The Mayor (Murray Hamilton)’s Timeline and Summary

Vaughn hears that Brody's attempting to close the beaches and persuades him not to.
He holds a town meeting and assures everyone that the beaches will reopen in 24 hours.
He stops Brody and Hooper from cutting open the tiger shark on the dock.
He doesn't believe them when they say the shark's still out there and refuses to close the beaches for the 4th of July.
He convinces his stooge to go swimming with his family and assures people on TV that everything's hunk-dory in Amity.
He finally gets severely shaken by the pond attack and is strong-armed by Brody into hiring Quint to kill the shark.