# Inequality Experimentalist

The inequality experimentalist is a method used to compare experimental conditions and select new conditions based on a pairwise distance metric. Here's how it works:

Given: - Existing experimental conditions represented by $$\vec{x}$$ in the set $$X$$. - Candidate experimental conditions represented by $$\vec{x}'$$ in the set $$X'$$. - A pairwise distance metric $$d(\vec{x}, \vec{x}')$$ that calculates the distance between $$\vec{x}$$ and $$\vec{x}'$$. - A threshold value (default = 0) that determines the maximum allowable distance for two conditions to be considered equal. - A number $$n$$ of conditions to sample.

The inequality experimentalist operates as follows:

1. For each candidate condition $$\vec{x}'$$ in $$X'$$ calculate an $$inequality$$ $$score$$:
2. Calculate the distances $$d(\vec{x}, \vec{x}')$$ between $$\vec{x}$$ and $$\vec{x}'$$ using the pairwise distance metric for all $$\vec{x}$$ in $$X$$.
3. If $$d(\vec{x}, \vec{x}')$$ is greater than the threshold:
• Consider $$\vec{x}'$$ as different from the existing condition $$\vec{x}$$.
• add 1 to the $$inequality$$ $$score$$ for $$\vec{x'}$$
4. If $$d(\vec{x}, \vec{x}')$$ is less than the threshold:
• Consider $$\vec{x}'$$ as equal to the existing condition $$\vec{x}$$.
• Do not add 1 to the score for $$\vec{x'}$$

The $$n$$ $$\vec{x'}$$ with the highest $$inequality$$ $$scores$$ are chosen as new conditions.