What algorithm to apply to convey that one is better than the other and eventually get a table?

Question

PHP

I need to display a table ordered from best to worst.
It is necessary to transfer to the algorithm that one is better than the other, and he, in turn, must sort this table accordingly.
The whole catch is that one can convey that A is better than B, and the other vice versa. And this must be taken into account.
Plus, there can be a lot of comparisons
(for example, A was compared with B and with C and with D),
but there are few of some
(for example, D was compared only with A).
We need subjective opinions to be reduced to an objective average.
There are a bunch of objects that are compared with each other, there are a bunch of voters who choose which of the two they like more .. and from this you need to assemble a table.
Just the number of voters is not suitable, because. there can only be 1 vote for A, but he says that A is better than everyone else.
I've already tried many different things.
I can't seem to find the best approach.

Answer 1

The impossibility theorem proves that it is impossible to build a completely just system. It is necessary, taking into account the subject area, to consider various options for generalizing collective assessments and choose the most convenient or appropriate one.
A good article on Habré with some ranking methods.

Answer 2

You need to express this "one is better" in a numerical equivalent, and in absolute terms, and not relative to others.
For example, not "car A is faster than car B", but "car A has a maximum speed of 100, and car B has a maximum speed of 300".
If there are several comparison criteria, give a weighted average.
For example, if the car has speed and maneuverability parameters, and you need to give an overall rating, then you need to clearly determine what contribution each parameter makes to the overall rating (mathematical, by a formula. For example, weights), make an overall rating based on the formula and already sort by her.

Answer 3

"We need to pass into the algorithm that one is better than the other."
Instead of whether to transfer any accurate parameter? Or is there no such thing (well, or is the task just to select it)?
"The catch is that one can convey that A is better than B, and the other vice versa"
Divide the ratings into categories (read "better in connection with something") or (if there is a clear advantage) - discard one of the parties, No?
ps by the way, if there is no clear advantage, it may be possible to break users into N clusters according to their votes, train N estimating grids, and then classify the user and give him the output of the corresponding network. But here I won't give you any specifics.

Answer 4

if this is a query in MySQL, then you can add "ORDER BY `rate`" to the query