Iterative voting and multi-mode control in preference aggregation

We analyze two different scenarios, which can be seen as two different sides of the same problem. Multimode control actions have been considered a malicious strategic actions. To protect the election, we study how difficult it is to exploit these actions in a system with equal budgets. In an equal budget configuration, actions have different separated resources, but these have to be used equally. In particular, this can model the replace control action, where the chair has to delete as many candidates/voters as she added. We prove some new results on two well-known voting rules: Plurality and Copeland. The other studied scenario is iterative voting, which naturally uses manipulation. We study the stability of voting rules not yet considered. We identify some specific restrictions which guarantee that some specific voting rules always converge. After that, we use single and multiple control actions within iterative voting, in order to understand if the malicious side of control can overcome the stability of the iterative voting systems.