What must be demonstrated for the election of government officials to be perceived as legitimate?

For the election to be legitimate all the legal votes must be counted accurately.

If there is a voter fraud or the irregularities with the voting process the elections can not be perceived as legitimate. The legal votes have to be counted properly and the results announced. An elected government official has to be someone chosen solely by the number of votes.

It's most likely choice a, it makes the most sense in my opinion.