Round Robin Matching

When participants grouped in pairs each round, perfect stranger matching is equivalent to arranging a round robin tournament in which every player meets every other player exactly once.

Algorithm

The algorithm for round robin matching implemented in the perfect-strangers package is as follows. First construct the grouping matrix for the first round, \(\mathbf{G}^{(0)}\), using any pairing strategy, for example:

Then pick an element of the matrix to fix in place. In this example we use the top left element.

For each subsequent round, rotate the elements of the matrix (either clockwise or anti-clockwise) one position, keeping the fixed element in place.

Repeated rotation like this will cycle through every possible set of pairings for the participants.

Eliminating Bias

One issue with this algorithm is that participants will meet other participants in the same order as each other. In experiments which this might introduce bias, it is sufficient to generate all grouping matrices ahead of time and randomise their order.