當選舉制度改變或行政區域調整的時候，選舉區域必須因應這些變更而重新劃分。傳統的選區劃分方式常需花費大量的人力與時間，同時易產生公平性的爭議，透過電腦的分析並採取有系統的選區劃分方式可以有效地節省人力、時間等資源並減少爭議性。以電腦自動分析來劃分選區有許多議題值得探討，諸如如何在有限的時間內完成選區劃分、如何規劃並維持選區形狀的完整性、如何產生足夠有代表性的解集合但又能避免解集合過於龐大、如何評估選區的優劣、如何偵測並避免重覆解等，都是目前有待分析的問題。我們嘗試以資訊科技的觀點來看選區劃分，並嚐試為上述問題提供看法與解答。 一般而言，影響選區劃分的因素大體可歸納為下列六類：人口一致性、選區連接性、形狀完整性、避免過度切割行政區域、保障少數族群利益以及尊重自然疆界等。並非所有的因素都適合以電腦來分析或處理，我們將針對人口一致性、選區連接性、形狀完整性等問題做討論。 過去我們曾提出人口比例二分法來劃分簡單的選區，透過計算幾何學和人工智慧的技巧可將選區依人口比例劃分成兩份。然而採用此法處理多重選區劃分時所產生的解集合數量過於龐大，目前的電腦無法有效處理。本論文中，我們提出了「不可分割」的觀念，透過事先設定的不可分割區並輔以砌磚法與重覆地使用人口比例法，我們成功的將多重選區劃分問題的解集合數目控制在電腦能處理的範圍之內。此外我們對選區形狀完整性提出了新的評估方式，可以更有效地篩選出較佳的解集合作進一步的分析。 實作中我們以台中市和桃園縣為對象來檢驗我們的方法，實驗結果顯示我們的方法成功地為台中市(劃分成三個選區)與桃園縣(劃分成六個選區)找到了數以十萬計的選區劃分方式。我們從通過高標準評估的解集合中，挑選出若干個解與中選會公佈的選區劃分方式比較，結果顯示我們的劃分方式有明顯的優勢。另外，我們將歷史選舉資料中選民投票的傾向套入實驗的選區劃分結果中，可以分析並預測未來的選舉結果。 總結而言，我們提出了一套系統化的方式成功地為多重選區劃分的問題找到了大量的合理解，透過進一步的評估，不同的劃分方式能滿足不同的需求。另外，我們所提出的不可分割的觀念，不僅能有效的降低解集合的數目，未來還可以應用到避免行政區域之過度切割、保障少數族群利益與尊重自然疆界等問題上。

選區劃分近年來在台灣一直是備受關注的問題，由於選舉法規的修改以及行政區域的調整，選區必須重新調整，因此自動化的選區劃分方法也逐漸受到重視。過去的研究往往以不同的方法自動的劃分選區，而這類的方法常使用類似的功能進行選區劃分與評估。研究者彼此間缺乏一套可互享資源的標準或機制，往往導致新的研究者必須耗費甚多的時間來重新設計或開發這些類似的功能。 本論文中，我們提出一套機制以及整合此套機制的系統架構，可以減少自動化劃分選區軟體的開發成本。我們結合地理資訊系統內部結構，淬取圖層中的線段，改良自動劃分選區所採用的單元，再利用線段在各圖層間的相位關係，建立新的相鄰定義與相鄰關係，從而能改善選區劃分的方法與劃分結果評估之效能。 實作中，我們以所有台灣23個縣市的圖層來測試我們的機制，實驗結果顯示我們的機制可以有效的判斷選區邊界對選區形狀完整性造成的影響，同時，採用淬取之線段來計算，能大幅降低評估選區形狀所需之時間。 / Electoral districting has received more attentions in Taiwan in recent years due to the change of electoral regulations or the change of the administrative districts. As a result, automatic electoral districting mechanism has also gotten more attentions gradually. Previous researches used various approaches in solving these problems and tend to adopt similar mechanisms in region districting or in results evaluation. The lack of standards or mechanisms in sharing the developing resources yields tremendous time wasting in rebuilding such functions. In this thesis, we proposed a set of mechanisms as well as the system architecture that integrates these mechanisms. Using this system, one can reduce the costs in developing automatic electoral districting software. We also designed a system architecture that integrates these mechanisms and helps to reduce the maintenance costs. We extracted the arc properties from the coverage data layer in GIS to improve the basic unit used in the automatic electoral districting. We proposed a new concept of adjacency relations and used the topological relations in various data layers to construct these new adjacency relations. Using these new relations, one could improve the electoral districting developing processes as well as the efficiency of performance evaluations. We used all twenty-three counties and cities of Taiwan to test our mechanisms. Experimental results shown that our mechanisms could determine the influences of districts’ boundaries to the districts’ shapes effectively. Moreover, using the extract arcs, one could reduce the time required in evaluating the districts’ shape dramatically.

選區劃分長期以來被視為只是行政上的業務，缺乏一套較為完整的理論。各項選區劃分的原則彼此之間也存在著結構上的矛盾，使得各國實際劃分選區時，常常必須在各項原則之間進行取捨。本研究採用歷史與制度研究法以及比較研究法，來探索不同的選區劃分方式背後所隱含的代表精神為何，希望能將選區劃分與代表理論相結合，為將來我國面臨選區劃分原則衝突時，提供一個思考如何進行取捨的方向。 全權委託模式以及委任模式是代議模式的兩個典型，但實際上代表們不可能只選取其一來面對所有議題。代表們要以何種代議模式為主，除了視各選區不同的狀況之外，我們也可以從選區的設計不同，來分析代表應該扮演何種角色。 今日英國選區劃分的特色，在於其相當注重維護社群的完整，所以容許選區之間有較大程度的人口數差距；美國的選區劃分則比較注重各選區人口數均等原則，因此對於地區的切割與重組較為普遍。值得注意的是，今日美國的選區劃分仍然可以見到各種不同形式的傑利蠑螈劃分法。 從第七屆開始，台灣的立法委員選舉制度將改成所謂單一選區兩票制。在改制之後，可以預見區域立法委員與其選區之間的關係會更為密切，這也將使立法委員偏重於扮演委任代表的角色。

選舉是實行民主政治最有效的方法之一，而選區劃分的方式將直接或間接的影響投票結果與民主政治理念的施行。 然而在選舉法規或行政區域發生變動時，舊有的選區劃分方式需要隨之調整。而傳統人工的方式具有許多缺點，如：耗費人力資源、人口分配不均、難以兼顧形狀及行政區完整等等。若每次行政區域發生變動，都需要重新劃分，將花費許多不必要的人力、物力及時間，因此利用電腦以完成自動劃分的技術逐漸受到重視。 本論文中我們打破現有的政治與人文鴻溝，嘗試以系統化的方法對選區劃分作全面性的查驗。我們利用計算幾何學的特性與人工智慧搜尋的技巧，儘量找出可能的劃分方式再進行評估。我們依據中選會的建議採用村裡為劃分之最小行政區域，從數以十萬計之合理解中，根據形狀等客觀條件篩選出較佳之劃分方式，進而將歷史投票行為加入考量，以對篩選出的劃分方式作進一步評估與分析。 實作中我們以台南市為對象，在不同的人口限制及形狀條件下，分別比較所能找到的合理解數目。同時選出一部分的劃分方式，和中選會的劃分方式比較，結果顯示我們的方法可以全面性的分析選區劃分，不同的劃分方式可能產生不同的選舉結果。 / Election is one of the most effective way of conducting democratic politics, and mean of electoral redistricting shall post effect, either directly or indirectly, on electoral outcome as well as delivering ideas of democratic politics. As election regulations or administrational districts experience alterations, the present electoral districting is forcefully accompanied with adjustments. Electoral redistricting using traditional human labor works reveal several flaws such as: human resource wastage, uneven population distributions, hard to maintain shape contiguity and compactness, as well as the completeness of administration districts. Every single alteration experience in administration district requires redistribution, thus expensing on unnecessary human labor, resources and time. As such, it had brought great attention on techniques of automatic redistribution by means of modern computer technologies. In this thesis, we shall breakthrough a giant gap between politics and humanity; conduct a thorough examination on systematic approach on electoral redistricting. We are going to utilize characteristics of computational geometry and artificial intelligence searching techniques to find out every conceivable means of redistricting then evaluation the performance of them. By recommendation of Central Election Commission (hence CEM), we will adopt the classification of township as basic unit of administrational district, from counts of thousand adequate explanations, by objective factors of shape accordance and others, select the better means of redistricting methods, and afterward put into concern of historical voting behavior, conduct a further evaluation and analysis upon chosen redistricting method. In actual practices we had selected Tainan City as the experiment target, under different population limitations and factors of form, compare the searchable numbers of decent explanation respectively. We choose some redistricting outcomes, and put into comparison with redistricting method of the CEM. The results indicated our approach is able to conduct a thorough redistricting analysis, as well as more diversified comparing to CEM's outcome. The result of this experiment also reveals different election outcome with adoption of different redistricting methods.

台灣地區在2010年的行政區域調整中，有三個區域進行縣市合併，合併後的縣市其選區必須重新劃分，而進行劃分時有三個因素可以做為縣市合併後衍生之選區劃分原則，分別是縣市融合、大市效應與優勢現象。這三個因素在以往的選區劃分中甚少被提及，因此本論文特別討論考慮這三個因素的選區劃分。 由於大市效應或優勢現象產生的原因是單一選區中有太多的選舉人口來自縣市合併前的同一行政區，因此我們在劃分前處理中，先對人口過多的行政區進行分割，然後進行選區劃分。為促進縣市融合，我們優先考慮將原縣市交界區域的行政區域劃分至選區，然後才考慮非交界區的行政區域。劃分的過程中，我們參考最多限制優先的原則，透過貪婪演算法進行劃分，劃分結束後再進行選區調整，以求能滿足中選會對選區人口數等相關的規定。 我們在論文中提出了選區評估的指標，可以對縣市融合、大市效應與優勢現象進行衡量與評估，以便作為劃分結果的比較與參考。 最後我們透過對合併後的高雄縣市進行選區劃分，以說明我們整體的概念與方法。根據我們的劃分原則與方法，我們的劃分結果產生6個縣市融合的選區，而中選會所公布的選區劃分結果，沒有任何符合縣市融合精神的選區。同時，相較於中選會的結果，我們的劃分方式有較好的大市效應指標與優勢現象指標。 / During the administrative district adjustment of Taiwan in 2010, three regions conducted the city and county merges. The electoral districts must be redistricted after these merges. There are new issues, related to the merge of city and county, which have seldom being discussed before, namely, the city-county integration, the overpopulation-region effect, and the dominance phenomenon. In this thesis, we will consider these issues as the new principles to be included in electoral districting. The reason that causes overpopulation-region effect or dominance phenomenon is due to too much of population comes from the same administrative district in the city of county prior to the merge. One could avoid these by dividing the overpopulation borough before carrying out the electoral districting. In order to promote the city and county integration, we give priority to these administrative districts on the junction regions of the original city and county configurations before considering the administrative districts on the non-junction regions. The most constraint principles and greedy algorithms are employed in the actual electoral districting processes. After the first districting, we conduct a region adjustment to comply with the regulations of the Central Election Commission (CEC). We also proposed the assessment indices that can be used to evaluate the possible effects due to the city-county integration, the overpopulation-region effect, and the dominance phenomenon. Using these indices, one can compare the results of various districting outcomes. Finally, we illustrated our idea and methods by actually districting the merged region of Kaohsiung city and county. According to our mechanism, we produced six city-county integrated electoral districts where no city-county integrated electoral district was found in the CEC’s districting results. In addition, the districting results produced by our method have better overpopulation-region effect index and better dominance phenomenon index than that announced by CEC.