A voting rule is said to be vulnerable to the truncation paradox if some voters may want to favor a more preferable outcome by providing only a part of their sincere rankings on the competing candidates rather than listing their entire preference rankings on all the competing candidates. This voting paradox was first introduced by Brams (1982). This paper provides for three-candidate elections and for large electorates, a characterization and an evaluation of the likelihood of the truncation paradox for the whole family of one-shot scoring rules and runoff scoring rules. We assume three scoring models for dealing with incomplete rankings: the pessimistic, the optimistic and the averaged scoring models. We find that under the optimistic model, all the one-shot scoring rules are immune to the truncation paradox and this paradox is more likely to occur under the pessimistic scoring model than under the averaged scoring model. For each of the scoring runoff rules, we find that the likelihood of the truncation paradox is higher under the pessimistic scoring model and it is lower under the optimistic scoring model. Our analysis is performed under the Impartial Anonymous Culture assumption.