Lets say we have two things as input, $N$ scalars (measurements) that we know are erroneous to some degree (i.e. the correct values are somewhat similar).
In addition, we also have a roughly more reliable order $O$ among the measurements. Using the ordering:
$O = <u_1, u_2, u_3 ... u_n>$ we can deduct that with some known probability, $p > 0.5$ the ordering is correct, $[i \geq j \rightarrow u_i \geq u_j]$ is true. Now, how would you then adjust the scalar values accordingly?
Currently:
- Creating a new set of values, cloning the original scalars.
- Making the minimal needed changes in order to satisfy the order. i.e. slightly increasing or decreasing the original values until we get a corrctly ordered $\{v_1, v_2, v_3 ... v_n\}$ such that $\sum\limits_{i=1}^n (u_i - v_i)^2$ is minimal.
- Doing a weighted average between the newly generated values and the original ones, using $p$ as the weight for the new value.
While $p$ is unknown, we can guesstimate it from data that is manually inspected.
