How Credible is the Prediction of a Party-Based Election?

In a party-based election, the voters are grouped into parties and all voters of a party are assumed to vote according to the party preferences over the candidates. Hence, once the party preferences are declared the outcome of the election can be predicted. However, in the actual election, the members of some “instable" parties often leave their own parties to join other parties. We introduce two parameters to measure the credibility of the prediction based on party preferences: MIN is the minimum number of voters leaving the instable parties such that the prediction is no longer true, while MAX is the maximum number of voters leaving the instable parties such that the prediction remains valid. Concerning the complexity of computing MIN and MAX, we consider both positional scoring rules (Plurality, Veto, r-Approval and Borda) and Condorcetconsistent rules (Copeland and Maximin). We show that for all considered scoring rules, MIN is polynomial-time computable, while it is NP-hard to compute MIN for Copeland and Maximin. With the only exception of Borda, MAX can be computed in polynomial time for other scoring rules. We have NP-hardness results for the computation of MAX under Borda, Maximin and Copeland.