Anonymous judging was implemented with the new judging system, which was introduced after the 2002 Olympic judging scandal. It was an attempt to take away the ability of judges to negotiate things like judging blocs.
The researcher, Eric Zitzewitz, took a look at how much higher a skater's marks were from their home-country judges under the old 6.0 scoring system. He found that home judges added an average of .2 points to a mark, which was often enough to boost a skater's rank one position. He then examined how skaters were scoring under the new judging system when they had a home judge on the judging panel.
Zitzewitz analyzes whether having a home-country judge on the panel still results in a higher average score. He finds that the home-country bias gets even worse when anonymous judges can hide from a scrutinizing press and public, despite the barriers that anonymity may create for effective backroom deal-making. The home-judge advantage under the new system is about 20 percent higher than in the days of full disclosure. (Zitzewitz can't say how much of this increase in bias is from the home-country judge himself, and how much from others he's persuaded to go along with him; how each judge has scored a performance—and which judges' scores are counted—are kept secret.)
Anonymous judging to me just always seemed like a way for the International Skating Union to be less accountable for the obvious judging bias. I think it's always been obvious that it cannot help to ensure fair judging.