Arrow's Impossibility Theorem and the distinction between Voting and Deciding

Arrow’s Impossibility Theorem in social choice finds different interpretations. Bordes-Tideman (1991) and Tideman (2006) suggest that collective rationality would be an illusion and that practical voting procedures do not tend to require completeness or transitivity. Colignatus (1990 and 2011) makes the distinction between voting and deciding. A voting field arises when pairwise comparisons are made without an overall winner, like in chess or basketball matches. Such (complete) comparisons can form cycles that need not be transitive. When transitivity is imposed then a decision is made who is the best. A cycle or deadlock may turn into indifference, that can be resolved by a tie-breaking rule. Since the objective behind a voting process is to determine a winner, then it is part of the very definition of collective rationality that there is completeness and transitivity, and then the voting field is extended with a decision.