The three main ideals that all political systems strive to achieve are freedom order and equality. Why do these values compete with one another?
I don't think all political systems strive for those three goals. Each of those terms would have to be specifically defined. However, democracy is not always an orderly system because to have order, everyone must do what the government wants them to do.
http://www.bu.edu/wcp/Papers/Poli/PoliBalz.htm