Logic, Psychology, Emotion

'Facts' are frequently misleading or based on poor scientific procedure/methods. Many people on either side of the political spectrum and in less political arguments use 'facts' as a basis for their argument with the pretence that facts are separate from the feelings and opinions of people.

An example: If you are at a party and your friends have already left and you aren't having a good time what is the logical thing to do? You may say that leaving or trying to speak to someone new is a valid reaction, this is a logical solution to an emotional response. You can rationalize that you are wasting your time by standing alone at a party but the further you take it the more you lead into nihilism which is not a point of this argument but a valid avenue for a later discussion.

Example 2: The trolley problem. The logical thing to do is to save the most people or to save the person / animal / thing closest to you but the reason for why you would pick that is an emotional connection or the desire to not receive a negative emotional reaction.

I'd love to hear someone's perspective on this in a broader sense as well as a definitive example of where logic can be separate from emotions for a human in a complex situation.