When comes to a decision maker being able to choose between two or more available options, many of the economic models consider that he or she is always capable of so. In Economics, this means that it is assumed that the decision maker has complete preferences. However, some authors have been struggling to accept this assumption. One of them was Aumann (1962) who stated that: ‘Of all the axioms of utility theory, the completeness axiom is perhaps the most questionable. Like others of the axioms, it is inaccurate as a description of real life; but unlike them, we find it hard to accept even from the normative viewpoint’. For this reason, some economists started to include in their models the fact of that decision makers not being able to rank available options.
This kind of situation may happen in the real-world aggregation. If a single individual is not able of ranking different options, we can expect the same to happen with multi-agent systems. One of the most well-known cases is the voting system. Konczak and Lang (2005) explain the two main sources: The ﬁrst one is intrinsic incompleteness where the voter is unable or unwilling to give complete information, i.e., a total order on all candidates. The second one is epistemic incompleteness where the voters do have preferences speciﬁed by total orders but at the time of decision making these total orders are not fully available.
First and foremost, in order to understand this problem it is necessary to understand how the voting system works. To do so, we need to know the difference between full preferential voting and optional preferential voting. Full preferential voting occurs when the voter must show a preference for all candidates listed for the ballot paper to be formal, while in the optional preference voting the voter need only to indicate a preference for the candidate of his/her first choice and the allocation of any further preference is optional.
Although in Portugal we are only used to optional preferential types of voting, full preferential ones are also possible, as is the case of Australia. What happens in Australia is that surprisingly (or not) most of the times there is a proportion of ballot papers filled in with an invalid sequence of preferences. We can think about some reasons to this happen as inability or accident. But the fact is that as the number of candidates in the ballot paper increases, it is more likely the rate of informal votes to increase as well. After all, with only three available options, the decision maker is able to set 6 preference relations (we need to have into account that in this case no indifference relations are possible), with four available options he has to choose between 24 preference relations, with five available options (which is not that much) he has to choose between 120 preference relations, and so on and so forth. So, probably it may not seem as easy as one might think.
This could lead us to agree that going for the optional preferential types of voting is a better solution for the political system. But we need to be careful once optional preferential types of voting also have their disadvantages. One of them is known as the Tactical Voting, in which the voters have an incentive to vote for one of the two candidates they predict are most likely to win (even if they prefer other candidates), because voting for the preferred ones is seen as a “wasted” vote with no impact on the final result.
We can see that electoral processes have many issues beyond the most objective ones. All of this will probably make us end up agreeing with Kenneth Arrow, who said that no method can obtain at the same time all the advantages desired in a voting system.