While people aren't likely to cast votes that are perfectly related to utility, I still see scores as more akin to utility than to something like money, where the increase in utility drops off the higher up the scale you go.

So what I'm saying is that I see a 5 and a 0 as in the same ballpark as a 3 and a 2, rather than the 3 and 2 being preferable for equity reasons.

How good score voting is generally is a separate debate obviously, but where it gives the same tie as a pairwise method, I don't see any reason in principle to prefer one result over another. But as a tie-break, it's probably fine to choose the result you might consider less divisive.

An interesting follow-up question would be whether you would consider divisiveness over score where there isn't an exact score tie (but is a pairwise tie still) or whether it's only useful as a tie-breaker. You could, for example, reduce C's score of 3 to 2. That way, the pairwise result is still a tie but on average scores, A and B are now marginally ahead of C despite being more divisive. Is there still an argument to elect C?

I suppose he's used that assumption because a hereditary monarch is essentially a leader arbitrarily picked, like in random winner (as opposed to random ballot). But this is obviously very simplistic. When you have an all-powerful monarch versus some other system, the entire political and cultural landscape is likely to be very different and that isn't modelled by this.

I've been looking at this and I don't think it is the best. One (minor) problem is that when you're summing the scores, for voters that haven't had any candidates elected and also gave a score of 0 to the candidate in question, you get 0/0. Obviously you just need to count it as 0 to get it to work, but it can make one suspicious that there are problems lurking beneath.

But the main problem is that it fails scale invariance. Well it passes in a multiplicative way as it is defined on the wiki, but not if you add to the scores.

For example, if everyone scores 1 to 10 instead of 0 to 9 (so just adds 1 to every score), you can get a different result. KP + SPAV (also known as Sequential Proportional Score Voting or SPSV) passes this. I know it might seem unsatisfactory to "split" the voter with KP, but in terms of passing criteria, it seems to do the job.

@bternarytau said in Way too many categories:

@andy-dienes said in Way too many categories:

Single Winner
Proportional Representation
Other Reform Discussion
News / Advocacy / Projects
Meta / Forum Business

This seems like a good set of categories, though it does awkwardly place non-proportional multi-winner methods under "Other Reform Discussion".

I thought this as well. I think a better category would be Multi-Winner Methods rather than one for PR specifically.

Well, it partly depends on what you do with equal ranks or incomplete ballots. If an unranked candidate is scored as 0 then a 4-3-2-1 system would be different from 3-2-1-0. But if it's done in a more sensible way, they would be equivalent.

@marylander said in Rule X extended to score ballots:

On the other hand, RRV and STV choose winner sets where all voters are strictly worse off than under the SSS winner set,

It's weird that RRV has done that since its mechanism is just to maximise the "satisfaction" score for each voter. I presume then that this is to do with electing sequentially rather than something fundamental to RRV itself. And I would also presume that electing sequentially can throw out weird anomalies for any voting method, and I don't see any particular reason why any method should be more susceptible than any other method to this.

As an aside, regardless of what one thinks of Thiele methods in general, I do not consider RRV to be a good implementation of it.

Well, aside from that, I think Arrow's Theorem is overstated in terms of its importance anyway. Pretty much all ranked-ballot methods fail IIA and if they don't they are unreasonable in some other manner. This has been known for ages anyway as it is a logical consequence of the Condorcet paradox.

So Arrow's Theorem was no great paradigm shift in our understanding. It's a non-event if you ask me.

@robla said in Paradox of Causality from Arrow’s Impossibility Theorem:

Kenneth Arrow absolutely deserved his Nobel Prize, because Arrow's Theorem was (and is) a big deal. The exact choice of criteria was beside the point; what Arrow did was describe a few "common sense" criteria and then showed them to be mutually exclusive.

But my point is that we already knew that. Amongst Arrow's criteria is IIA. And that's the one that always fails in reasonable methods. It's not like some methds fail this, others fail that. How many methods are there that are just dictatorships, for example? It's IIA all the way. Arrow's Theorem can be reworded in plain English as "With a few reasonable background assumptions, any reasonable ranked-ballot voting method fails IIA." And that has been known for centuries. Arrow just dressed it up differently.

If the leader appoints the new leader, you could just have two people bouncing the leadership back and forth between them without caring about what people think of them. Or even if you added a rule saying you can only be leader once, a large enough group of like-minded people could just pass it around.

@marylander said in Rule X extended to score ballots:

@toby-pereira Do you think that EJR in particular is clumsy, or all of them in general?

Yes, because as I said in the archived discussion - "all these criteria seem oddly weak in that they only make demands about a single voter, or in proportional justified representation just one voter per candidate that the group "deserves"."

@jack-waugh said in STAR-like method ("reverse STAR"?):

@rob OK, I'll bite -- what do you think is fairer, and on what grounds?

You're saying it's the fairest. I think the onus is on you to justify that!

@rob said in Are Equal-ranking Condorcet Systems susceptible to Duverger’s law?:

So what is that algorithm? I mean, it could be Condorcet, and I have no problem with that, but I can't see how the term "proportional representation" applies. It just sounds like multi-winner.... there isn't anything proportional about it.
The only way the term "proportional representation" would apply (by my understanding of the term) is if we assume that there are some number of parties, and each candidate and each voter is in one and only one party. If a 3rd of the voters are in the Bull Moose party, then a third of those elected should be in the Bull Moose party. The further you get away from that, the less "proportional representation" seems to be a meaningful descriptor.
All of my complaints regarding PR (and with so many people's insistence that it is so much better than single winner methods such as Condorcet methods) are based on the assumption that voter X below is considered to have "better representation" if d, f and e are elected (because candidate d is very close to voter X), than if a, b and c are elected.

For the algorithm, you will be aware of Single Transferable Vote, which gives PR without any mention of parties. If voters happen to vote along party lines, it gives party PR, of course. That's just one example, without having to mention obscure methods invented by people on this forum.

And as for a, b, c versus d, e, f, I discussed that in the other thread here. I'm not sure it's worth quoting though because it's quite long.

@rob said in Are Equal-ranking Condorcet Systems susceptible to Duverger’s law?:

I guess the main thing that bugs me about it is that, in most cases, it's artificially forcing people into groups, which is what I hate about the system we have now. Maybe it would be more than two groups, and I guess that's better, but I just don't get the need to force people into groups and to entrench those groups.

Just on this bit, non-party-list PR doesn't force people into groups. You vote for (rank, rate, whatever) whichever of the available candidates you want, regardless of how much in common they might have with each other or which party or group they are perceived as being in. The PR algorithm then just elects the slate of candidates that best represents the electorate (according to its own algorithm). Voters are not then assigned one representative of those elected; they are all available as representatives. E.g. in a region with five representatives they are all "yours". At no point are you forced into a group.

@mosbrooker said in What would a perfect voting system look like?:

‘A’ is the leader and B is, somehow, the fairly chosen alternative. ‘A’ will spend a lot of time eyeballing B. The relationship will be contentious at the least and openly hostile at the worse.
And all people who are not A or B would have to suck it up and deal with the result of this fighting. Nothing substantial would get done. The island would spiral into a state of disrepair. They wouldn’t even know what to do if a pandemic hit.

I don't see why this should happen at all. A leader is ousted and someone replaces him/her. The old leader has lost the support of the masses, so people are free to ignore any "eyeballing" that may or may not take place, and I don't see why it should.

@mosbrooker It's not the continuous approval vote that is the main problem here. It's that the current leader gets to pick the new one. Are there not other methods for this? Like a vote. Even some sort of random pick.

@cfrank said in What would a perfect voting system look like?:

@mosbrooker allowing appointments of the successor doesn’t make any sense to me.

Me neither. I'm not sure what the motivation for this bit is. Other than being simple, but that's not enough.

If the leader appoints the new leader, you could just have two people bouncing the leadership back and forth between them without caring about what people think of them. Or even if you added a rule saying you can only be leader once, a large enough group of like-minded people could just pass it around.

Without getting into a definition of "representation" for now, I've always had the feeling that it's better to have a more diverse parliament that represents the electorate in a more proportional way than one that represents the electorate in the best way for a single candidate and then multiplying that by the number of candidates, if you see what I mean.

If you have single-winner constituencies and the single most representative candidate gets elected in each one, you could potentially end up with a lot of near-clones, and in a sense it seems to make having a large parliament a bit pointless.

In fact, it probably wouldn't end up that way because of geographical differences in voting behaviour, but that brings me onto the next point, which I believe is similar to that raised by @Andy-Dienes in the thread that this is an off-shoot from. You can get very different parliaments with exactly the same voting behaviour purely depending on the geographical distribution of the voters. You could end up with a bunch of near clones if there isn't much geographical difference in voter behaviour, or you could end up with something close to PR if you get geographical clusters of voters, or more likely something in between.

But since representatives make up the national parliament rather than simply act as an isolated representative for a group of people, I don't think such potential variation based on the same ballots is good voting method behaviour.

I think a method that gives similar results regardless of how one jumbles up the voters across the country is (all others things being equal) better than one that is very dependent on the geographical distribution of voters.

As Andy says, why split along geographical lines - why not let the voters just vote for what they want and the splits will come from that?

And as I said in the first paragraph, I think more diversity in parliament is good - and as for what diversity is, it's the diversity people vote for, not the predetermined things that people might have in mind like race, sex, age etc.

The "average" position in parliament is still going to be similar to what you'd have with Condorcet winners, but I think you'd get a wider range of issues considered and debated. It's not simply that you'd get "extreme" views and these would get voted down anyway. You'd get people raising people's consciousness on issues that might not otherwise be considered - issues that aren't based on "extreme" politics, but that people simply aren't very aware of and would be happy to support if they were.

And I'm not sure I would want too much like-mindedness in a parliament anyway. And I think you'd be more likely to get conforming behaviour where people go along with what they perceive to be the group view and don't question something until it becomes too late.

I think it's different for companies with their "benevolent dictator". Some companies succeed and some fail under a dictator, but a country is far too important to have the possibility of failing and you can't trust it to a dictatorship, even if in some cases it might work out.

I still think that's too many categories actually as I think I said in the other thread. I certainly don't see the need to split single and multi-winner, because some stuff cuts across both categories. Essentially I'd have one forum for voting methods and then two or three for other stuff - e.g. forum matters, off-topic or whatver.

@rob said in Unfortunate “Publicity” for IRV a la Steve Forbes:

@cfrank Wow, what an idiot. He says:

despite what proponents proclaim, it’s not democratic. For instance, a person running in a multicandidate field could place third or fourth in the actual voting yet win the election.

WTF is "the actual voting"? The "actual voting" is ranked choice under IRV tabulation. The winner is the one that, um, wins.

If it makes any difference, in the accompanying video he says "the popular vote" rather than "the actual voting". I'm not sure if he wrote the article, or if it just has his name on because someone just made it from what he said.