順序資料整體代表性之研究及其在管理決策上的意涵

Abstract

多元社會中，個人可以選擇自己偏好的事物。許多活動 設計的目的（譬如：公共政策或產品行銷），都希望能滿 足更多個人的需求及偏好。因此彙集個別偏好，使得活動 能更能滿足整體需求及偏好，成為管理上值得研究的課題。 本論文嘗試依據團體成員對各種不同項目的偏好，整理 出整體項目偏好順序，並評估整體排序與個別排序之相近 程度。此外，在整體排序項目裡面，有些項目的排序位置 與個別資料中的排序位置較為契合，這種個別項目在整體 排序的位置與該項目在個別資料中排序位置的契合程度， 也值得進一步研究。個別排序中共識較高的項目，可先行 規劃執行，以便局部提高整體效果或降低整體阻力。另外 比較不同特質團體間的整體排序差異及其個別項目間的集 中程度，可方便決策者按照不同特質的團體偏好，對目標 做不同的規劃或對資源做不同的配置。 本論文所提出的整體排序方法，並不侷限於尋找「最適 解」，而是能對任何形式的項目排序，衡量它與排序資料 整體契合程度，以便發現個體偏好中是否存在顯著的整體 偏好；或者在特定順序配置下，所能滿足的個體偏好程度。 在特定排序前提下，個別項目與排序資料中的局部契合程 度評量，為本論文所提出的原創性探討，可方便決策者評 估個別項目在團體中所獲得的認同強弱程度。 綜合上述研究成果，本論文提供分析團體偏好之數量研 究方法。本方法可以運用在順序型問卷資料分析、多目標 決策評估、團體共識測量、管理目標優先順序評定，及質 性資料等等之分析。

With n individuals ranking m objects, an overall ranking depicted by an order vector can be used to extract the ranking structure of the ordinal data set. There are several existing methods dealing with overall ranking, but most of them fail to resolve one or several of the following problems: (1) dominant minority ranking, (2) ranking orders partially reverse in a subset of ranking items, and (3) insensitive to structure change in the order data set. An exhaustive comparison approach is proposed in this dissertation to solve the above problems. In addition, an overall concordant order ratio (OCOR) evaluating the goodness of fit of the order vector is proposed to represent the order structure. And marginal concordant order ratios (MCOR) evaluating the individual item fits within the order vector are also proposed to provide additional measures to evaluate alternative overall ranking and its ability to represent the order structure in the data set. These measures can be used to reveal the goodness of individual item ranking so that partial items would be ranked to eliminate non-informative ranking items. The exhaustive comparison approach proposed in the dissertation compares all possible order vectors instead of "#34 order vector to help data analyst to consider "feasible"ranking solutions rather than "desired"ranking solution. This approach enables decision makers to consider satisfactory states instead of waiting for an optimal state, which might not be attainable. Empirical survey data are used to demonstrate the proposed methodology and computation of OCOR and MCORs. The analytical findings are also presented to illustrate the possible usefulness related to management decision making.