This might look strange, but the largest democracy, India, and the richest democracy, United States, both currently have flawed presidential election systems, and both these systems can elect the wrong president under certain circumstances against the will of its people. The basic difficulty in devising a proper election scheme is what is known as Arrow's Paradox, and the Fractional Voting System (FVS) that we are proposing here is meant to circumvent this paradox.

 

To make the problem a little more clear, it is necessary to give a definition of the will of the people. Professor Kenneth Arrow of the United States in 1950 attempted to give the following definition for the will of the people. The definition was not exactly a total success, even though Arrow was awarded a Nobel Prize in 1972 for his research in economics. He argued that the two directive principles (he called them axioms) of any voting system should be:

 

Directive Principle 1 (Unanimity): If every voter prefers one candidate over the others, so does the voting system.

 

Directive Principle 2 (Independence): The preference of the voting system between any pair of candidates depends only on the preferences of the voters between these candidates.

 

The strange thing about these directive principles, which look so innocuous, is that it is impossible to satisfy both of them together in any reasonable way. Arrow showed that the only way to implement these principles is to have a dictatorship. When Arrow came out with his so called Dictator Theorem (also known as the Impossibility Theorem), Professor Paul Samuelson, himself a Nobel Laureate in 1970, wrote: "Men have always sought ideal democracy--the perfect voting system... What Kenneth Arrow proved once and for all is that there cannot possibly be found such an ideal voting scheme. The search of the great minds of recorded history for the perfect democracy, it turns out, is the search for a chimera."

 

Should we take Samuelson literally and resign to our fate that no reasonable elections are possible and we can have no collective will? The answer is an emphatic no, and what we want to question is the hypothesis from which Arrow starts. It is the usual preference order used the voting systems that we have reservations about. Is the preference order the only way to express the likes and dislikes of a voter? It is in answering this question that we find a clue for the resolution of the paradox.

 

In the fractional voting system we propose, every voter has a definite number of votes (we will take 100 as a convenient number) that he can freely disperse amongst the candidates in any proportion he pleases. Thus, in FVS each voter does not give a preference order, but instead gives his fractional voting.

 

Here is how do we conduct our Presidential election according to FVS: Each member of the electoral college distributes the value of his vote amongst the candidates in any proportion of his choice. After the voting, as usual, the candidate getting the largest number of votes is declared the winner.

 

For a detailed explanation of FVS and and a general discussion of psephology, visit