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.