There is a political/personality division, that is quite strong. And this is how the traits of openness and conscientiousness are connected to the conservative and liberal thoughts.
The main idea is, that the higher the openness of the people, the more likely the are to hold liberal views and vote liberal. The higher the conscientiousness of people, the more likely the are to hold conservative views and vote conservative. So people that are high conscientiousness and low openness are the mainstream conservatives and the people that are low on the consciousnesses and high on openness are the mainstream liberal.
The people that are high or low on both of these dimensions, then it depends on the other factors as well, for example the importance of each trait in a person, the social environment and so on.
The trait conscientiousness can be divided into two traits: orderliness and industriousness. The first one causes them to want the clear line between the concepts, they want clear rules and they want a more stable environment. They are not very keen on the change. The second one cause them to value hard work and perseverance, so they are more likely to believe that everything can be achieved with hard work and people that are poor are there because of laziness.
The trait openness can also be divided into two traits: ascetics and intellect. The first one causes them to prefer things that are beautiful. The second one causes them to prefer the smart new solutions that will now solve all the problems, regardless of how the last smart new solution worked.
There was also a study that showed some of the other connections as well. Agreeable people are more likely to prefer liberal economics and conservative social policies. The people with high neuroticism prefer liberal, and the people with high extroversion prefer conservative. But all of these effects are smaller than the upper ones with conscientiousness and openness.
This is why it is hard to talk across political lines. I can see in the Slovenian politics, where there is hardly any talk across the political lines. It is like they are constantly talking across each other, with blaming each other why they can not see each other point of view.
But it is like how an extroverted and introverted person can have problems understand each other's position on the social interaction, so it is hard for the temperamentally different people to understand each other view. And in a democracy that is still very young (25 years) we had yet to develop a good way of holding dialog.
Maybe using the personality types, this dialog could be cast in a different light.