Comment by mbeex

Left/Right: First thing - add more axes. The most used standard example from politics or economics is liberalism/libertarism (not diving into the subtleties of definitions, their history, usage in different parts of the world, etc.). Look for more such axes, leave the political conceptual world behind.

After that, try Principal Component Analysis and look, what remains from these dimensions and the labels describing them. Think up names for the Eigenvectors / new axes. Investigate further. For example, look where people are concentrating in this high-dimensional space.