Location and species and hunting method will make the answer to this question vary. The question doesn't specify, but most answers here assume that the original poster is asking about ruffed grouse in the eastern half of the country.There is a significant difference if you are hunting forest grouse vs prairie grouse, and wing shooting vs ground/perching shots. And "partridge" in the West means real partridge, Grey partridge (Huns) or Chuckar. If all you are doing is shooting ruffed grouse in the "pre-flight condition" it really doesn't matter. As posted by several here previously, half an ounce of anything between #8 to #4 will kill a sitting ruffed grouse, from shotguns choked anywhere from full choke to cylinder.
If hunting wild flushing late season sharptails, a load of 1-1/8 oz of #5 or perhaps 1-1/4 oz of 4 shot out of full choke would be appropriate. The same birds in early season may be more efficiently taken with an ounce of #6 and improved cylinder. Forest grouse like Ruffed, and Spruce grouse shot on the flush over a pointing dog will be a good candidate for anything from 3/4 oz of 7-1/2 to 1-1/8 oz of 6's and cylinder to nothing more than modified choke. Grouse shot on the flush by a hunter without a dog may require a touch more choke and one size bigger shot. Blue grouse flushed from high trees on the West coast may require more reach, similar to sharptails.
I personally hunt with a pointing dog, shoot only flushed birds, and mostly use a 20 ga or 16 ga and an ounce of #6 out of IC/Mod for most of my hunting. Works well for ruffed, spruce, sharptail, and huns in most locations in the early to mid season.
