Representative democracy is the most prevalent system of government in the western world. It is comprised of constitutional monarchies (UK), parliamentary republics (Canada or Germany), and constitutional republics (United States). The most elected officials are policed by the constitution, which classifies a system of checks and balances to regulate any substantial centralization of power.
Representative democracies have become more commonplace than any other kind. America, for example, guarantees freedoms to the people, possibly more so than any other nation. Participatory democracy, on the other hand, is considered an ideology that removes the middle- man. It places policy responsibilities directly in the hands of the citizens.
In any case, there is not a country that can be termed as a participatory democracy. The best example which even comes close to it is represented by voting in the United States. Participatory democracy has the network and power to build communities based on mutualism. There would have to be progressive causes to favor this type of democracy.