There are a lot of differing opinions on this subject. Here is one. What you are talking about is dual agency. As a broker owner and a practicing Realtor, I do not subscribe to the idea of dual agency. It is legal in Illinois, but is not legal in some other states.
The pros are, as the seller, you can often negotiate a lower rate, as the broker will get both sides of the transaction/sale. Sometimes this allows them to accept a lower buyer offer, a potential plus for the buyer. Maybe not. Some would say that another pro for both sides is that you are dealing with the same person and that person knows everything about the sale and the parties.
My opinion is that the only pro is the potential cost savings, but the cons definately outweigh the pros. In a negotiation, there are certain information and strategies that are only known to the client and the agent. If the agent is working both sides - they know everything. That is not an advantage for anyone. It is like playing chess with yourself. How can you employ a strategy to win if you know your next move.
Also - as a Realtor, we can't reveal any information to another party, unless our client consents. In this case, any human being is going to have a difficult time separating information and equally representing both sides to the best of their ability without, even accidentally, violating that trust and confidentiality.
A listing agent who has a buyer contact them directly will want to represent both sides, but as a practice, I don't allow that. If I or one of my agents is presented with this situation, as the broker, I designate another agent to represent the buyer to ensure that both parties receive the best service and ultimate care to make certain their interests and only their interests are being represented.
As a buyer or a seller it is your legal right to refuse dual agency. In a listing agreement or a sales contract, the buyer and seller must agree to dual agency. You can ask the agent to have the broker designate another agent to represent either you or the other party.