Rating based on the average rating and the number of votes?

Question

Ratings

There is a website where users rate different companies.
There is K - the number of votes, N - the average rating included in the interval [1, 5].
We need some indicator T(K, N), which is a function of the average company score and the number of votes.
Companies will be sorted by this indicator.
The indicator should take into account the fact that the lower the number of votes, the more likely it is that the assessment differs from the objective one (for simplicity, we will consider the average assessment of all land users to be objective :)).
So far, I have only come up with this formula:
N = K+(K-3)*(N-1)*k/N _max , where N _max is the maximum number of votes, k is some coefficient selected from common sense, looking at real data.
Maybe I'm reinventing the wheel and there are some mathematically justified and vitally proven formulas for such things?

Answer 1

There are ready-made and currently working algorithms, for example, the IMDB rating, which is based on Bayes' theorem. The formula is very well written here: www.wowwebdesigns.com/formula.php There is also an old article on Collective Choice for review: www.lifewithalacrity.com/2005/12/collective_choi.html All popular ranking systems are painted here.
WR = (v / (v+m)) * R + (m / (v+m)) * C
R = средний рейтинг данного объекта
v = количество голосов за данный объект
m = (опционально) минимальное число голосов, необходимых для отображения в топ 25
C = средний рейтинг всех объектов


Answer 2

I would use something like:
weighted average score for this criterion * credibility k-ent.
reliability k-ent = weighted average of all ratings for each criterion reduced to 1.
i.e. if more than the weighted average number of votes voted for your criterion, then the weight of this rating increases.
meaning - the more ratings - the greater the weight of the result.