I think the fact that Twitter is overwhelming a negative place is a bigger issue.
I spend a lot of time on Facebook and the ability to back-up one's opinions in greater detail with (relatively) longer arguments is pretty crucial tool for having constructive interaction.
After trying many time to cull the people I follow to create a more positive space, I ended up starting a new account and only following people whose positive:negative content is really high. So far it's working well.