A Parameterized Perspective on Protecting Elections

Abstract

We study the parameterized complexity of the optimal defense and optimal attack problems in voting. In both the problems, the input is a set of voter groups (every voter group is a set of votes) and two integers k a and k d corresponding to respectively the number of voter groups the attacker can attack and the number of voter groups the defender can defend. A voter group gets removed from the election if it is attacked but not defended. In the optimal defense problem, we want to know if it is possible for the defender to commit to a strategy of defending at most k d voter groups such that, no matter which k a voter groups the attacker attacks, the outcome of the election does not change. In the optimal attack problem, we want to know if it is possible for the attacker to commit to a strategy of attacking k a voter groups such that, no matter which k d voter groups the defender defends, the outcome of the election is always different from the original (without any attack) one. We show that both the optimal defense problem and the optimal attack problem are computationally intractable for every scoring rule and the Condorcet voting rule even when we have only 3 candidates. We also show that the optimal defense problem for every scoring rule and the Condorcet voting rule is W[2]-hard for both the parameters k a and k d , while it admits a fixed parameter tractable algorithm parameterized by the combined parameter (k a , k d ). The optimal attack problem for every scoring rule and the Condorcet voting rule turns out to be much harder -it is W[1]-hard even for the combined parameter (k a , k d ). We propose two greedy algorithms for the OPTIMAL DEFENSE problem and empirically show that they perform effectively on reasonable voting profiles.

AI and core electoral processes: Mapping the horizons

“…This provides a backdrop into the nonexistence (as far as we could assess) of bespoke AI techniques for polling booth protection prioritization. There has been emerging theoretical AI work on prioritizing protection of "voter groups" to ensure result stability in elections (Dey et al 2019(Dey et al , 2021, under conditions that we regard as quite synthetic; these may need much adaptation to be used within the task of prioritizing polling booths to protect. Our choice of identifying problematic polling booths as an avenue for AI usage is strongly motivated by observations of burgeoning AI development in a task that is very similar in spirit, that of hot spot policing that seeks to identify crime-prone locations, which we describe below.…”

A Parameterized Perspective on Attacking and Defending Elections

“…While we build most closely on the work of Elkind et al [5], and much of the work on manipulation in the literature of social choice does not consider the possibility of a counter-attack, we note that some recent investigations have been carried out in a spirit that is similar to our present contribution. Dey et al [3] also consider a parameterized approach to protecting elections, where the voting rule in question is the Condorcet rule. They build on the work of Yin et al [10], who study a pre-emptive approach to protecting elections.…”

A Parameterized Perspective on Attacking and Defending Elections

“…While we build most closely on the work of Elkind et al [5], and much of the work on manipulation in the literature of social choice does not consider the possibility of a counterattack, we note that some recent investigations have been carried out in a spirit that is similar to our present contribution. Dey et al [3] also consider a parameterized approach to protecting elections, where the voting rule in question is the Condorcet rule. They build on the work of Yin et al [10], who study a pre-emptive approach to protecting elections.…”