Sadly it seems like so many competitions are biased esp. when it comes down to subjective judging. Just look at the ice skating judges from the winter Olympics a few years ago (
http://en.wikipedia.org/wiki/2002_Winter_Olympics_figure_skating_scandal). For a competition in which the competitors do not need to be present during the judging (as the judging is about what the competitor accomplished prior to the judging), then the best way to remove some of those biases is to have the judging blind. For the chilli cook-off, for example, they should seat the judges in a different room and bring numbered cups to the judges to taste. This way there is less of a chance for the judges to vote based on who made the chilli and more on just the qualities of the chilli.
I could see a few other features about the chilli other than taste that could be judged, although taste should be weighted more than the other factors. Things like texture, presentation, aroma, etc. could also be considered when rating the quality of a chilli. For example if one chilli seemed to have a layer of grease sitting on the top, it shouldn't be rated as high even if the taste of the stuff below the grease was excellent. They could also consider different styles, giving a prize for each category and a final one for best in show (eg Texas-style, Southern-style, Green chilli, etc.) since it is sometimes difficult to compare 2 drastically different styles.