To what extent does the model of processing sincereincomplete rankings affect the likelihood of the truncation paradox?

For a given voting rule, if voters can favor a preferred 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 rule is said to be vulnerable to the truncation paradox. In this paper, we show that the way of dealing with the truncated ballot can really impact the occurrence of the paradox: this paradox never occurs with any one-shot scoring rules when truncated ballot a treated according the optimistic model. The optimistic model is, along with the pessimistic model and the averaged model, the three most common ways of dealing with truncated preferences. The few papers that assess the likelihood of the occurrence of this paradox implicitly assume the pessimistic model. In this paper, we assess the likelihood of the truncation paradox under the two other models for three-candidate elections and large electorates. We focus on whole families of one-shot scoring rules, iterative scoring rules both with one-by-one eliminations and with elimination by the average. This assessment confirms that the choice of model may really matter: under the optimistic model, all the one-shot scoring rules are immune to the truncation paradox, whereas it is is more likely to occur under the pessimistic model than under the averaged model; for each of the scoring runoff rules, we find that the likelihood of the truncation paradox is higher under the pessimistic model, and lower under the optimistic model. Our analysis is performed under the Impartial Anonymous Culture assumption.