There's a class of questions that Popper called 'Who should rule?'. For example, 'Who should hold power?', and then lots of derived questions like 'How should they be educated?.' These are questions that have been asked ever since history begun and are at the root of all squabbles around governing.
Popper pointed out that this class of questions is rooted in the same misconception as the question ‘How are scientific theories derived from sensory data?’ which defines Empiricism. It is seeking a system that derives or justifies the right choice of leader or government, from existing data – such as inherited entitlements, the opinion of the majority, the manner in which a person has been educated, etc.
The same misconception also underlies Blind Optimism and Blind Pessimism: they both expect progress to be made by applying a simple rule to existing knowledge, to establish which future possibilities to ignore and which to rely on. In other words, explanation-less progress.
If the political process is seen as an engine for putting the right rulers in power, then it justifies violence, for until that right system is in place, no ruler is legitimate; and once it is in place, and its designated rulers are ruling, opposition to them is opposition to rightness. The problem then becomes how to thwart anyone who is working against the rulers or their policies.
Popper therefore applies his basic ‘how can we detect and eliminate errors?’ to political philosophy in the form how can we rid ourselves of bad governments without violence?
No leader is perfect, and Arrow's theorem proves that no system of governing is completely fair.
Therefore systems of government are not to be judged by the quality of their leaders or policies, but by how easily bad leaders or policies are removed.
The only way to remove bad leaders or policies, without using violence, is through cultivating a culture of free-speech and Criticism.