Controlling Borda Elections by Adding or Deleting either Votes or Candidates: Complete and Top-Truncated Votes
Aizhong Zhou, Fengbo Wang, Jiong Guo

TL;DR
This paper investigates the complexity of controlling Borda elections through vote and candidate modifications, establishing new hardness results and exploring the effects of top-truncated votes on control problem complexity.
Contribution
It completes the parameterized complexity classification for Borda control problems and analyzes the impact of top-truncated votes on these complexities.
Findings
W[2]-hardness for certain control problems with vote/candidate modifications
NP-hardness persists with top-truncated votes even for small t
FPT results for control problems with top-truncated votes using specific parameters
Abstract
An election is defined as a pair of a set of candidates C=\{c_1,\cdots,c_m\} and a multiset of votes V=\{v_1,\cdots,v_n\}, where each vote is a linear order of the candidates. The Borda election rule is characterized by a vector \langle m-1,m-2,\cdots,0\rangle, which means that the candidate ranked at the i-th position of a vote v receives a score m-i from v, and the candidate receiving the most score from all votes wins the election. Here, we consider the control problems of a Borda election, where the chair of the election attempts to influence the election outcome by adding or deleting either votes or candidates with the intention to make a special candidate win (constructive control) or lose (destructive control) the election. Control problems have been extensively studied for Borda elections from both classical and parameterized complexity viewpoints. We complete the parameterized…
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Taxonomy
TopicsLocal Government Finance and Decentralization · Game Theory and Voting Systems
