This short commentary on Peters (Philosophy & Technology 35, 2022) identifies the entrenchment of political positions as one additional concern related to algorithmic political bias, beyond those identified by Peters. First, it is observed that the political positions detected and predicted by algorithms are typically contingent and largely explained by “political tribalism”, as argued by Brennan (2016). Second, following Hacking (1999), the social construction of political identities is analyzed and it is concluded that algorithmic political bias can contribute to such identities. Third, following Nozick (1989), it is argued that purist political positions may stand in the way of the pursuit of all worthy values and goals to be pursued in the political realm and that to the extent that algorithmic political bias entrenches political positions, it also hinders this healthy “zigzag of politics”. © 2022, The Author(s).