[1] It consists of the analysis of problems arising from the aggregation of preferences of a group of agents from a computational perspective.
The usefulness of a particular voting system can be severely limited if it takes a very long time to calculate the winner of an election.
For rules such as the Schulze method or ranked pairs, more sophisticated algorithms can be used to show polynomial runtime.
[11] Many tournament solutions have been proposed,[12] and computational social choice theorists have studied the complexity of the associated winner determination problems.
This task is polynomial time solvable in many cases, including for single-peaked and single-crossing preferences, but can be hard for more general classes.
This is the case when a fixed-size parliament or a committee is to be elected, though multiwinner voting rules can also be used to select a set of recommendations or facilities or a shared bundle of items.
Work in computational social choice has focused on defining such voting rules, understanding their properties, and studying the complexity of the associated winner determination problems.