Nurmi (1987) investigated the relationship between voting rules by determining the frequency that two rules pick the same winner. We use statistical techniques such as hierarchical clustering and multidimensional scaling to further understand the relationships between rules. We use the urn model with a parameter representing contagion to model the presence of social homogeneity within the group of agents and investigate how the classification tree of the rules changes when the homogeneity of the voting population is increased. We discovered that the topology of the classification tree changes quite substantially when the parameter of homogeneity is increased from 0 to 1. We describe the most interesting changes and explain some of them. Most common social choice rules are included, 26 in total.
A number of procedures for checking the satisfiability of formulas in the important branching time temporal logic CTL* have recently been proposed. This paper instead focuses on automatic generation and verification of rewrite rules for computation tree logics; shows that non-local computation tree logics can be used to verify rewrite rules, including for CTL*; presents an efficient tableau for the non-local bundled variant NL-BCTL*; and shows that NL-BCTL* is 2EXPTIME-complete.We show that such rules can quickly simplify CTL* formulas. These simplified formulas are shorter and easier to reason with using existing decision procedures for CTL*, as demonstrated by significant speed-ups across a wide range of benchmark formulas.While CTL* is not widely used due to the complexity of its reasoning tasks, it is strictly more expressive than LTL or CTL. Furthermore, there are applications for theorem-proving and model-checking.
We use Hotelling's spatial model of competition to investigate the position-taking behavior of political candidates under a class of electoral systems known as scoring rules, though the model also has a natural interpretation in the firm location context. Candidates choose ideological positions so as to maximize their support in society. Convergent Nash equilibria in which all candidates adopt the same policy were characterized by Cox (1987). Here, we investigate nonconvergent equilibria, where candidates adopt divergent policies. We identify a number of classes of scoring rules exhibiting a range of different equilibrium properties. For some of these, nonconvergent equilibria do not exist. For others, nonconvergent equilibria in which candidates cluster at positions spread across the issue space are observed. In particular, we prove that the class of convex rules does not have Nash equilibria (convergent or nonconvergent) with the exception of some derivatives of Borda rule. We also look at "two-party" equilibria. Implications for the firm location model are discussed. for helpful discussions and suggestions and also participants of the 1st ATE Symposium held on 12-13 December, 2013, at Massey University, Auckland. We thank John McCabe-Dansted for help with computational experiments. Last but not least we thank the anonymous referees for many useful suggestions.
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