A well-known fact about positional election procedures is that its ranking of m alternatives can change when some of the alternatives are removed from consideration—given a positional procedure on each of 2, 3, …, m alternatives and a collective preference order for each distinct subset of the m alternatives. Saari has established that with few exceptions, we can find a voter profile for which the collective preference order for each subset under the according positional procedure is the one given. However, Saari's results do not quantify the likelihood of finding such voter profiles. For small numbers of alternatives, William Gehrlein developed a statistical model to explore the probabilities that particular collective preference orders on subsets of alternatives can occur for large electorates. One goal of this research is to determine whether changes in the collective preference order as alternatives are removed can be considered to be the norm or an outlier for positional procedures. This dissertation extends the research headed by Gehrlein in two directions. One, I generalize his statistical model to explore probabilities for iterated election procedures. Gehrlein's model previously produced results only for three alternatives and in limited cases for four alternatives. I have extended this model to produce results for up to five alternatives, including analysis of instant-runoff voting and runoff elections. Two, Gehrlein's model required specific conditions on the probability distribution of individual voter preferences across the population. I relax this assumption so that for any probability distribution of individual voter preferences across the population, I can explore the probability that a collective preference order is inconsistent with the outcomes when alternatives are removed. These results provide a foundation for discussing the impact of removing alternatives on elections across all large electorates. I also apply these results to two recent United States elections wherein a third-party candidate received a significant share of the votes: the 1992 U.S. Presidential election and the 1998 Minnesota Gubernatorial election. Overall, my research will suggest that as the number of alternatives increases, the likelihood of finding changes in the collective preference order as alternatives are removed will approach one.

To evaluate voting rules, it would be good to know what universe election outcomes are drawn from. Election theorists have postulated that elections might be drawn from various stochastic preference models, including the IC and IAC conditions, but these models induce empirically contradicted predictions. We use two distinct data sets, FairVote and German Politbarometer survey. Based on the data information, we suggest approaches that differ from those probabilistic models to better approximate the actual data in Chapter 3 and 4. Chapter 5 applies the spatial model for four-candidate in a three-dimensional setting. We also offer a significant gap between the actual and simulated data under the IAC conditions by comparing their statistical characteristics. / Doctor of Philosophy / Through the 1884 Third Reform Act, the plurality rule (or first-past-the-post system) runs to elect parliament members for the first time. More than a hundred years passed after the Act, and election theorists have suggested various alternatives, the plurality rule is the second most used rule worldwide for national elections for now. One main reason is that researchers do not reach an agreement on the best alternative rule. Theorists have evaluated different voting rules under probabilistic assumptions, but real-world examples contradict the predictions of these models. In this dissertation, we suggest different approaches provide a better approximation to the actual data. In Chapter 3 and 4, we go backward: analyze how voters of each preference order are distributed in real data first, then set a model for estimating the frequency of paradox. In chapter 5, we extend an existing model with higher dimensionality. Then using the model, we offer empirical evidence showing the gap between the actual and simulated data under a popular probabilistic model.

By conducting an explorative study it is tried to determine whether a sample of film enthusiasts can produce a similar result in judging for the 87th Academy Awards for movies in 2014 like the actual Academy members or not. An online survey has been created and the votes cast by the participants have been tabulated. It can be shown that the results of the simulated awards voting in the survey are quite similar to the actual Academy decision. However, additional adjustments and further studies are recommended to ensure the results.

By conducting an explorative study it is tried to determine whether a sample of film enthusiasts can produce a similar result in judging for the 87th Academy Awards for movies in 2014 like the actual Academy members or not. An online survey has been created and the votes cast by the participants have been tabulated. It can be shown that the results of the simulated awards voting in the survey are quite similar to the actual Academy decision. However, additional adjustments and further studies are recommended to ensure the results.