Best posts made by Toby Pereira

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"."

Also Droop Quota isn't a method. You can have e.g. largest remainder or highest averages methods that use the Droop quota.

@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.

@brozai I suppose I find them both clumsy and weak. Take Justified Representation. It refers to the case where a Hare quota of voters all approve one candidate. Intuitively, you might think that as a solid Hare quota, they should all get this candidate elected. But further reflection suggests this isn't always possible.

For example, there might be two candidates to be elected in an election. Three candidates are approved by 50%, 51% and 51% of the electorate respectively with no correlation between voting for one or any of the others. In this case the two on 51% would be elected, so not the candidate on 50%.

Of the voters who approved the 50% candidate (it has a full Hare quota), slightly under a quarter of them would not have a candidate elected.

It would be impossible to guarantee that every voter in a Hare quota group gets a candidate elected. So how do we make a criterion around it? Well, they went for the minimum possible option - one of the voters must have a candidate elected. At that stage it just seems like a pointless nod towards something they were probably trying to achieve but realised they had to back out of.

I don't have any specific examples in mind to create a clone failure, but if you have an A>B>C>A cycle, then by cloning one of the candidates, you can award the win to the candidate that pairwise beats that candidate. Clone A and C wins; clone B and A wins; clone C and B wins. So to make something up on the fly (not necessarily realistic):

14: A>B>C
10: B>C>A
5: C>A>B

In this example, A beats B 19 to 10; B beats C 24 to 5 and C beats A 15 to 14. C has the worst pairwise win and the worst pairwise loss. But clone A and C will win. (Sorry for not going into Codepens.)

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

So.... in a general sense, whether were talking about voting methods, seat belts, motorcycle helmets, or vaccines (sorry! political! ), I'm far more interested in knowing the degree of protection, as opposed to the simple boolean answer to whether or not it provides 100% protection. In my opinion, the latter is rarely useful, and often destructive to the goal of making any improvements at all.

My current feeling on it is that the benefit this method has in simplicity and ease of explaining far outweighs any risk of clones causing a problem. I'm aware that Schultz and ranked pairs seem to solve this, but they do it at the cost of complexity which, in my opinion, is simply unmarketable. Meanwhile STAR seems easier to sell than Schultz or ranked pairs, but if there is ever an election where there is a Condorcet winner, and STAR chooses a different candidate, I would consider that a serious flaw... partly because it is directly observable that this happened, after the fact. (a la Burlington 2009 with IRV) There would be no end to people claiming it elected the wrong candidate.

I agree with some of this. It seems to me that you want to find the simplest Condorcet method, since in terms of results, there won't be much between them.

So then the question becomes - is this the simplest Condorcet method? I don't know but it's probably quite good in that respect. I don't actually think ranked pairs is complex to understand, although I think Schulze is. Also there's the method that I think is called "Benham" where you sequentially eliminate the candidate with the fewest first places until a Condorcet winner exists. Though you don't have to use the word "Condorcet" in describing it. Just a candidate that head-to-head beats all the others.

There are of course cases where it's debatable whether you'd want the Condorcet winner to be elected. E.g.

49: A>>C>B
49: B>>C>A
2: C

Basically, two mainstream polarising candidates and a non-entity who is the Condorcet winner.

@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.

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've just been looking through old threads and found this one.

@nevinbr said in Least-bad Single-winner Ranking Method?:

Objectively, the answer is Game Theory Voting. However, it is basically impossible to explain to, well, anyone.

This method was also discussed at greater length on the old CES Google Group here. But the point is that while it is optimal in the sense that you might want to optimise this one particular thing, you might not want to optimise that one particular thing, so it would be wrong to say that it's objectively the best method.

In fact, when you look at what it is trying to achieve, it becomes quite clear that it's really just a bit of game theory fun rather than a method seriously trying to optimise something that a human would want to optimise. And you can see that by an example that you gave in the CES thread.

To expand on that last point, consider the following election with 3 candidates and 100 voters:

49 ABC

48 CAB

3 BCA

This has a Condorcet cycle:

A beats B by 94

B beats C by 4

C beats A by 2

At first glance, we notice that A has the largest victory and the smallest defeat, as well as the highest Borda total. However, the GT method elects A just 4% of the time.

Can that really be optimal?

Let’s think about it.

Okay, B gets crushed by A and barely squeaks by C. We don’t want to get crushed because that is bad for our long-term average, so B probably should not win. And if B loses (or didn’t run at all) then C defeats A.

It seems that A’s victory over B is mostly ephemeral. As much as we would like to score that +94 to improve our long-term average, the only way it happens is if we pick A and the system we’re up against picks B. But since B shouldn’t win, we expect the other system won’t pick B either.

In particular, if we usually pick A and the other system usually picks C, then we are going to lose frequently. We would rather be that other system and pick C most often, which is exactly what GT does. The optimal distribution is:

A wins 4%

B wins 2%

C wins 94%

Moreover, in any 3-way Condorcet cycle, the probability of each candidate winning is always proportional to the margin of victory between the other two candidates. And this is provably optimal.

In the example ballots, it seems clear that A is the best winner. However, under this method, because B definitely isn't a good winner, other methods won't select B so the A>B pairwise win might as well be ignored. Better concentrate on A v C instead and since C wins that, C is the overall best pick.

So what this method does is not pick the candidate that is somehow judged to be best for society, but the candidate that has the best average margin of victory against a candidate picked by another method playing this same game. And this method would never lose on average against another method (though obviously might tie - e.g. against itself). I don't see how this optimality relates to real life at all and why it would be good for us to adopt it.

To make this clear, the ranked pairs method is a Condorcet method that a lot of people like. But I could devise a method that elects a candidate that pairwise beats the ranked pairs winner whenever one exists. Otherwise elect the ranked pairs winner. According the metric used here, this method is better than ranked pairs - when these two methods are viewed as the only choices at least. But is this method better tban ranked pairs by any reasonable measure? Of course not.

An interesting academic exercise, but nothing more. Certainly not objectively the best single-winner voting method.

@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.

@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.

Great idea! Some thoughts:

I would probably mention that IRV is also known as Alternative Vote. In the UK, we had a referendum on using it for our parliamentary elections, and that was the name it went under.

For ranked-choice Condorcet, for the examples I'd probably include some of the better known methods like ranked pairs or Schulze, so it's clearer at a glance what the category is. Otherwise it might confuse people into thinking it's some esoteric group rather than what it actually is.

For median methods, I would exclude the word "cardinal". As you say, Majority Judgement differs from your description anyway because it uses letter grades rather than cardinal scores but that it falls into this category anyway. I would just make the category wider so that it is included without having to add a caveat.

At the risk of incurring the wrath of @Keith-Edmonds I wouldn't have STLR. As far as I know (and it's possible I'm wrong), it is just his pet method and has gained no wider traction. And if you include that method, then there are dozens of others you could add too. It is also based on what I would consider to be the misguided notion of utility ratios. In any case, it does seem to stick out as the most esoteric method in the list.