• chaogomu@lemmy.world
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    24 hours ago

    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.

    • zarkanian@sh.itjust.works
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      1 hour ago

      further, any attempt to create a viable Third Party is not only doomed to failure

      The Republicans were originally a “third party”. It used to be Democrats vs. Whigs.

      Duverger’s Law isn’t like a law against jaywalking. It just says that first-past-the-post systems create two-party systems, which is true. It doesn’t tell you who you should vote for.

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

      Al Gore actually won, depending upon how you count the votes. Additionally, you’re operating on the assumption that Nader voters would’ve voted for Gore, instead of just staying home.

      In fact, there were a lot of Democrats who voted for Bush, and their numbers dwarf Nader voters by several orders of magnitude. If you want to play that game, then it’s Democrats who are responsible for Bush winning, not the Green Party.