We associate with any game G another game, which is a variant of it, and which we call . Winning strategies for have a lower recursive degree than winning strategies for G: if a player has a winning strategy of recursive degree 1 over G, then it has a recursive winning strategy over , and vice versa. Through we can express in algorithmic form, as a recursive winning strategy, many common proofs of non-constructive Mathematics, namely exactly the theorems of the (...) sub-classical logic Limit Computable Mathematics , Hayashi and Nakata ). (shrink)
This article investigates the relationship among the weak Pareto principle, the strong Pareto principle, and positive responsiveness in the context of voting. First, it is shown that under a mild domain condition, if an anonymous and neutral collective choice rule (CCR) is complete and transitive, then the weak Pareto principle and the strong Pareto principle are equivalent. Next, it is shown that under another mild domain condition, if a neutral CCR is transitive, then the strong Pareto principle and positive responsiveness (...) are equivalent. By applying these results, we obtain a new characterization of the method of majority decision. (shrink)
This paper aims to reexamine the axiom of the independence of irrelevant alternatives in the theory of social choice. A generalized notion of independence is introduced to clarify an informational requirement of binary independence which is usually imposed in the Arrovian framework. We characterize the implication of binary independence.
The Trends in International Mathematics and Science Study found that even though children from all East Asian countries outperformed American children, American students reported higher self-evaluation of their math and science abilities than did students from East Asian countries such as China, Korea, and Japan (Mullis, Martin, Gonzalez, & Chrostowski, 2004). Such cross-cultural differences in self-appraisal ﬁt the stereotype of the modest East Asian and contribute to the received view that East Asians have less positive self-concepts than Americans. This view (...) was summarized recently by Heine, Lehman, Markus, and Kitayama (1999) as follows: ‘‘The need for positive self-regard, as it is currently conceptualized, is not a universal, but rather is rooted in significant aspects of North American culture’’ (p. 766; but cf. Sedikides, Gaertner, & Vevea. (shrink)
This paper examines social choice theory with the strong Pareto principle. The notion of conditional decisiveness is introduced to clarify the underlying power structure behind strongly Paretian aggregation rules satisfying binary independence. We discuss the various degrees of social rationality: transitivity, semi-transitivity, the interval-order property, quasi-transitivity, and acyclicity.
A syntactically optional constituent in a sentence can be deleted if it is recoverable from the preceding context. This does not mean, however, that all such constituents are deletable. This paper hypothesizes that there is a pecking order of deletion, which dictates that deletion should proceed from less important to more important information. Evidence is drawn from English, Russian and Japanese in support of this hypothesis. Interaction of this constraint with various syntactic rules in each individual language is examined, and (...) it it hypothesized that unacceptability does not result when the above peeking order of deletion principle is violated due to the structural pressure of the language. Further discourse deletion data from Russian and Japanese are introduced, and principles that control them are formulated and justified. (shrink)
The slogan, or the KISS principle has been the basic guideline in agent-based modeling. While the KISS principle or parsimony is vital in modeling attempts, conventional agent-based models remain abstract and are rarely incorporated or validated with empirical data, leaving the links between theoretical models and empirical phenomena rather loose. This article reexamines the KISS principle and discusses the recent modeling attempts that incorporate and validate agent-based models with spatial data, moving beyond the KISS principle. This article also provides a (...) working example of such time and space specified agent-based models that incorporates Schelling's classic model of residential segregation with detailed geo-referenced demographic data on the city of Chicago derived from the US Census 2010. (shrink)
This squib aims to show that the acceptability status of sluicing examples with an implicit antecedent in islands varies and discusses what is responsible for this variability. After investigating two representative structural approaches to sluicing that posit unpronounced structure in ellipsis sites, namely, Chung et al.’s Representing language: Essays in honor of Judith Aissen, 2010) LF-recovery analysis and Merchant’s PF-deletion analysis, we demonstrate that the acceptability data presented are challenging for both of them. Acceptable sluicing examples with implicit correlates in (...) islands cast doubt on Chung, Ladusaw, and McCloskey’s strict locality requirement, while unacceptable or degraded sluicing examples necessitate additional constraints for Merchant, who employs E-type anaphora as an escape hatch for island violations in sluicing. The gradient nature of the acceptability status of the examples under discussion calls for a non-structural factor that controls their acceptability. We speculate that it is discourse activation of implicit correlates that plays this crucial role. (shrink)