Problem: Evenly distribute pairs of Essays. The suggest solution is to use a simple graph, with average degree of 3.
Approach:
Generate a random Graph, selected uniformly, with an average degree of 3
https://en.wikipedia.org/wiki/Random_regular_graph
http://networkx.lanl.gov/reference/generated/networkx.generators.random_graphs.random_regular_graph.html
https://egtheory.wordpress.com/2012/03/29/random-regular-graphs/
If the number of nodes are odd, we remove it so we can generate the graph
We then add the isoltaed node back in and randomly add edges - some essays will be graded a few times more
The graph only needs to be generated once, and is random. Once we have, we pull out the connected pairs and put them all on a stack.
When a request comes in for pairs of essays to evaluate the stack is used Scoring of Essays
Problem: To infer a ranking based on the grading done by the students, and then calibrate scoring based on the teachers grading.
Approach:
Use a pairwise comparison : https://en.wikipedia.org/wiki/Pairwise_comparison
Teacher grades some of the essays there are two ways that this could be done: * Using the score, cluster the essays and select an essay at random to be graded * Use furthest point first to select essays to be graded
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