-tests either they did or from someone else. I've seen better articles with more test details but I can't seem to find them again.
The New York Times similarly blind taste-tested 21 vodkas. Grey Goose and Ketel One failed to finish in the top 10. The winner? Smirnoff. The lowest priced vodka placed highest. [1]
Smirnoff is nowhere near the cheapest vodka. That's not a bottom shelf vodka. It is literally not on the bottom shelf of liquor stores. C.f. Popov vodka for literally _half_ the price of Smirnoff (and literally on the bottom shelf). Popov, by the way, is undrinkable.
Any vodka which is twice as expensive as another vodka cannot be called "bottom shelf."
Any vodka which is twice as expensive as another vodka cannot be called "bottom shelf."