在德國多層級聯邦體制和單一選區兩票聯立制(Mixed-member pro-portional representation, MMP)作用下，聯邦眾議院(Bundestag)與邦議會(Landtag)選舉，常因不同層級間之政治連結(Politikverflechtung)，形成相互影響的關係。故選民常將聯邦政府的執政效能，在邦議會選舉中直接歸責於執政黨在邦層級對應的參選政黨，而邦議會選舉因此也被視為「測試性選舉」(Testwahl)。依「次級選舉」(The Second-order Election) 理論之假設推斷，聯邦眾議院與邦議會選舉屬第一級和次級選舉間之關係，故選民在選舉週期及不同層級選舉重要性考量下，於各黨間顯示出高度變遷性。然僅從選舉結果觀察，無法得知選民的政黨偏好在前後兩次選舉間如何轉移，以及其選票之變遷程度。因此，若要測量選民真實意向，須利用集體層次之選舉資料進行分析。惟集體資料係由個體資料集結而成，特性就如同厚資料，無法於其中區分個體行為資訊，因此需以「區位推論方法」(ecological inference, EI)，進行「跨層次推論」(cross-level inference)，以集體資料回推個體層次投票行為及建構厚資料知識。為此，本文運用「Gary King的區位推論模型」(Gary King’s EI model) 及「階層貝式模型」(hierarchical Bayesian model)，估計巴登—符騰堡邦(Baden-Württemberg)2013至2017年聯邦眾議院與邦議會選舉間之選民投票穩定及變遷程度，以檢驗各項依「次級選舉」理論建構之假設，同時並從厚資料研究之觀點，解釋選民投票行為之轉變趨勢和對政治勢力消長之影響。
Under the influence of the German multi-level federal system and mixed- member proportional representation (MMP), the Bundestag (the Federal Parliament) and the Landtag (the Representative Assembly) elections often form interrelated and interactive relations due to the political connections (Politikverflechtung) characteristic of different government levels. Therefore, in an ongoing Landtag election, voters often directly attribute the federal government’s ruling efficiency to the ruling party’s standing counterpart in Landtag. Hence, Landtag is often regarded as a “Testwahl.” According to the hypothesis constructed based on a second-order election, Bundestag and Landtag elections fall under the first-order and second-order election relations. Therefore, with the election cycle and different levels of election taken into account, voters show a high degree of political party inclination change. However, how the voters’ political inclination changes in the two elections and the extent of vote transfer cannot be determined when based solely on the observations of the election results. In order to measure the true intentions of voters, it is necessary to adopt collective-election data to carry out the analyses. However, since collective data is made up of individual data sets, its “thick” data” nature makes it impossible to distinguish individual behavior information; thus, the need for ecological inference (EI) to implement “cross-level inference,” is needed to infer the implications of the voting behavior behind the thick data, to interpret factors contributing to voting choices, and to construct the trend of individual voting stability and change.
In order to achieve the purpose of constructing voting behavior knowledge through collective data, the ecological inference methods used in this study for cross-level inference include Gary King’s EI model and the hierarchical Bayesian model, through which the voters‘ voting stability and degree of change during the Bundestag and Landtag elections spanning 2013 to 2017 were estimated. At the same time, the model estimation results were used to examine the hypotheses established based on the second-order election theory, explaining the change in voter’s voting behavior and the influence of the political power growth and decline.
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