I think the purpose of democracy should primarily be to avoid civil conflict and only secondarily be to represent the median voter. First past the post voting ensures a two-party system which means that people will make compromises while voting and not outsource that responsibility to politicians. The latter might cause voters to not own the consequences of trading favors (which is necessary for coalition building) and potentially lead to civil conflict.
I think representing the median voter is the best way to avoid conflict.
Imagine you have a shared workspace and people vote on the temperature to set the thermostat. Do you think he best way to avoid conflict is to have a system that encourages people to cluster into warm nature and cool nature people, one or the other get their way? Or is it best to simply settle on the median, which tends to be right in the middle and no one is miserable.
