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.
Simple question, where are the Whigs today? Gone? Because that’s what it takes to have a different party. The Whigs imploded, and the Democratic Republicans then swept the elections for a couple of years until the Republican Party coalesced.
Gore did not in fact win. Not because he didn’t have more votes, but because it was close enough that Republicans could steal the election. I Ralph Nader had not been on the ballot, Gore would have easily pulled the win. But several thousand unimpeachable votes.
This is called the Spoiler Effect. It’s the mechanism by with Durverger’s Law works. A vote for a third party is a vote against your own interests. Ralph Nader voters were horrified to learn that they helped Bush win the election.
But all this debate here is effectively in a vacuum. We’re not actually talking about the current election. A vote for a socialist third party in this year’s election is a wasted vote. Full Stop. You’ll not impress anyone, and the socialist candidate will not care about you. And that’s because the “socialist” candidate is likely a Republican plant. Because the two major parties know about the Spoiler Effect, and Republicans specifically have been funding the “left leaning” third parties to split the vote so that they can win.
If you as an individual want to harm yourself, I’ll not really care. I can’t stop you. But if you start advocating for others to join you, I’ll call you out as a Republican plant, working to fuck over the rest of us.