Voting cycles do exist, but much less frequently in practice than is predicted. This paper develops an estimate of the probability of a cycle that closer to what the data reveal. In the absence of an abundance of actual voting data in which voters rank candidates, survey data is the best alternative. We use German Politbarometer data, which offers two benefits for empirical analysis of voting systems; the fact that participants score the candidates and the large number of observations. We develop hypotheses and models based on cardinality. Specifically, we consider a 'median' of collected evaluations as a significant factor in predicting the winner of head-to-head comparisons, estimating the probability of a cycle from the probability of two sets of three events occurring. The model predicts a significantly lower voting cycle frequency than models based on the IC and IAC assumptions. Our approach involves 1) assigning three candidates presumed positions of first, second and third 2) noting the gaps between pairs of candidates in apparent estimated merit, and then 3) computing the probability that the three pairwise comparisons will have a combination of outcomes that results in a cycle.

(Working)
Instant Runoff Voting (IRV) or “the alternative vote” is now used by some countries and large cities in the US. Studies have concerned about a severe disadvantage of IRV, monotonicity failure, with theoretical approaches, but not much with data analysis. We address empirical analysis with two particular data sets, actual elections (FairVote) and surveys (Politbarometer). We estimate the frequency of Condorcet paradox and Condorcet inconsistent result of IRV, which is deeply related to the monotonicity criterion. We check the vote gap between the Condorcet winner and the Condorcet loser for Condorcet paradox, and that of between the Condorcet winner and a candidate who got fewer votes in two non-Condorcet winners by plurality rule for Condorcet inconsistency. About 1,000 synthetic elections, we found one Condorcet Paradox and twenty Condorcet inconsistencies (frequency of monotonicity failure is 2.15%). Our model provides 2.18~5.46% and 2.35~2.71% from two data sets.

(working)
When there are two alternatives, the best way to decide one for group decision-making is majority rule. However, when there are more than two available options, it is not straightforward. Most of the previous literature of relevant fields focused on the three-candidate election, and when researchers were adopting spatial model, it is one-dimensional or two-dimensional. This paper targets a normal spatial model (Good and Tideman, 1976) with four candidates in three-dimensional attribute space. Most of our research is about the modeling process and technical details, parameterization of the models that can best describe the actual rank data. Furthermore, we test whether bimodal multivariate normal distribution assumption is more likely than unimodal multivariate normal distribution by AIC and BIC criteria.

(working)