Liberalism,non-binary choice and Pareto principle

It is shown in this paper that a very mild form of Pareto principle is compatible with a set of restrictive conditions. Deriving a choice set identical with the set of alternatives in the case of paradox of voting amounts to begging the problem. If we restrict that the choice set should be a proper sub-set of the original set, the paradox will be revived. In the realistic sense liberalism may well be treated as an outcome of the choice rather than as a basic value judgement. Choice of Rules of the Game ought to be the first step and then only society can seek the optimal situation under those Rules.I am very grateful to P. K. Pattanaik for helpful discussions and valuable comments on the first draft. I am also grateful to Prof. Amartya Sen whose lectures at the Delhi School of Economics introduced me to the theory of social choice.