Vodka is normally made by fermenting and then distilling grains or potatoes. Since neither are Paleo, we can hardly expect the result of distilling them to be Paleo.
Fermented v. Distilled
Alcohol is made when the sugars in a substance are allowed to ferment. It is a natural process, and animals have been known to forage for fermenting fruit. Distillation, on the other hand, is an industrialized process that was not invented until a few thousand years ago, long after we had introduced agriculture and grains into our diet. The result is a much heavier hit of alcohol and sugar to our system than our bodies know what to do with, hence the “buzz” that we get as our livers frantically try to figure out what to do with all this stuff.
Paleo and Nutrient-Dense Foods (And Beverages)
Part of living a Paleo lifestyle includes consuming nutrient dense foods (and beverages) and hard liquors really have nothing to offer. Although the unflavored distilled liquors are free of carbohydrates, they also don’t have the beneficial antioxidants that you find in wine or hard cider, which is just another reason to ditch the vodka.
Mark Sisson has a guide on what to drink on a low-carb diet here.