Literally: public – even – no – private
Alternately: Impartial; unprejudiced; unswayed by personal interests. Fair.
Notes: This comes from our friend the Han shi waizhuan (Japanese 『韓詩外伝』 = Kanshi gaiden). It also has an expanded Japanese-style reading, 公平にして私無し (kouhei ni shite watakushi nashi), approximately “being impartial, without self.”
Naturally, writing mushi as homophone 無視 (“ignore”) is an error.
This phrase is considered an antonym of 依怙贔屓, and I have to say that the one is much, much healthier than the other for the general public, on multiple levels.