The quality of not being partisan, of remaining politically independent(noun)
Wiktionary.org : Text is available under the Creative Commons Attribution-ShareAlike License
Use "nonpartisanship" in a sentence
"Someone: ... much of the current nonpartisanship is in fact very partisan ... see this is fun."
"In fact, much of the current nonpartisanship is in fact very partisan -- towards liberals."
"Talking about "nonpartisanship" (which I think is silly, since even the most partisan talk about rising above the fray) does not change the fact that leaders have to act in a partisan way quite often."