I think Nascar uses this system to discourage undervaluing entries: owners declare a value for their car, and Nascar has the right to buy the car at that valuation. They would only do this if the car was under by a significant margin, so there's a huge incentive to give a fair estimate for the car.
Its also a little similar to a system used to resolve splitting a 50/50 owned company: the person who wants to buy out the other partner must first give the price they'll pay, and then the second partner must choose between buying them out at that price, or selling their share.
Pretty much the same as the "one splits, the other chooses which half they want" that my brother and I would use to guarantee fair splits of cookies or cake.
Its also a little similar to a system used to resolve splitting a 50/50 owned company: the person who wants to buy out the other partner must first give the price they'll pay, and then the second partner must choose between buying them out at that price, or selling their share.