How can the police serve as a pillar of democracy?

The preservation of order is important to a democracy. For democracy to be meaningful, people have to know that their rights are protected from intrusions by other people. The police therefore play a vital role in a democracy. This is especially the case in societies where significant factions have an interest in disrupting the peaceful political process. We can see an example of this in Nigeria (which I believe, based on other questions recently posted, this question is alluding to). In elections held in the spring of 2015, the terrorist organization Boko Haram made frequent and violent attempts to disrupt the political process, and the ability of state police to stop these attempts was important to the safety of the voters and the legitimacy of the political process. To cite another example, African-Americans in the southern United States were granted the right to vote by the Fifteenth Amendment to the Constitution, but this right was meaningless. Southern states kept them from voting by several different means, most of which were extralegal. The Voting Rights Act of 1965 provided for the use of federal authority, including federal marshals, to ensure that their voting rights were protected. So sometimes police power is necessary to give meaning to democracy.