On the Parameterized Complexity of Controlling Amendment and Successive Winners

TL;DR

This paper explores the parameterized computational complexity of controlling amendment and successive winner procedures in voting, providing a detailed landscape of their resistance to strategic manipulation.

Contribution

It offers the first comprehensive parameterized complexity analysis of control problems for these procedures, including a generalized amendment procedure.

Findings

Complexity results vary with different parameters.

The study reveals the extent of resistance to strategic control.

Provides a detailed complexity landscape for these voting procedures.

Abstract

The successive and the amendment procedures have been widely employed in parliamentary and legislative decision making and have undergone extensive study in the literature from various perspectives. However, investigating them through the lens of computational complexity theory has not been as thoroughly conducted as for many other prevalent voting procedures heretofore. To the best of our knowledge, there is only one paper which explores the complexity of several strategic voting problems under these two procedures, prior to our current work. To provide a better understanding of to what extent the two procedures resist strategic behavior, we study the parameterized complexity of constructive/destructive control by adding/deleting voters/candidates for both procedures. To enhance the generalizability of our results, we also examine a more generalized form of the amendment procedure. Our exploration yields a comprehensive (parameterized) complexity landscape of these problems with respect to numerous parameters.