Who pays for a new fence that is shared with next door neighbor?

IN THEORY, the construction and maintenance of a fence directly on the property line should be shared equally by the two neighbors. What one SHOULD do is CASUALLY bring the old, ugly fence up in conversation with the neighbor. Mention how ugly the old fence is, the lack of privacy, and how it lessens the value of BOTH properties. You are waiting PATIENTLY for THEM to say that the fence needs to be replace. This can take a few conversations. But as soon as THEY mention a new fence, then you jump in and offer to pay for 1/2 of it if they're interested...and even willing to make the arrangements if that would be helpful. Of course, now it's too late for that. And even if that had happened, then they'd have a half say in the budget and the type of new fence to go in. By paying for it yourself, you gained that discretion and that's worth something. At the end of the day, a new fence is like divorce; the one who wants it most usually pays.