How does the presence of a law in democracy confer stability on the society?

Law as defined by the Briticanna Encyclopedia, is the discipline and profession concerned with the customs, practices, and rules of conduct of community that are recognized as binding by the community. Our group has identified this as one of the three distinctive characteristics of democracy because this is one of the main reasons why democracy is so successful. It is somewhat a moral consensus that both the general community and the leaders must look up to and respect closely. This means that even the leaders themselves, if found guilty for any crime governed under law, will be duly dealt with the punishment as stated in the law. Our group feels that this means the leaders are of an equal moral standing as the general community and have to abide to the same set of rules. In a way, the law is like a moral compass for the society. Compare and contrast this to the time when Hitler reigned in Germany and chaos shrouded the country. In this authoritarian case, there was no law to speak of whatsoever because Hitler was the law. He was him who decided that Jews polluted the country, with no logical basis, and thus ordered for their immediate extermination. Therefore, this meant that Jews were unfairly discriminated against and they had to live their lives in constant fear and trepidation. Moving on to the boundary of extremity, we look at Singapore of the present. Experts often marvel at the way Singapore has grown from a dusty fishing town to a cosmopolitian South-Eastern hub. In my opinion, law plays a vital role in this development. Singapore citizens know what actions will result in what consequences, and thus to avoid the neccesary jurisdiction, they ensure that they play their part as socially responsible citizens who live up to Singapore's reputation as one of the world's countries with low crime rates. To sum up, I shall identify the link more explicitly. With the presence of law, citizens have a moral compass to stringently adhere to. Therefore, to escape the jurisdiction and play their part as responsible citizens, they do not committ crimes and there would thus be a stable social and economical scene.
(P.S Stability is ensured in all aspects because the law is ALL- ENCOMPASSING)