Net Borda rules with desirability

We apply the concept of desirability of alternatives to the clas-sic Borda scoring system. We employ a linear order over the finite set of alternatives and an outside option and define the desirability as follows: each alternative is (un)desirable if and only if it is better (worse) than the out-side option. Additionally, we assume that each voter assigns the Borda scores to all alternatives and the outside option. Thus, there is an extra gap of one point between desirable and undesirable alternatives. We then define two–type net Borda rules which output the highest–scored alternatives. The first is the type– I net Borda rule which allows that the social choice includes the outside option. The second is the type–II net Borda rules which does not allow that the social choice includes the outside option. We show an advantage in consid-ering the desirability of alternatives by comparing the outputs of type-II net Borda and classic Borda rules since their co–domains are the same. Further-more, we provide an axiomatic characterisation of the type–II net Borda rule and find that the type–II net Borda rule satisfies more proper conditions than the classic Borda rule when we consider the desirability of alternatives.