Strategy-proofness requires that truth-telling is a (weakly) dominant strategy for all individuals in a collective decision making process.
For every aggregation rule that is not strategy-proof we need to consider the possibility that individuals voted strategically and thus we cannot interpret the result as the aggregation of the true preferences but rather as the aggregation of strategic votes. Thus, for such rules, it is much harder, if not impossible to examine how good the result represents the true preferences of a group.
Unfortunately, strategy-proofness is a restrictive condition. The famous Gibbard-Satterthwaite theorem states that on the universal domain all strategy-proof voting rules whose range contains more than two alternatives are dictatorial.
One way of escaping dictatorship is by considering restricted preference domains, such as the domain of single-peaked preferences. There one can find strategy-proof and non-dictatorial voting rules.
Our research focuses on restricted preference domains and how strategy-proofness is compatible with other desirable properties such as participation on such domains.