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Most of us, having only a vague understanding of the Senate's possible functions and past realizations, see it as illegitimate or undemocratic, and wish to correct the situation by applying one of two stereotypical and superficial recipes: election or abolition.
The Constitution defined a container, but not the content. Nothing in it says that the Senate has to be a partisan body. It has become so by choice, due to a particular political culture. Filling the Senate with non-partisan members is a practical first step to its cultural evolution.