A general class of simple majority decision rules based on linguistic opinions

Monotonicity-based consensus states for the monometric rationalisation of ranking rules with application in decision making

“…For improving the performance of the simple majority rule, several authors have encouraged the use of degrees of preferences in social choice theory [64,123,131]; quoting a well-known phrase by Sen [150], "... the method of majority decision takes no account of intensities of preference, and it is certainly arguable that what matters is not merely the number who prefer x to y and the number who prefer y to x, but also by how much each prefers one alternative to the other".…”

“…This is due to the fact that both the majority winner and the Condorcet winner disregard an important part of the preferences of the voters; quoting a well-known phrase by Sen [150], "... the method of majority decision takes no 1 The concept of a majority winner is not related with that of the (simple) majority rule [54,64,76,95,149] whenever more than two candidates are considered. account of intensities of preference, and it is certainly arguable that what matters is not merely the number who prefer x to y and the number who prefer y to x, but also by how much each prefers one alternative to the other".…”

Modeling rationality in a linguistic framework

“…In those cases, the use of linguistic labels (or finite scales as in Mayor and Torrens [32]) to grade preferences could be more appropriate to capture the lack of precision in human behavior (see Zadeh [47][48][49], Herrera et al [26,27], Herrera and Herrera-Viedma [25], García-Lapresta [17] and García-Lapresta et al [19], among others).…”

Extension of Some Voting Systems to the Field of Gradual Preferences

“…In this sense, valued and fuzzy preferences consider numerical values for declaring intensities of preference (see Nurmi [57], Tanino [63], Fodor and Roubens [25], De Baets and Fodor [12], García-Lapresta and Llamazares [29,30], Llamazares and García-Lapresta [44], Llamazares [41,43] and Fodor and De Baets [23], among others). After Zadeh [83], linguistic preferences have been very used in the Decision Theory framework (see Delgado et al [14,15], Yager [76], Herrera et al [36,37,38], Bordogna et al [5], Herrera and Herrera-Viedma [35]) and in voting systems (see García-Lapresta [28] and García-Lapresta et al [31]). …”