Normalized Range Voting Broadly Resists Control

We study the behavior of Range Voting and Normalized Range Voting with respect to electoral control. Electoral control encompasses attempts from an election chair to alter the structure of an election in order to change the outcome. We show that a voting system resists a case of control by proving that performing that case of control is computationally infeasible. Range Voting is a natural extension of approval voting, and Normalized Range Voting is a simple variant which alters each vote to maximize the potential impact of each voter. We show that Normalized Range Voting has among the largest number of control resistances among natural voting systems.

💡 Research Summary

The paper investigates the computational resistance of Range Voting (RV) and its variant Normalized Range Voting (NRV) to a comprehensive set of electoral control actions. Electoral control refers to the ability of an election chair to alter the structure of an election—by adding or deleting candidates or voters, partitioning the candidate set, or partitioning the electorate—in order to change the election outcome. A voting system is said to “resist” a particular type of control if the corresponding decision problem is computationally infeasible (i.e., NP‑hard).

The authors begin by formally defining RV: each voter assigns an integer score from 0 to k to every candidate, and the candidate with the highest total score wins. RV is a natural quantitative extension of approval voting, allowing voters to express intensity of preference. However, because scores are bounded, a manipulative chair can sometimes exploit the limited range to force a desired winner.

NRV modifies RV by normalizing each voter’s score vector. For a voter whose minimum and maximum scores are min and max, every score s is transformed to (s − min)·k/(max − min). This linear scaling forces every voter to use the full interval