I don't want to rank people according to who I like the best.
I don't want to say that I like one person more than another.
ーI don't want to rank people according to who I like the best.
「誰が一番好きか順位をつけたくない」
rank で「(階級・順位に)位置づける」
according to who I like the best で「誰が一番好きかに従って・応じて」
ーI don't want to say that I like one person more than another.
「ある人を他の人よりももっと好きだと言いたくない」
to say that I like one person more than another 「ある人を他の人よりももっと好きだと言う」を使っても「順位をつける」ニュアンスが出せます。
ご参考まで!