How to select the next matchup to best reduce uncertainty in a ranking So say I have 30 teams and I want to schedule their games with the objective getting the most information concerning who's better than who as quick as I can.  How do I do this.  Let's say we have a ranking system like elo.  After every game we pick the next pair.  How do we quantify the uncertainty in our system and how do we then pick the pairing that will most reduce this uncertainty.
I'm totally out of my depth here and can't even figure out what terms to search for.
 A: If you want to most reduce uncertainty: play a round robin. Then play another one. Then another one. And so on.
If you want to rank as quick as you can in a tournament, use swiss-system tournement.
If you're interested in quantifying the uncertainty, check ratings reliability in Glicko system, or in its nephew TrueSkill.
If you're interested in fullfilling the objective getting the most information concerning who's better than who, choose a ranking system, like most known Elo, or aforementioned Glicko or TrueSkill, or rankade, our free to use ranking system (here's a comparison), use it, and play a lot.

Edit after comments:


*

*Opposite to Elo and Glicko, rankade can manage multiplayer matches, so if you want just giving them each two items asking them which is higher and which is lower, you can ask users to compare 3+ items (it's difficult to compare 10+ things, but doing this for something like 3-7 items should be easy and useful), getting the most useful information before the user gets bored and leaves.

*You can build something easy for creating next matchup. If all items have to be checked same number of times, just minimize delta for matchups (see aformentioned swiss system). If number of matches should be different for items, try something like minimizing
$$
m = (n_p)^a \cdot { \left [ n_1 + n_2 \over 2 \right ]^b}  \cdot \Delta_p
$$
where $n_p$ is the number of matches played for chosen pair, $n_1$ and $n_2$ are the numbers of matches played for two chosen item, $a$ and $b$ are custom exponents, and $\Delta_p$ is difference in their ranking score.
