Secrecy sets the voter free to vote how she thinks is best for her. For example, social ratings are biased in favor of the top ratings because the voter prefers to keep her friends happy by not downvoting their content. That not necessarily distorts the ranking of content, which matters, but does change average ratings.
The alternative is the troll theory. Secret voting hurts responsibility because no one will find out what the voter did in the voting booth. Let's check.
This is Wikipedia's article feedback voting:
I used a sample of 12 million votes from a one-year dump (thanks to Matthias Mullie from the Wikimedia Foundation for pointing at this file). Here, zero means no vote at all, and anonymous voters tend to leave more gaps behind.
Registered users serve as a control group for anonymous (secret) voting. They are more responsible, because registration is time consuming and indicates deeper involvement in the community. Casted votes:
Compared to YouTube, the scale is more informative in general: voters use a larger fraction of mid-range ratings. Anonymous visitors set the lowest rating more frequently, but the difference is small.
In addition, summary statistics for the sample:
And correlation across rating dimensions:
The average rating set in a particular day: