What should be the role of citizens in creating public policy?

There is really no one answer to this, as it is not a matter of fact but one of opinion. Different individuals and different cultures have different beliefs about this topic.
In some societies, such as ancient Athens, direct democracy was practiced with citizens voting directly on matters of public policy. On the positive side, this gives citizens a direct and immediate voice in the running of their state. On the negative side, this may only be practical for states containing a few thousand citizens. Also, there is a problem that the average citizen in not necessarily an expert on policy matters. Referendums such as those held in the state of California descend from this ideal. The problem, though, is that people can vote for such popular measures as reducing taxing and improving services separately, without addressing the problem that one cannot reduce revenue and increase spending without running up an unsustainable deficit. 
At the other extreme, countries such as modern China give the average citizen little voice in determining policy. The Chinese communist party would claim that this benefits the country as a whole in providing a expert, efficient, technocratic mode of government that can make and implement wise and impartial policies. On the negative side, though, autocracies become kleptocracies, with the wealthy and powerful forming an elite of billionaires while the average citizen remains impoverished and powerless.
Another possibility is representative government, which operates under the assumption that citizens can vote for people to represent them and to appoint able technocrats in a civil service. Most modern democracies operate this way. Representative government is a compromise between direct popular influence and technocracy in theory, but the same problem of lack of voter expertise arises. Any system in which people vote directly requires a well-funded, mandatory educational system so that voters can make informed choices.