The separation, and separation-deviation methodology for group decision making and aggregate Ranking
The separation, and separation-deviation methodology for group decision making and aggregate Ranking
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用于群体决策和聚合排名的分离和分离偏差方法
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发表时间：
2010
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通讯作者：
D. Hochbaum
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作者：
D. Hochbaum
在一般的群体决策场景中，决策者审查备选方案，然后提供他们自己的个人排名。综合排名问题是要获得一个公平的排名，并代表个人的排名。我们在这里认为，使用基数成对比较提供了几个优势，得分明智的模型。然后将聚集组排序问题形式化为分离模型和分离偏差模型。该模型的前提是在评论者的输入中使用隐含或显式的成对比较，并分配一个综合排名，该排名最小化了不同意分数的惩罚，以及不同意成对偏好强度的惩罚。后者允许将置信水平纳入审查者提供的关于具体成对比较以及具体分数的投入。分离和分离偏差模型已被证明是有效地解决，凸处罚。我们提出了几个组排名的情况下，成对比较的输入，如体育比赛。我们表明，使用基数，而不是序数，成对比较和建议的分离模型是有利的。在组排名上下文中，成对比较本身并不可用，使用隐含的成对比较也有优势。后者的背景包括例如NSF审查小组，选择获奖项目，确定国家信用风险和客户细分。我们统一的群体决策问题的网页排名和排名学术论文的引用。我们比较和对比的分离方法与PageRank和主特征向量的方法。问题的聚合排名“最佳”与成对比较被证明是链接到一个问题，我们称之为逆等径问题。图形表示提供了洞察力，并能够根据其与个体排名观察的偏差引入聚合排名质量的特定性能度量。我们发现，凸罚款偏离审查员的输入问题是多项式时间可解的，由组合和多项式时间算法相关的网络流量。因此，该方法非常有效。我们进一步展示了图形属性是如何与所产生的聚合排名的质量。我们的图形表示范式提供了一个统一的框架，聚合排名，群体决策和数据挖掘的问题。
In a generic group decision scenario, the decision makers review alternatives and then provide their own individual ranking. The aggregate ranking problem is to obtain a ranking that is fair and representative of the individual rankings. We argue here that using cardinal pairwise comparisons provides several advantages over score-wise models. The aggregate group ranking problem is then formalized as the separation model and separation-deviation model. The premise of the models is to use the implied or explicit pairwise comparisons in the reviewers’ input and assign an aggregate ranking that minimized the penalty of not agreeing with the scores, and the penalty for not agreeing on the intensity of the pairwise preference. The latter permits to incorporate confidence levels in the input provided by reviewers on specific pairwise comparisons, as well as on specific scores. Both separation and separation-deviation models have been shown to be solved efficiently, for convex penalties. We present several group ranking scenarios where the pairwise comparisons are the input, such as sports competitions. We show that using cardinal, rather than ordinal, pairwise comparisons and the proposed separation model is advantageous. In group ranking contexts, where pairwise comparisons are not inherently available, there is also an advantage of using implied pairwise comparisons. The latter contexts include e.g. NSF review panels, choosing winning projects, determining countries credit risk, and customer segmentation. We unify the group decision problem with the problem of web pages rankings and ranking academic papers in terms of citations. We compare and contrast the separation approach with PageRank and the principal eigenvector methods. The problem of aggregating rankings “optimally” with pairwise comparisons is shown to be linked to a problem we call the inverse equal paths problem. The graph representation provides insights and enables the introduction of a specific performance measure for the quality of the aggregate ranking as per its deviations from the individual rankings observations. We show that for convex penalties of deviating from the reviewers’ inputs the problem is polynomial time solvable, by combinatorial and polynomial time algorithms related to network flows. As such the approach is very efficient. We demonstrate further how graph properties are related to the quality of the resulting aggregate ranking. Our graph representation paradigm provides a unifying framework for problems of aggregate ranking, group decision making and data mining.