How to mend the fence when neighbors set up high defense?

High wind blows down the good neighbor fence, neighbor ”Bill” wants to get the fence repaired paying as little as possible and not caring about the skill or craftsmanship of who does it, so long as it is cheap. Neighbor “Karen” wants to hire someone with good skills, a solid reputation, that guarantee their work, she is willing to spend an above median price to get it done right and well. Since they both have to pay half, how do they mend the fence if they can’t come together on the repair person or handyman? So long as they are at odds over cost, craftsmanship, etc. the fence remains unrepaired. Have you ever been in a stalemate like that, and how did you break it?