These kinds of more complex political mapping is helpful in understanding the problems of the discussion of left vs right. I’d add other dimensions as well.
A person can be ideologically extreme in any number of these areas or someone can be politically flexible. The problem with the ideological extremists is that they’re often the loudest and get the most media attention, but I’ve often suspected that the average person is probably more moderate. This creates an imbalance in power.
Also, there is a dimension of preference for and against hierarchy. For example, some libertarians are against big government not because they’re for personal freedom and egalitarianism, but because they prefer the hierarchy to be localized (and so more easily controlled by themselves and their group) or because they’re for uncontrolled capitalistic power. On the other hand, someone could see the necessity of big government to ensure personal freedom and egalitarianism, but if they dislike hierarchy they’d rather big government be based on a more direct democracy with strong institutions that enforce accountability.
I’m sure even further dimensions could be added. I’m wondering if what this mapping shows is that psychological tendencies (whether genetic or learned) forms the structure of what is being analyzed. Traits researchers tend to break it down into five most fundamental traits with various numbers of sub-traits.