How do you develop Confidence Intervals based on non average data

Question

I am collecting votes from an election poll. The rules for voting allows the voter to select ten out of 36 candidates for election. Any candidate whom receives at least 75% of the vote or more wins the race.

I'm trying to decipher two things. One, what confidence level should I have with a certain sample size of the votes cast? What is the proper method for determining if the sample of votes that I have is indicative of the results of the entire election.

The second question is how to I determine the range of likely proportion of the vote for each candidate based on the sampling of votes gathered, and the number of votes outstanding. I'm unsure as to what terminology or process is used to decipher either of these questions.

Answer 1

Looks like a strange election system! With the rules as stated, if I have understood correctly, the number of elected persons is itself a random variable.

But the analysis should be simple. For each candidate, of the 36, he is either named among the ten or he is not. So, for candidate $i$, count the number of times he is included among the ten in your sample, and divide by the sample size. If this is a simple random sample, then simply calculate a confidence interval (for a total of 36 intervals, one for each candidate) as you would have done for any yes/no-question with a simple random sample. If the sampling method is more complex, do likewise with method appropriate for that sampling method.