Summary: Two linguistic-based voting systems have been introduced in recent years, namely: Majority judgement [{\it M. Balinski} and {\it R. Laraki}, “A theory of measuring, electing and ranking”, Proc. Natl. Acad. Sci. USA 104, 8720‒8725 (2007); in: \url{http://ceco.polytechnique.fr/jugement-majoritaire.html}] and range voting [{\it W. D. Smith}, “Range voting” (2000); in: \url{http://www.math.temple.edu/~wds/homepage/rangevote.pdf}]. The keys for them are aggregation procedures based on the median and the arithmetic mean of the grades assessed to the alternatives, respectively. In this paper a comprehensive framework based on centered OWA operators [{\it R. R. Yager}, Soft Comput. 11, No.~7, 631‒639 (2007; Zbl 1113.68106)] and the 2-tuple model [{\it F. Herrera} and {\it L. Martínez} [“A 2-tuple fuzzy linguistic representation model for computing with words”, IEEE Trans. Fuzzy Syst. 8, 746‒752 (2000)] is provided to enclose such distinct approaches. In addition, we show how to avoid some drawbacks of majority judgement and range voting by means of the use of suitable aggregation functions.