This might not exactly be a classification problem. Some of the comments are partially negative. Some could be partially postive, so treating it as a hard class wouldn't be good. To think in a different way consider predictiing a rating a person would give to a movie based on his review, on a scale of 0 to 10. RMSE would be better suited as a metric compared to some classification metric in this case. Also these tweets are labelled with some disagreement, so 2 out of 3 people could think its positive, one could say neutral. So a distance between my models prediction and the agreement could be something I am looking for.

yeah! But what are we looking for? we have a tweet and we want to predict the sentiment of this tweet. In the end we want the sentiment. 0.6 0.4126 0.5 are nothing, we want to have the right predictions. That's why attacking it as a classification problem is 100% better than this way.

Yeah. I ask my self for this question. At first I think it was classification