@malin Oh damn, that is bad. My computer’s motherboard died a few months ago. Pretty expensive to fix. Just got a job offer for a tech consultancy position I applied to.

@anguslm nice!

@malin I also did some more thought experiments on voting methods. It turns out my method of judging systems by seeing who would win in each possible pairing and if one would beat all other candidates, they should be the winner, is called the Condorcet method. It doesn't provide a winner in all circumstances however as cyclic collective preferences can be created (Condorcet paradox) though I suppose you could have coalitions for Condorcet ties. That's not much use for referendums however, so I wanted to try to make a system that returns a winner for Condorcet paradoxes, but returns the Condorcet winner whenever there is one.

My reverse STV method (VTS?) fails at that as if you create a 40, 30, 20, 10% grouping with the 40% group hating A, and all the rest putting A as their first choice but splitting their last vote between the other 3, A will get eliminated in the first round despite being the clear Condorcet winner.

My current favoured method is to basically just take a Condorcet method and subtract the majority percentage of their losses from the majority percentage of their wins to give a final score. Highest final score wins.

@anguslm VTS is officially my new political affiliation.

Unfortunately no ordinary voting method can avoid a dictator, include a condorcet winner and be pareto optimal (or have I misremembered a variable?). For that we need cardinal preference expression, though I have no idea how voters could express that with something like STV, or VTS.

@malin I found an article which seems to show this condition: https://www.cs.cmu.edu/~arielpro/mfai_papers/lecture6.pdf
Section 4.1 onwards

From what I understand, if the loser of the vote can alter the result to their favour by tactical voting, the system is manipulable. If they can alter the vote but it results in a worse outcome, it's not pareto optimal. If they can't alter the vote it's dictatorial. But the example they provide has only two voters, which seems to be the cause of the problem as it's trying to create a voting system which can resolve ties, which seems unnecessary. If voters 1 and 2 were replaced by 60% and 40% of the electorate respectively, the fact that group 1 will get their preference (a) no matter which order group 2 put their preferences in, is not a problem as they are a majority. It doesn't work for two people because you can't really have a democracy of two.

@anguslm I'll need a look when I'm home and sober. There's definitely a proof I looked over involving the impossibility of 3 conditions which people want.

Voting for 2 seems like it's not voting but misapplication of Mathematics to a discussion.

@anguslm I just remembered this, and yes! That looks like the one I remember, though this thing's covering a lot of ground very quickly.

I never did learn what all of the Maths symbols mean.