Gene

Constructive

Process (computing)

Engineering

Microeconomics

Condorcet method

Robustness (evolution)

Rank (graph theory)

Social choice theory

Operating system

Economics

Biochemistry

Civil engineering

Computer science

Schulze method

Operations research

Mathematics

Politics

Political science

Axiom

Artificial intelligence

Geometry

Combinatorics

Mathematical economics

Chemistry

Voting

Schulze's rule and ranked pairs are two Condorcet methods that both satisfy many natural axiomatic properties. Schulze's rule is used in the elections of many organizations, including the Wikimedia Foundation, the Pirate Party of Sweden and Germany, the Debian project, and the Gento Project. Both rules are immune to control by cloning alternatives, but little is otherwise known about their strategic robustness, including resistance to manipulation by one or more voters, control by adding or deleting alternatives, adding or deleting votes, and bribery. Considering computational barriers, we show that these types of strategic behavior are NP-hard for ranked pairs (both constructive, in making an alternative a winner, and destructive, in precluding an alternative from being a winner). Schulze's rule, in comparison, remains vulnerable at least to constructive manipulation by a single voter and destructive manipulation by a coalition. As the first such polynomial-time rule known to resist all such manipulations, and considering also the broad axiomatic support, ranked pairs seems worthwhile to consider for practical applications.

A Complexity-of-Strategic-Behavior Comparison between Schulze's Rule and Ranked Pairs