Hi Omid,
I'd love to see some in-depth testing of this topic done, but to my knowledge, I've never seen anyone delve into this deeply. Nevertheless, I've seen lots of people ask about this. Here's the basic premise:
We know Google doesn't like duplicate content, yet, when we publish a business description on a local business listing, there is a high likelihood of that description getting replicated across the web due to the way data is shared within the Local Search Ecosystem. Does Google care about this type of duplication? Can it harm rankings? Can having varied descriptions help?
My personal opinion is that duplication is baked into the local search ecosystem and is largely unavoidable. After all, your business NAP (name, address, phone) is duplicate content when it is published across multiple platforms and logic dictates that Google has no problem with this.
However, as I've said, I don't know of any real studies of this but your question prompted me to have a brief chat with Darren Shaw and Andrew Shotland and we were in pretty solid agreement about this.
Darren says: I have heard many people suggest that there are benefits to mixing up your description on your citations, but, it's unrealstic to imagine doing this on EVERY citation ... Maybe making 15 different versions and spreading those around.
I have not seen any evidence to support that there are benefits in doing this though ... just speculation
Andrew says: If anything, it's the IYPs that need to worry about it, not the businesses ... basically the same as a bunch of ecommerce sites having the same SKU description
I think Andrew raises an especially valid point! If there were to be ANY penalty associated with duplicate descriptions (which I highly doubt) it would be something for the IYP/directory who is publishing the content to worry about...not the local business owner.
So, my take on this is that it would be very interesting to experiment with whether varying the business descriptions as much as you can had any observable positive effect on rankings, but that I highly doubt duplicate descriptions have any negative effect - certainly not on the business owner.
That being said - you Local SEO researchers out there - if you're looking for a study to do, this would be a fun one! Hope this helps, Omid!