Just because you’re too lazy to actually look them up, doesn’t mean that they aren’t full of equations.

This is one Proof of Arrow’s Theorem;

Let G be a coalition with size ≥ 2. Partition the coalition into nonempty subsets G 1 , G 2.

Fix distinct x , y , z. Design the following voting pattern (notice that it is the cyclic voting pattern which causes the Condorcet paradox):

voters in G 1 : x ≻ i y ≻ i z voters in G 2 : z ≻ i x ≻ i y voters outside G : y ≻ i z ≻ i x

(Items other than x , y , z are not relevant.)

Since G is decisive, we have x ≻ y. So at least one is true: x ≻ z or z ≻ y.

If x ≻ z, then G 1 is weakly decisive over ( x , z ) . If z ≻ y, then G 2 is weakly decisive over ( z , y ). Now apply the field expansion lemma.

See how helpful that is? No, Well, if you had a phd in math or political science it would be.

This is the wiki link if you want the full Proofs. And that’s just Arrow’s Theorem.

Durverger’s Law is both simpler, and more targeted. It simply states that if you have a system of government where there is single winner elections and plurality voting, you will inevitable have a two party system, and that further, any attempt to create a viable Third Party is not only doomed to failure, but is actively harmful to the interests of those Third Party voters.

In other words, the Spoiler Effect, Like what happened with Ralph Nader in 2000. He’s the reason why Bush won.