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投票穩定與變遷之分析方法:定群類別資料之馬可夫鍊模型

Analyzing Electoral Stability and Change: Markov Chain Models for Longitudinal Categorical Data

摘要


選民在歷屆的選舉中,究竟是傾向於把票投給同一政黨的候選人,還是把票投給不同政黨的候選人,不僅攸關個別政黨與候選人的選舉成敗,而且還影響到政黨之間勢力的起伏消長,甚至會牽動政黨體系的整體變遷,其重要性,不言而喻。也正因如此,政治學者亟思理出歷屆選舉各黨勢力消長的軌跡,描述並說明選民投票的穩定與變遷(electoral stability and change)。儘管有關選民投票變動的研究已經卷帙浩繁,然而其方向與幅度究竟應如何估算、分析,在學界卻仍無定見。 本文的目的,是將方法學中研究「常與變」的一般原則應用到「投票穩定與變遷」這個重要的主題,釐清總變量(gross Change)與淨變量(net change)的差異,整理出文獻中使用的幾種資料形態與分析方法、比較其優缺點。由於定群追蹤的個體資料(Panel data)可兼顧總變量與淨變量之估計,是很理想的數據資料型態,而為了彰顯此一特色,在分析方法上則又以「間斷時間暨間斷空間之馬可夫鍊模型」(discrete-time discrete-space Markov chain models)最適合,因為其「移轉機率」(transition probabilities)的參數和「固票、挖票、跑票」等耳熟能詳的選舉策略語彙、以及「選票穩定度、選票流入或流失之變遷率」等學理概念相當契合,既能捕捉類別變數隨著間隔的時間點前後相依、與時推移的變化軌跡,又能進而同時估計總變量與淨變量的多寡,更能進一步以母群的異質性說明其動態演變模式。本文最後以日本選舉研究的三波定群追蹤民調為基礎,舉例說明如何應用馬可夫鍊模型分析自民黨在1993、1996、2000年三次眾院選舉中選票之穩定與變遷。

並列摘要


How voters cast their votes in successive elections determines not only the fate of candidates but also the rise and fall of political parties and sometimes even causes party system changes. The subject of electoral stability and change, due to its significance in theory and practice, has long attracted the attention of political scientists around the world. Despite the voluminous publications cumulated so far, however, there are still heated debates regarding how best to model this dynamic electoral process and to estimate the amount of changes. The purpose of this paper is two-folds. First, it clarifies some confusion in the literature caused by its failing to distinguish gross change from net change and to recognize the strengths and weaknesses of various types of data in evaluating these two changes. After pointing out how panel data prevail over repeated cross-sections and aggregate data in estimating both forms of changes, we then proceed to identify a statistical model that best fits the categorical measurement of electoral changes dominant in panel surveys. The second part of this paper, therefore, pinpoints discrete-time discrete-state Markov chain models as ideal tools for describing the dynamic electoral process and further analyzing the sources of change patterns. The transition probabilities of Markov models coincide with the theoretical concepts of flow-of-the-votes and reflect the way state dependence shapes the trajectories of electoral changes. Finally, we apply a mixed Markov model to the three-wave Japanese Election Study (JES) panel data set to illustrate the potential of this technique.

參考文獻


王鼎銘、蘇俊斌、黃紀、郭銘峰(2004)。日本自民黨之選票穩定度研究:1993、1996及2000年眾議院選舉之定群追蹤分析。選舉研究。11(2),81-109。
黃紀、吳重禮(2003)。政治分析與研究方法:論2002年立法院行使考試院正副院長同意權之投票模式。問題與研究。42(1),1-17。
Achen, Christopher H.,W. Phillips Shively(1995).Cross-Level Inference.Chicago:The University of Chicago Press.
Agresti, Alan(2002).Categorical Data Analysis.New York:Wiley.
Amemiya, Takeshi(1985).Advanced Econometrics.Cambridge:Harvard University Press.

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