Are the Pitiful Leftists Really Going to Sell Themselves to the Laughable "Arrow's Impossibility Theorem"?

Chán Zhōng Shuō Chán

Today, the pitiful leftists are making themselves ridiculous again? Someone has trotted out the so-called "Arrow's Impossibility Theorem" to prove the impossibility of voting elections. Are the pitiful leftists really going to sell themselves to the laughable "Arrow's Impossibility Theorem"? It seems the left truly has nowhere left to turn!

The so-called Arrow's Impossibility Theorem is based on the so-called "voting paradox" proposed by the 18th-century French thinker Condorcet. As long as this foundation is demolished, the impossibility theorem becomes a joke. And that Frenchman's "voting paradox" was always just a joke from someone who failed mathematics. Specifically:

Suppose persons A, B, and C face three alternatives a, b, and c, with the following preference orderings:

A (a > b > c)

B (b > c > a)

C (c > a > b)

Note: A (a > b > c) means — A prefers a over b, and prefers b over c.

If we pit "a" against "b," the preference ordering is as follows:

A (a > b)

B (b > a)

C (a > b)

Social preference ordering: (a > b)

If we pit "b" against "c," the preference ordering is as follows:

A (b > c)

B (b > c)

C (c > b)

Social preference ordering: (b > c)

If we pit "a" against "c," the preference ordering is as follows:

A (a > c)

B (c > a)

C (c > a)

Social preference ordering: (c > a)

Thus we obtain three social preference orderings — (a > b), (b > c), (c > a). The voting results show that "social preference" has the following fact: society prefers a over b, prefers b over c, and prefers c over a. Obviously, this so-called "social preference ordering" contains an internal contradiction: society prefers a over c, yet also considers a inferior to c! Therefore, according to the majority rule of voting, a rational social preference ordering cannot be derived.

However, anyone with mathematical common sense knows that the premise for all this argumentation to hold is that a "partial order" structure can be established within it. But such a premise does not exist. In actual voting processes, there is simply no situation where a partial order holds. This so-called paradox is nothing more than a laughable conclusion derived from a false assumption. Of course, since research on mathematical structures had not yet begun in the 18th century and the French did not know what a "partial order" structure was, they can be forgiven for this blunder. But to still be making this same blunder now — don't you find it embarrassing, leftists!