Which type of listing would allow a homeowner to limit the commission paid to their broker if they sell their house independently?

The correct choice is an open listing. This type of listing provides homeowners with the flexibility to sell their property independently without incurring a full commission. In an open listing arrangement, the homeowner is free to work with multiple brokers and can sell the property on their own. If the homeowner successfully sells the property themselves, they typically do not owe any commission to a broker, or they may only pay a reduced fee if a broker is involved in the sale.

Exclusive listings and exclusive right-to-sell listings generally imply that the agent has a guaranteed commission regardless of who sells the property, thus not allowing for a commission limitation based on a private sale. A net listing, on the other hand, allows an agent to keep any amount over a predetermined net price, which could effectively incentivize the agent to sell at a higher price rather than address limitations on commissions for independent sales.

In summary, an open listing uniquely offers homeowners the opportunity to limit or avoid paying a full commission if they handle the sale themselves, making it the best answer to the question posed.