This will vary by the individual, and how strict you are - and of course, no matter what you do, calorie intake will still play some sort of a role.
But putting it in numbers... after a good 3.5 years of calorie counting and losing 90lbs, I managed to get about 10 lbs the first week with a rather strict paleo diet.
I've "struggled" a bit since, meaning my average weight loss a week has gone down to roughly a pound (or just under). But if nothing else, I'd say paleo is made to rattle your dietary cage.
