In Cuba, there have been several national referenda or petitions on major constitutional or governmental matters which have been reported to have extremely high support for the "official" position (that favored by the government). Most notably, in 2002, a referendum on whether socialism should remain the only permitted form of government reportedly received more than 99% of the votes with a 98% turnout.1 Even the recent constitutional referendum, which was generally characterized as having much more opposition than previous ones, was supported by 90% of the population with similar turnout. In a world in which leaders with 60% or 70% in elections are considered wildly popular, this seems either noteworthy or unusual.
Of course, the government has largely not permitted opponents of the referenda to campaign in many of these cases, along with otherwise suppressing attempts to publicly advocate the contrary position, which might naturally be expected to tilt the voting toward their preferred outcome. Still, the margins of these results are surprising. For the purposes of comparison, in the United States, generally considered a country with a relatively positive view of capitalism, only 71% of the conservative Republican Party expressed a positive view of capitalism in 2010, let alone declaring that it should be made an irrevocable part of the constitution.
So what accounts for the popularity of the officially favored position in Cuban referenda? Are the ideas or policies voted upon in the referendum simply extremely popular in Cuba relative to most ideas in many other countries? Are there overwhelming incentives that would make opponents reluctant to express a contrary opinion (e.g. bonuses for workers at state enterprises for voting in the correct manner, fines for voting "incorrectly" or something of the sort)? Is the vote even overtly manipulated in any way (i.e. outright inaccurate reporting of results)?
I have been unable to find the original source where I found this figure earlier today, but based on Cuba's population of around 11.2 million in 2002, a population pyramid showing about 28% below the age of majority in the same year, and the Cuban government's claim of 8.1 million signatures, the figure appears to be correct if we take the reported figures at face value.