Computational complexity characterization of protecting elections from bribery

The bribery problem in election has received considerable attention the literature, upon which various algorithmic and complexity results have been obtained. In this setting, it is natural to ask whether we can protect an from potential attacks. We consider a scenario where protector (or defender) voter at some cost such that protected cannot be bribed (e.g., by isolating bribers). This leads following bi-level decision problem: Is possible for proper subset of voters no briber with fixed budget alter result? goal paper give full characterization associated protection problems. conduct extensive study on provide results. When compared problems studied observe significantly harder general. Indeed, becomes Σ 2 p -complete even very restricted special cases, while most lie NP. However, not necessarily case always harder. Some still solved polynomial time, them remain as hard same setting.