Liberty and equality are values that individuals hold dear. After adding the value of self-government to liberty and equality, politics are created which introduces competition for power.
In general the values may be the same, but the interpretation of liberty and equality are quite different. Values are formed by many inputs such as education and class as well as culture, family and societal experiences.
Two middle class women may have the same values and meet each other often in groups which work for equality among races or for freeing innocent people being held in jail. Both are middle aged ...