Developing an algorithm for this will depend on understanding what the various results of a 5-star rating mean. People are not consistently rational, and their use of rating systems reflects this. People tend to 5-star rate things as follows ("product" can mean a material thing, site content, or whatever):
One Star: I'm mad. Either the product is awful, or the person offended me, or I'm in a really bad mood. In any case, I need to vent.
Two Stars: The product is bad. Possibly with some minimal redeeming quality. Or, I understand that people value the content of a
2-star review more than that of a 1-star review, and I want people to
read my review. But this thing isn't good.
Three Stars: It had some value. Something about it was lame. I'm not angry. I would buy (or read) something else next time if I have the option, but I
might buy (or read) something like this again if I have no other options.
Four Stars: It's good. Or, It's great, but I reserve 5 stars for things that are perfect. Or it's great, but had one
problem that detracted a bit from it. Or it just worked fairly well. Either way, I am basically happy.
Five Stars: It's great. Or, it's good and this is my default if you don't anger me. Or it did everything it was supposed to so I can't
justify taking a star away.
What you'll notice looking at these, is that there is little to no meaningful difference between 1 and 2 stars, or between 4 and 5 stars. In fact, often 2-star reviews indicate a higher likelihood of a bad product than 1-star reviews. On Amazon for example, you will often find 1-star reviews written as "Box smashed by UPS and couldn't use it." They are often triggered by extraneous anger rather than the product itself. For content, this might manifest as "Good article, but I hate this guy."
And, 5-star reviews are often the lazy default. It might mean "great product", or it might mean "I plugged it in and it worked, and I don't think about things much." Or even "Hmm... A little weak, but my grandson wrote it." Whereas a 4-star review reliably means "I really considered this and found it to be good." So while in most statistical situations a reduction in granularity detracts from the quality of the result, in this case it improves it. I suggest treating each review as tri-state where 1-2 stars means negative. 3 stars means nothing. And 4-5 stars means positive.
Having gotten to this point, I find the ratio of positive to negative to be most predictive of quality. And, the number of reviews to achieve full confidence to often be around 20... Though in cases where there is not a financial incentive to cheat, this could be as low as 5.
The following generic code produces a number between -100 and +100, with new product (no reviews) starting at 0. Max deviation from zero due to reviews is limited based on number of reviews.
int fullConfidence = 20; // Review count for full confidence
float confidenceFactor = 1.0;
// This is a flat progression. Optionally scale confidence mod on a curve.
if(reviewCount < fullConfidence )
confidenceFactor = reviewCount * (1 / fullConfidence );
// Also optionally insert a minimum number of reviews before any impact:
// confidenceFactor = (reviewCount - min) * (1 / (fullConfidence - min));
// Get percent of positive and percent of negative reviews here.
float qualityRating = (percentPositive - percentNegative) * confidenceFactor ;
Good luck.
