Rolling the dice might be good, but only if you can select to stay silent, and if the roll is dependent on character stats (initiative is the most suitable, may be modified with charisma in mind). Or just go with the fastest player.
Thow the bigest problem is that we have to pick one chose. The best way would be to let every willing charcter to say what they wanted, and progress the dialog taking all of them into account.
Yeah, you could select to stay silent by just letting the timer go out without picking an option. Perfectly valid choice. Although I'm not advocating that the roll is modified by character stats. Just a general modifier that applies to everyone equally when it's needed. That's the only real way to keep it fair.
And, uh... while in an ideal world it would be nice to be able to select all of our options at the same time, I'm not sure if that would actually be feasible in-game.
