The purpose of this paper is to investigate a relationship between a local government expenditure and a population size in Japan. The previous papers reported that a U shaped per capita expenditure curve is observed by a cross-sectional data. However, the these results might include omitted variable biases both the population size and the fixed effect for each municipality. Therefore, this paper tries to estimate the cubic function related to the population size. Also, in order to address the omitted variable biases related to the fixed effect, we estimate the fixed effect model using the panel data from FY1996 to FY2010. We found the first evidence of cubic function formed expenditure curve related to the population size. For the small municipalities, the form captures an increasing effect the population size on the local government expenditure. The medium-sized municipalities can have the decreasing effect. On the contrary, the large municipalities can have an increasing effect. In addition, we showed the relationship between the fixed effect for each municipality and the population size has the U shaped form. In other words, we could improve"the remaining omitted variable biases"about both the population size and the fixed effect on the previous papers.

　This paper investigates the vertical effect on municipal personnel expenditure influenced by the factor of prefectural governments. We focus on the personnel expenditure after the great east Japan earthquake in 2011. After that, Central government in Japan strongly required local governments to follow official pay cut. This shock gave rise to varied responses from local governments. Our approaches are HLM (Hierarchical Linear Modeling) with simultaneous analysis of several group used in social psychology and Panel Data Analysis in economics. We found that municipal personnel expenditure is influenced by the factor of partisanship of governors or pay level in prefectural governments. If the governor of the Liberal Democratic Party cuts official pay, the mayors of the same partisanship will follow. In addition, the change of government brings fiscal discipline to the prefectures which the governors of the same partisanships lead. Our examination indeed shows that there is such vertical fiscal interdependence that hasn't been examined by previous studies in fiscal economics.

　This article claims that the recent prevalence of the concept of causality based on potential outcomes explains the decline of formal models and the rise of experiments observed in publication trends in political science in the United States. Observational data analysis, a mainstream approach in political science, necessitated formal models as strong theories to ensure empirical-statistical models to meet the conditions in the classical concept of causality, especially temporal precedence and the exclusion of alternative explanations for cause-effect linkages. Rather than specifying statistical models with the aid of formal models for causal inference, however, designing randomized experiments are the most straight-forward and desirable way of satisfying the conditional independence assumption (CIA) in the recently prevailing concept of causality based on potential outcomes. For this reason, the significance of formal models has been devaluated, and experimental methods have rapidly evolved with technological advances associated with the Internet, and have established its position in political science in the United States.

　This paper discusses the relationship between formal and quantitative analysis in political science from the point of view of the formal modeler. The first part details the two theoretical benefits of formal models that have no impact on empirical analysis: (i) the indication of each political system's important characteristics and (ii) normative analysis. In the second part, I discuss whether we should start analysis with formal or quantitative analysis when writing a paper based on theory and evidence. If we start with the construction of a formal model, we tend to face many difficulties, such as a scarcity of data. On the other hand, if we start with quantitative analysis, we tend to have less theoretical benefits, and readers may feel that a formal model is not necessary. Therefore, researchers should balance between theoretical and empirical contributions.

　This paper provides a brief introduction to an empirical comparison of cooperative and non-cooperative game formulations in the context of bargaining games. More specifically, after discussing the preliminary basics of cooperative and non-cooperative frameworks for a bargaining situation, I explain the setting, the methodology, and the results in Adachi and Watanabe (2008) and Mitsutsune and Adachi (2014), both of which study the cabinet formation in Japan in the period of 1958 to 1993. In terms of empirical contents, the main difference between a cooperative and a non-cooperative settings is that in the latter, the "first-mover advantage" can be incorporated. In the specific context of the two studies, the non-cooperative framework performs better than the cooperative framework in explaining the data, although in other contexts such as vertical transactions in product distributions systems, the opposite may be true. Overall, I argue that empirical comparisons of cooperative and non-cooperative games enriches our understanding of strategic aspects of the real world.

"One Person, One Vote: One Vote, One Value" is one of the fundamental principles of representative democracy. In order to measure the extent to which this principle is attained, two indexes are mainly employed. Mass media and judiciaries use the ratio of the largest to the smallest districts and academic researchers utilize Samuels and Snyder's (2001) MAL, the sum of the absolute difference between the seat share and the population share in each district. However, these indexes have several limitations. Therefore, we cannot accurately and precisely capture the historical transition of malapportionment in Japan. In this study, we employ a new index based on α-divergence, introduced to this field by Wada and Kamahara (2016) . This index has two valuable properties. First, by changing the parameter α, we obtain several variants of the index that conform with philosophies of seat distribution. Second, the index decomposes the overall degree of malapportionment into two factors of malapportionment: apportionment and districting. This study aims to comprehensively show the historical transition of malapportionment in Japan's House of Representatives by using this index.

　Although existing studies often find a distributive bias for overrepresented areas, they fail to explain when such a bias becomes salient. The bottleneck is partially the result of their assumption that targeting overrepresented areas is a cost-efficient strategy. However, this is not always the case, because voters in such areas do not necessarily respond to money. This study argues that risk-averse parties invest in overrepresented areas only when they can avoid the risk of freeriding by opposition supporters. Specifically, hegemonic parties are supposedly risk-averse, because their survival depends on the credibility in rewarding supporters and punishing opponents. Through a systematic analysis of the Malaysian ruling party (BN), this study demonstrates that the BN targets overrepresented areas only with a risk-immune item. This holds true even after controlling the latent endogeneity of malapportionment.

　We focus on districts without voting in prefectural election, and argue why district without voting occur using the data of single-member districts in prefectural election, which the largest number of district without a vote and the only number of candidate is lower than 2 that Duverger's law and M+1 rule indicates. Calculating the ratio of the districts without voting by prefectural election since 2000, it is appeared that the only election that the ratio of the districts without voting decreased is the election in 2007, which there are many redistricting and changes of the seat of districts because of "Heisei no daigappei (municipal mergers)." Therefore, we evaluate two research questions, 1) redistricting causes the number of candidates to increase and the number of districts without voting to decrease, 2) the change of the seat of district cause the number of candidates to increase and the number of districts without voting to decrease, using the data of single-member districts in prefectural election. Moreover, we argue whether the number of candidate in next election after redistricting and change of the seat of district is 2, Duverger's law indicates, or 1 (without voting).