How to convert up/down votes into a single number?

Question

I've got a website with voting system where people can vote a review either up or down. For example: “Did you find this review helpful? [Yes] or [No]?”

In order to order the reviews by how much they were appreciated I'd like a single number to order them by. Just using the percentage of up votes doesn't cut it because it doesn't take the total number of votes into account. A review with 2 up votes and 0 down votes (100%) should not be shown before a review with 95 up votes and 5 down votes (95%).

Any ideas on which formula to use? Thanks.

Answer 1

You need only assign the value of $ 0$ to a downvote, and $1$ to an upvote, or, $(-1)\to \;$downvote, $1 \to\;$upvote. Then any review's score could be the sum of those upvote/downvote assignments.

You can play around with such assigned "weightings", to end up with a single numeric score to represent the quality of the review.

E.g. questions and answers here at math.se computes the "score" of both answers and questions using the assignment: $(-1)\to \;$[downvote], $1 \to\;$[upvote].

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EDIT: As @gt6989b, the above scheme, does not take into account the distribution of scores, etc.

NOTE:
It all depends on what criteria you consider to be most relevant to the determination of the value of the rank of a given review.

Answer 2

Some examples have already been given, but a quite simple yet general way to do this would be to say +x for an upvote and -y for a downvote. On SO the weights are +10 and -2 for questions and +2 -1 for comments (if im not mistaken).

This is based on how people behave and what they would like to reward.

So, now you can just play around a bit with x and y untill you see the result that you like.

Edit: another commonly used system is to use the percentage, but exclude the ones with fewer than z votes.