Pretty much exactly as it sounds, give the player the ability to deny mandates. No longer should we have to put up with some tosser who demands we don't export barrels or demand we make him an instrument we don't have the components for or some other stupid shit.
In order for this to be balanced, there has to be some kind of limitation/penalty. I came up with 2 different solutions to this, but if anyone has a better way of balancing this out I'd love to hear it.
The first is to limit the player to 1 denial per year/two years.
The second method is to make the Noble giving the mandate very upset. If you deny 3 mandates in a row without giving the Noble sufficient time to cool off, he will go insane like a dwarf who failed a strange mood, perhaps start giving impossible mandates you can't deny and attacking workers, and eventually the Noble will commit suicide or dehydrate. Cool down time or agitation level might be affected by personality traits.
This also adds a level of gambling to the game. You can deny a mandate you don't like, but you risk your mayor or whatever giving you an even worse mandate, as well as the fact that you're agitating him, and if he's a mayor, he was elected based on social skills and number of friends, that could lead to a tantrum spiral.