Reply #5: OP is referring to Cuba's municipal (local) elections.

[Billy Burnett]

Cuba's system is a variant parliamentary system, where the leadership is chosen from among the elected parliamentarians in Cuba's National Assembly (parliament).

http://www.poptel.org.uk/cuba-solidarity/democracy.htm

This system in Cuba is based upon universal adult suffrage for all those aged 16 and over. Nobody is excluded from voting, except convicted criminals or those who have left the country. Voter turnouts have usually been in the region of 95% of those eligible .

There are direct elections to municipal, provincial and national assemblies, the latter represent Cuba's parliament.

Electoral candidates are not chosen by small committees of political parties. No political party, including the Communist Party, is permitted to nominate or campaign for any given candidates.