Question:

In lecture, we introduced the literature on ballot order effects with a somewhat stylized example. Here we work through the example in more detail to explore the concept of a probability mass function.

There is a great deal of literature indicating that the ordering of candidates on a ballot has an effect on their vote-share. In an attempt to increase the fairness of the process, New Hampshire randomly chooses a letter from the alphabet and then lists the candidates in alphabetical order starting with that letter. As in the lecture, our goal is to characterize the distribution of possible ballot placements for Barack Obama. As in lecture, let the random variable X be Barack Obama’s position on the New Hampshire primary ballot.

To simplify the problem slightly, assume the shortened candidate list below. (Note that removing candidates changes the problem from what we did in class. The same principles apply but the answers will be different.)

1. Write down the PMF of Barack Obama's ballot positioning with New Hampshire's ballot ordering rule and the shortened list of candidates.
2. Gov 2000 only: Create two graphs (similar to those in lecture) showing (1) the PMF from part A and (2) the CDF of the distribution.
3. Calculate the expected value of X (Barack Obama's ballot position) and the variance of X. Show your work.
4. Assume that the ballot ordering effects are the same for all candidates and are known to be the following for a five-candidate ballot:
   
   Calculate the expected ballot order effect for Barack Obama.
5. Now for comparison, calculate the expected ballot order effect for Hillary Clinton. Do you think New Hampshire's ballot ordering scheme is fair?

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