[panic]

You can also model each vote as an "agent" that tries its best to move the star rating toward its desired value. If the current rating is a 4, each "agent" with a vote less than 4 will throw a 1 into the average, and each vote greater than 4 will throw a 5. This process converges, though the rating tends strongly toward 3 (or whatever the middle value is).

[paulgb]

Good answer, this has a nice property that it can be applied to any reasonably behaved average-based system to get an honest mechanism. For a plain average it is equivalent to the median.

[ajennings]

Not actually equivalent to the median.

If all the scores are 1s and 5s, then the median will be a 1 or a 5, but the average will be somewhere in between.

The problem is slightly easier to understand if we consider the grading scale from 0 to 100. Then every agent, trying to manipulate the score as much as they can toward their "ideal grade", will submit a grade of 0 or 100.

The average will converge to the unique number, X, where X percent of the graders want the final grade to be above (or equal to) X.

[paulgb]

Yes, you're right and I was wrong.