Arrow’s impossibility theorem
The theory states that no rank-order voting system can be designed to satisfy three fairness criteria:
- If every voter prefers alternative X over alternative Y, then the group prefers X over Y.
- If every voter preference between X and Y remains unchanged, then the group’s preference between X and Y will remain unchanged.
- There is no ‘dictator’ with the power to determine the group’s preference.
Gibbard-Satterthware theorem
The theorem extends Arrow’s impossibility theorem and holds that for three or more candidates, one of the following three things must hold for every voting rule:
1. The rule is dictatorial (i.e., there is a single individual who can choose the winner), or
2. There is some candidate who can never win, under the rule, or
3. The rule is susceptible to tactical voting, in the sense that there are conditions under which a voter with full knowledge of how the other voters are to vote and of the rule being used would have an incentive to vote in a manner that does not reflect his or her preferences.
Kalyanaraman theorem to resolve the liberal paradox of impossibility of
Extending these theorems to the Wendy porno problem posited as liberalism vs. measuring social benefit, Kalyanaraman theorem posits:
- Individual freedoms do not add up to social benefit
- Social benefit is measured by an ethical order (like dharma in Hindu studies context)
- This dharma is a cosmic-consciousness global ethical order, inviolate, dictatorial always resulting in net measurable social benefit.
In this positing, dharma is defined as net social benefit which irons out individual pluses and minuses. If such ironing out results in a positive outcome, that is a measure of abhyudayam (social welfare). This is the ethical principle which is the underlying tenet of Hindu studies for millennia.
This is NOT an original formulation. This is just a translation of a Hindu tradition: dharmo rakshati rakshitah‘dharma protects those who protect (dharma)’.
The formulation is simple: the measure of a social value system is the measure suggested by pitr-s (ancestors) whose contributions to the social order have resulted in today's social order.
There is nothing like an absolute freedom as a right. This freedom is the result of performance of absolute responsibility by every individual who makes up the social order.
The impossibility theorem thus gets resolved by positing responsibilities (or duties) as the obverse of the rights 'coin'. This is exemplified in Vietnam Constitution.
S. Kalyanaraman
Sarasvati Research Center