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There does not seem to be any statistical Q&A so I assume all the statisticians are on this site.

This question is very theoretical and is based on analysing voting systems. I have a very simple example here that does not include millions of people across various demographics.

I have outlined 2 red lines that try to determine a voting trend.

  1. Top 2 candidates did very well with a mean vote of 40 between them
  2. Bottom 3 candidates have far less votes but seem to create their own trend.

The cyan lines are a visual attempt to establish trends and display established trends for these 2 groups. A total vote mean is identified in green and does not intersect with any trend.

enter image description here

The values of the elections are:

  • Voters that participated 96
  • Votes cast 96/288 (Each voter could vote for up to 3 candidates)

My main question is how do I calculate the probability of voters that cast 1 vote, 2 votes and 3 votes in a cumulative result.

share|cite|improve this question is the stats StackExchange -- however, you may still find help here with some questions. – Emily Aug 9 '12 at 16:11
Voters typically don't vote randomly. If you want to calculate probabilities, you'll need a probabilistic model first. Do you have one in mind? – joriki Aug 9 '12 at 16:24
I think the question it self is me asking what model I will need. to try and calculate the probability of a majority voting for a single candidate and/or also the percentile that cast 2 or more votes based on popularity... and allow me to adjust the number of voters and influence from popularity.. – ppumkin Aug 9 '12 at 18:30

It is not really clear that you are looking for a probability model. I think what you are looking for are probability estimates based on your observed sample data. Reasonable estimates can be obtained if it is safe to assume that the sample you have is a random sample from the target voter population. The estimates are simply the sample proportions. For the percentage casting 2 or more votes just count the voters that voted 2 or more times divided by the total number of voters.

For each candidate you can take the number of votes received divided by number of voters to get their probability of getting a vote. Now for your sample there will either be a candidate that gets a majority of votes or there will not. So to answer a question like what is the probability of a candidate getting a majority, you will either need to construct a model based on the data or you could bootstrap the sample and use the proportion of bootstrap samples that get a candidate with a majority as the the estimate of this probability.

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