When determining the winner of a competition like the Mathematical Contest in Modeling, there is generally a large number of papers to judge. Let's say that there are P=100 papers. A group of J judges is collected to accomplish the judging. Funding for the contest constrains both the number of judges that can be obtained and the amount of time that they can judge. For example, if P=100, then J=8 is typical.
Ideally, each judge would read all papers and rank-order them, but there are too many papers for this. Instead, there are a number of screening rounds in which each judge reads some number of papers and gives them scores. Then some selection scheme is used to reduce the number of papers under consideration: If the papers are rank-ordered, then the bottom 30% that each judge rank-orders could be rejected. Alternatively, if the judges do not rank-order the papers, but instead give them numerical scores (say, form 1 to 100), then all papers falling below some cutoff level could be rejected.
The new pool of papers is then passed back to the judges, and the process is repeated. A concern is that the total number of papers that each judge reads must be substantially less than P. The process is stopped when there are only W papers left.l. These are the winners. Typically, for P=100, we have W=3.
Your task is to determine a selection scheme, using a combination of rank-ordering, numerical scoring, and other methods, by which the final W papers will include only papers from among the \"best\" 2W papers. (By \"best\" we assume that there is an absolute rank-ordering to which all judges would agree.) For example, the top three papers found by your method will consist entirely of papers from among the \"best\" six papers. Among all such methods, the one that requires each judge to read the least number of papers is desired.
Note the possibility of systematic bias in a numerical scoring scheme. For example, for a specific collection of papers, one judge could average 70 points, while another could average 80 points. How would you scale your scheme to accommodate for changes in the contest parameters (P, J, and W)?
在确定一项竞赛的获胜者,数学建模竞赛等,通常有大量的论文来判断。假设有P = 100篇论文。一群J法官收集完成判断。竞赛经费约束法官的数量,可以获得,可以判断的时间。例如,如果P = 100,那么J = 8是典型。
论文的新池然后传回法官,和重复的过程。一个担忧是,论文的总数,每个法官必须大大低于p .读取过程停止时只有left.l W论文。这些都是赢家。通常,P = 100,我们有W = 3。
你的任务是确定选择方案,使用rank-ordering、数值评分,和其他方法,论文最后W将只包括论文从“最佳”2 W的论文。(通过“最佳”我们假设有一个绝对rank-ordering所有法官同意)。例如,前三篇论文发现你的方法将包括完全的论文从“最好”的6个文件。在所有这些方法中,要求每个法官的阅读最需要的论文数量。
注意系统性偏差的可能性在一个数值评分方案。例如,对于一个特定的文件的集合,一个法官可以平均70点,而另一个可能平均80分。你如何扩展计划,以适应竞争参数的变化(P、J和W)?
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