Let's suppose there are Y options to choose from. I'd like to run an experiment with a sample of n participants (from a larger population), each will choose 1 option from the Y alternative according to his preference (can be thought of as elections, where each voter needs to pick the candidate for presidency).
How do I calculate the required sample size to know that the results that placed whoever/whatever is positioned in the 1st place (according to # of votes) are statistically significant?
Furthermore, I know things start to get really complicated when you enter rankings into the discussion, but if possible would also be curious to know if there's a way to calculate sample size needed to make the ranking of alternatives itself statistically significant. Anyway, the first part of the question is the one I'm particularly interested in.