The famous impossibility theorem proved by Kenneth Arrow shows that the aggregation of individual preferences leads to inconsistency between the rationality constraints on preferences and the democraticity constraints on the aggregation procedure. A well-known way to circumvent the inconsistency is to consider profiles of preferences that share a common dimension of voting, e.g. the left-right ordering of candidates in parliaments. In this work, I propose a model to represent the information concerning preferences of groups depending on the dimension they assume. In particular, the logical framework here presented will be useful to express in a same formalism preferences over alternatives and justification of those preferences, providing a way to formalize the relationship between the verbalization of the relevant dimensions of voting and the preferences individual express.