As I see it, the Left and the Right both want pretty nearly the same society: One with peace, prosperity, brotherhood and justice for all. They differ sharply in how to attain this, though. There are two competing visions: The Left believes that Goodness must be implemented on the level of society, and will then manifest in the individual. The Right believes that Goodness must be brought into the world at the level of the individual, and will then add up to a good society.
If an individual fails to manifest Goodness (the behavior you'd want others to do to you) then the Left believes society must be tweaked to make a better environment for this type of individual. The Right believes the individual has failed to choose Good in his or her own personal life and should be encouraged to do so; if this fails, be removed from society.
In its pure form, the Left denies free will, while the Right believes it is absolute. Is either of these true? You can find out for yourself with a piece of cake and 24 hours of fasting. I am convinced that to the ordinary human, free will is very much a sliding scale. But by all means bring your own experiences.