Functional local operators of incomplete and nonempty сhoiсе of options

Functional voting operators are analyzed that reconsile individual choice functions into a «collective» choice function. Conditions are ascertained under which the functional voting operator which satisfies the locality condition is an operator of nonempty or incomplete choice. A description is provided of functional local operators which are simultaneously operators of nonempty and incomplete choice. For such operators an analog is established of the Arrow paradox which occurs when individual preferences are reconciled into a «collective» preference.