The only arguments I've heard for a "yes" vote for the Constitutional Convention are (in no particular order -- and with no editorializing from me):
(a) the current Constitution is too long and wordy and very difficult to understand
(b) the NYS Court system is Byzantine and ripe for cronyism
(c) more than 70% of the State is registered Democrat, and yet because of gerrymandering, the State Senate is Republican
(d) the State Government controls too much power and currently there's not enough "home rule"
I had to look for those reasons. There's been absolutely no vocal support for a "yes" vote. All I see downstate are signs and bumper stickers saying "vote no". Half are union-based. The other half say 'taxes are too high already'. Seems like both sides of the fence don't want to see this happen.