Who determines the market value of a property?

The property seller sets the price, especially for residential property, not the Appraiser. Sellers usually don't order an appraisal because they want to obtain the highest price for their home and therefore don't want to be bound by the Appraiser's assessment.

The real estate agent receives a percentage of the price as compensation and often represents the seller in the transaction and assists them in setting the sale price. They perform a Comparative Market Analysis (CMA), which real estate agents in most states are allowed to perform without an Appraiser's License or Certification. The CMA is vital to the agent’s preparation for a listing examining recent property sales in the neighborhood to arrive at a listing price. Typically the agent will suggest a price to the seller based on the CMA however the seller may choose to list their property for a higher price.