Strategic Manipulation with Incomplete Preferences: Possibilities and Impossibilities for Positional Scoring Rules

Many websites that recommend various services use crowdsourcing to collect reviews and rankings. These rankings, usually concerning a subset of all the offered alternatives, are then aggregated. Motivated by such scenarios, we axiomatise a family of positional scoring rules for profiles of possibly incomplete individual preferences. Many opportunities arise for the agents to manipulate the outcome in this setting. They may lie in order to obtain a better result by: (i) switching the order of a ranked pair of alternatives, (ii) omitting some of their truthful preferences, or (iii) reporting more preferences than the ones they truthfully hold. After formalising these new concepts, we characterise all positional scoring rules that are immune to manipulation.