How to count rating? - rating

Question

My question is more mathematical. there is a post in the site. User can like and dislike it. And below the post is written for example -5 dislikes and +23 likes. On the base of these values I want to make a rating with range 0-10 or (-10-0 and 0-10). How to make it correctly?

Answer 1

This may not answer your question as you need a rating between [-10,10] but this blog post describes the best way to give scores to items where there are positive and negative ratings (in your case, likes and dislikes).
A simple method like
(Positive ratings) - (Negative ratings), or
(Positive ratings) / (Total ratings)
will not give optimal results.
Instead he uses a method called Binomial proportion confidence interval.
The relevant part of the blog post is copied below:
CORRECT SOLUTION: Score = Lower bound of Wilson score confidence interval for a Bernoulli parameter
Say what: We need to balance the proportion of positive ratings with the uncertainty of a small number of observations. Fortunately, the math for this was worked out in 1927 by Edwin B. Wilson. What we want to ask is: Given the ratings I have, there is a 95% chance that the "real" fraction of positive ratings is at least what? Wilson gives the answer. Considering only positive and negative ratings (i.e. not a 5-star scale), the lower bound on the proportion of positive ratings is given by:
(source: evanmiller.org)
(Use minus where it says plus/minus to calculate the lower bound.) Here p is the observed fraction of positive ratings, zα/2 is the (1-α/2) quantile of the standard normal distribution, and n is the total number of ratings.
Here it is, implemented in Ruby, again from the blog post.
require 'statistics2'
def ci_lower_bound(pos, n, confidence)
if n == 0
return 0
end
z = Statistics2.pnormaldist(1-(1-confidence)/2)
phat = 1.0*pos/n
(phat + z*z/(2*n) - z * Math.sqrt((phat*(1-phat)+z*z/(4*n))/n))/(1+z*z/n)
end

Answer 2

This is extension to Shepherd's answer.
total_votes = num_likes + num_dislikes;
rating = round(10*num_likes/total_votes);
It depends on number of visitors to your app. Lets say if you expect about 100 users rate your app. When a first user click dislike, we will rate it as 0 based on above approach. But this is not logically right.. since our sample is very small to make it a zero. Same with only one positive - our app gets 10 rating.
A better thing would be to add a constant value to numerator and denominator. Lets say if our app has 100 visitors, its safe to assume that until we get 10 ups/downs, we should not go to extremes(neither 0 nor 10 rating). SO just add 5 to each likes and dislikes.
num_likes = num_likes + 5;
num_dislikes = num_dislikes + 5;
total_votes = num_likes + num_dislikes;
rating = round(10*(num_likes)/(total_votes));

Answer 3

It sounds like what you want is basically a percentage liked/disliked. I would do 0 to 10, rather than -10 to 10, because that could be confusing. So on a 0 to 10 scale, 0 would be "all dislikes" and 10 would be "all liked"
total_votes = num_likes + num_dislikes;
rating = round(10*num_likes/total_votes);
And that's basically it.