本文主要探討十二年國教的配對問題，以Gale & Shapley (1962)提出的大學錄取問題為模型基礎，分析台灣高中教育政策現況，針對免試入學分發、同分比序問題、就近入學政策，三方面進行討論，試圖提出改善方法。結果發現，免試入學分發使用的新計分制度，使學生有誘因謊報真實志願，存在配對結果被操控的可能。該計分制度也造成大量的同分現象，超額比序後將導致學生福利受損。而各學區的就近入學政策，發現開放名額學校、辦理時間、配額方式，均為影響就近入學率的潛在因素。因此，建議將志願積分制度與志願數量限制一併取消，同時增加分數上限及其他入學管道名額，以符合學生需求，設計出相對應的入學制度。

This paper discusses Taiwan high school education policy which is called 12-year compulsory education. The basic model is college admission problem proposed by Gale and Shapley in 1962. We focus on student assignment mechanism, and divide three subjects including the matching system, the tie-breaking problem and enrollment of adjacent district. The result shows that the scoring system used in new matching system would make students have incentive to misrepresent true preference. Furthermore, the system also derive the circumstance that a lot of students who have same scores can’t be distinguished, which damages welfare of students. On the other hand, the policies about enrollment of adjacent district we list have influence with three facts, which is the enrollment school, time and conduct of quota. Thus, we recommend to remove the preference score and the limit of preference lists. Simultaneously, adding the score ceiling and other admission seats to correspond with demanding of students, then draw appropriate entrance competition to satisfy students’ requirements.

論文審定書 i
謝辭 ii
摘要 iii
Abstract iv
第一章 緒論 1
第一節 研究動機 1
第二節 研究方法與目的 3
第二章 文獻回顧 4
第一節 大學錄取問題與學生配適問題 4
第二節 學校選擇問題 5
第三章 學校選擇問題與雙邊配對市場 8
第一節 Gale-Shapley學生最適穩定配對機制 8
第二節 性質介紹 10
第四章 免試入學分發性質分析 13
第一節 穩定性分析 13
第二節 抗操控性(strategy-proof)分析 15
第三節 志願數限制 16
第五章 同分比序問題 19
第一節 超額比序 19
第二節 同分的成因與改善方法 21
第六章 就近入學政策分析 23
第一節 各學區政策分析 23
第二節 歸納與討論 26
第七章 結論與建議 28
參考文獻 30

一、中文文獻：
1. 黃詩婷 (2007), “台灣的大學入學制度經濟分析,” 碩士論文,國立中山大學經濟學研究所。

二、英文文獻：
1. Abdulkadiroğlu, A. and Sönmez, T. (1998), “Random serial dictatorship and the core from random endowments in house allocation problems,” Econometrica, Vol. 66, No. 3, pp 689-701.

2. Abdulkadiroğlu, A. and Sönmez, T. (2003), “School choice: a mechanism design approach,” American Economic Review, Vol. 93, No.3, pp. 729-747.

3. Abdulkadiroğlu, A., Pathak, P. A. and Roth, A. E. (2005), “The new york city high school match,” American Economic Review, Vol. 95, No.2, pp. 364-367..

4. Abdulkadiroğlu, A., Pathak, P. A. and Roth, A. E. (2008), “Strategy-proofness versus efficiency in matching with indifferences: Redesigning the NYC high school match,” American, Economic Review, Vol. 99, No.5, pp. 1954-1978.

5. Balinski, M. and Sönmez, T. (1999), “A tale of two mechanism: student placement,” Journal of Economic Theory, Vol. 84, pp. 73-94.

6. Calsamiglia, C., Haeringer, G. and Klijn, F. (2010), “ Constrained school choice: an experimental study,” American Economic Review, Vol. 100, No. 4, pp. 1860-1874

7. Chen, Y. & Sönmez, T. (2006) , “School choice: an experimental study,” Journal of Economic Theory, Vol. 127, pp. 202-231.

8. Dubins, L. E. & Freedman, D. A. (1981), “Machiavelli and the Gale-Shapley algorithm,” The American Mathematical Monthly, Vol. 88, No. 7, pp.485-494.

9. Gale, D. and Shapley, L. S. (1962), “College admissions and the stability of marriage,” The American Mathematical Monthly, Vol. 69, pp.9-15.

10. Roth, A. E. (1982), “The economics of matching: stability and incentives,” Mathematics of Operations Research, Vol. 7, No. 4, pp. 617-628.

11. Shapley, L. S. & Scarf, H. (1974), “On cores and indivisibility,” Journal of Mathematical Economics, Vol. 1, No. 1, pp. 23-37.