Impact of biased scores on ranking in bipartite competition networks and inference of modular structure via generalized modularity

In the common jury-contestant competition format, a jury consisting of multiple judges grade contestants on their performances to determine their ranking. Unlike in another common competition format where two contestants play a head-to-head match to produce the winner such as in football or basketball, the objectivity of judges are often called into question, potentially undermining the public's trust in the fairness of the competition. In this work we show, by modeling the jury-contestant competition format as a weighted bipartite network, how one can identify biased scores and how they impact the competition and its structure. Analyzing the prestigious International Chopin Piano Competition of 2015 as an example with a well-publicized scoring controversy, we show that the presence of even a very small fraction of biased edges can gravely distort our inference of the network structure -in the example a single biased edge is shown to lead to an incorrect "solution" that also wrongly appears to be robust exclusively, dominating other reasonable solutions- highlighting the importance of bias detection and elimination in network inference. In the process our work also presents a modified modularity measure for the one-mode projection of weighted complete bipartite networks.