Cardassia at the time was being led by a Civilian Government for the first time in centuries.
They had just been sacked by the Klingons, which didn't sit well with anyone.
Maybe the civilian government wanted to give up, or maybe Dukat forced them out, but he had the military on his side and after the deal was finalized he was given not just Cardassia to Rule but the entire Alpha Quadrant to govern any way he chose once Dominion Victory had been acomplished.
A broker is a middleman.
Dukat was on top before he fell.