I can happily say that I tried this experiement last weekend on my 22 birthday. My friends and I had a brita with a slightly used filter. We bought the cheapo vodka ($12 for a 1.75 L) and sent it through the filter four times, in two batches.
Does it taste like good vodka? Can’t say. We didn’t have any good vodka to compare too. Did it taste better than before filtering? GOD YES. There was a clear enhancement in the flavor, and a decrease in the “burn,” as it were. I suspect that Roches is right, in that a mixture close to pure ethanol and water is what is achievedm however, isn’t this what some expensive vodka’s are? Some rely on the special impurities found only in their grain/water/etc… while others use their claim of “distilled and filtered elevtey-billion times” to promote themselves. So if that is the case, then yes, a cheap vodka can be made to taste like a good vodka. We even had a vodka expert (well…as good an expert we know) taste it and he said id did taste like good vodka. And as to the price, well, let’s compare.
Cheap vodka: $12
Brita filter (assuming a filter is ruined in the process and a new one must be used every time): $8
Total: $20 for a 1.75 L of vodka.
Good vodka is easily more expensive than that. Most are ~$20 for a liter, so yes, money is saved.
Personally, I still don’t think it makes the vodka good enough to drink on it’s own, either straight up or in something that relies on the flavor of the vodka (like a vodka martini) but it is PERFECT for mixed drinks, that is, perfect if you don’t want to taste the alcohol as much. I could easily put double the amount of vodka into a screwdriver and have it still taste less alcoholy than a normal one with cheap vodka. That’s not to say I didn’t taste any vodka, I did, but it was less pronounced and what I did taste wasn’t as bad as unfiltered.