The article shows that in a specific social choice setting, there is a way to make sure that a mechanism that encourages people to be honest about their preferences is just as good as one that forces them to be honest. This means that the outcomes for everyone involved will be the same, whether they have to tell the truth or not. The researchers used a clever method to prove this, building on previous work in the field. However, this equivalence doesn't always hold true in different situations or when looking at different aspects of the outcomes.