This folder contains R functions and an example for running two classes
of rank aggregation algorithms, namely Borda and Markov chain methods,
that take the underlying spaces from which the individual ranked lists 
come from into consideration explicitly.

The main fuction for running Borda's method is Borda, which contains
four aggregation functions: mean, median, geometric, and l2-norm.
The input is a list containing the individual ranked lists, while 
the output is the rankings associated with each of the four aggregation
function. Borda scores are also included in the output for 
studying information degradation.

For the Markov chain methods, the function for constructing the transition
matrices for MC1, MC2, and MC3 (all in one call to the function) is
trans.matrix. MC.ranks is the function that takes a transition matrix and 
returns the aggregate rankings. The output also contains stationary 
probabilities for studying information degradation.

After all the R objects in this directory (other than this read me file 
and the script) are loaded, one can test run the example using the codes
in the script.
