But, the one party thing isn't a thing.
The communist party only holds about 15% of the seats in the National Assembly (the Cuban Parliament).
http://www.poptel.org.uk/cuba-solidarity/democracy.htm
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.
Here are some of the major parties in Cuba. The union parties hold the majority of seats in the National Assembly.
* Partido Comunista de Cuba (PCC) {Communist Party of Cuba}
* Partido Demócrata Cristiano de Cuba (PDC) {Christian Democratic Party of Cuba} - Oswaldo Paya's Catholic party
* Partido Solidaridad Democrática (PSD) {Democratic Solidarity Party}
* Partido Social Revolucionario Democrático Cubano {Cuban Social Revolutionary Democratic Party}
* Coordinadora Social Demócrata de Cuba (CSDC) {Social Democratic Coordination of Cuba}
* Unión Liberal Cubana {Cuban Liberal Union}
http://www.gksoft.com/govt/en/cu.html
My family has voted in every election since the Revolution.