Thanks very much, Sam. Yeah. So just some introduction and context. My name is Luke Thorburn. I'm a PhD student at King's College London. I work mostly on the interaction between recommender systems and sort of human conflict and polarization. But on the recommender system side, thinking about different algorithms and the incentives they pose on a population for how people communicate and allocate attention. There's a lot of sort of governance issues there. You the the algorithm in in many ways governs how attention is allocated. So that that's that's what I see that the main crossover being here. And I have this paper with Avivo Vodger on bridging systems, which is all about how you can or trying to provide a framework for translating practices about bridging and peacebuilding and facilitation from offline analog context into online systems. If you're interested, there's a link at the top there. And that that the sort of published version of that will come out soon with the Knight Institute at Columbia. But today's talk is going to be a little bit more sort of abstract and theoretical, specifically talking about partisan sorting and unsorting, which some of you might be familiar with as a concept. I'll I'll explain it in due course. But, basically, it's motivated by three questions that have been mulling around in my head for the last six months or so. The first of those is if you're interested in sort of bridging divides between people, how do you define or quantify the extent to which that's happening in a in a large population? How do you put numbers on it? I I won't check the chat while I'm talking. So if you would like to interrupt, please do, but just sort of actually interrupt. The second question that I've been mulling over is, of all the ways to operationalize bridging in code, why is it that diverse approval is so common and successful? By diverse approval, I mean, this sort of pattern of interaction where you have people who would normally disagree with one another simultaneously finding some point of commonality around a piece of content or an idea or perspective. And this that's sort of, like, crudely illustrated there. And this this basic pattern is what's used in several places in Polis. If you're familiar with that software, it's used in community notes on X or Twitter. Notes are only shown publicly if they garner support from basically both sides of politics in The US, and it's been used in other places as well. And of all the ways that you could sort of try to translate peace building and conflict management processes into code, it's probably the most widespread by at least in sort of the the sphere that I'm thinking about. So I'm I'm wondering why that is. Is it just because it's the first idea that pops into bits heads, or is there some some deeper reason why it might be more successful than others? And then the third is to try and ground technical approaches to bridging like diverse approval in sort of deeper political, democratic, and and peacebuilding theory. So I think the answer to all those questions in some ways is sorting and partisan sorting and unsorting. This talk will have basically four parts. The first, what sorting this is. The second, we'll look at normative arguments why it might be more desirable to have higher or lower levels of sorting. The third, what are the mechanisms by which a population can change the level of sortedness? And finally, a couple of results on the sort of feasibility of of unsorting as a as a goal for governance systems. So to start with, I'm going to be using a basic model of societies as hypergraphs, meaning groups of people sorry. A collection of people, all of whom have various memberships of groups, and these groups overlap in various ways. This way of thinking might be familiar to many of you, and these groups could be defined by basically a scriptive sort of fixed attributes like age or race, could be attitudes, preferences, or opinions, or it could be behaviors sort of explicit voting patterns or consumption patterns, opt in organizational memberships and that kind of thing. And these overlapping groups, when they overlap, there's sort of an intuitive benefit that comes from having groups that aren't completely mutually exclusive that overlap. You've got two groups as you do here. Because they overlap, the people in the purple group know someone who is in the blue group and vice versa or they have some belief. If they don't know them personally, they have something in common with people in the other some people in the other group. And this sort of provides a a safeguard against conflict getting too out of control and sort of helps helps mesh the society together, speaking very crudely. So the first question that I was thinking about is how do you quantify the overall level of that kind of effect that's happening in when you have a large population with many groups that are overlapping, not just not just two. And I think the the first key to figuring out how to do this is to notice that there's a correspondence between hypergraphs or or groups as illustrated on the left and sort of spatial models or or distributions on the right. Hopefully, the color coding in this illustration is fairly intuitive, but, basically, we have a a yellow group and a green group. You could think of these as sort of opinion groups on policy issues. So maybe yellow is people who support climate change action, and green is people who are pro life. And if people are either in or out of those groups, and so you can represent that same information in a sort of Venn diagram on the left or in a sort of spatial distribution model on the right. In general, reality is more complex. The groups will be fuzzy. People will be in or out of them to varying degrees, and there'll be a lot more people. So it it will look something like this, and it might make sense to represent the spatial model not as discrete individuals, but as sort of distribution over over the degrees to which people are in or out of groups, which can obviously be sort of any any access, of sort of a continuous scale. So that's the general model. And then the the next key insight is that, the level of, cross cuttingness in the groups, which is sort of the degree where you if you can notice here that most of the people in the yellow group are not in the green group and vice versa. And that sort of that that that's potentially an undesirable state because it means that these groups are sort of at odds with one another. There's not that much overlap in them. And the the first oh, I'm sorry. The next insight is to recognize that that level of sort of cross cuttingness is in in the hypergraph is inversely proportional to the degree of dependence between the attributes and the spatial model. And that in turn is exactly the same thing as sorting or partisan sorting, which I'll flesh out a bit in a moment. Just to caveat all the illustrations, almost all the illustrations in this presentation are in two dimensions in general. They will the the same concepts apply in higher dimensions with many more groups. It's just much easier to visualize two dimensions. So what is sorting? This is first, I like to distinguish sorting from polarization. So in political science literature, when people quantify polarization, they usually quantify it as a property of a single axis. It's like the the degree of bimodality or or clustering along a single dimension. And so it's inherently a sort of one dimensional concept in terms of the the joint probability distribution. We've sort of built up polarization would be a property of one of the marginal distributions. It wouldn't be a property of the population as a whole, where sorting in contrast is inherently a property of the joint distribution between multiple memberships or multiple issues or or axes of variation. So that's you you can say the the debate over a particular issue is polarized, but you can't say the population as a whole is polarized if you're sticking to how it's normally sort of formalized. But you can say a population as a whole is is sorted. So that's one key distinction. And then to give a bit more intuition about what sorting is, in a highly sorted world, everyone who's in one group is not in another group and vice versa if we're just considering the simple world. And then as the world becomes less sorted, there's more and more people sitting at the intersections of these groups or indeed in neither group until at the the unsorted end of the spectrum, knowing that someone's in one group gives you very little information about whether or not they're in the other group and vice versa. So that that's sorting as it's described in political science literature. It's, I think, essentially the same thing, same concept as probabilistic dependence in the the distribute joint distribution I set up and also essentially the same thing as the amount of cross cutting affiliations or or people in the the population. So, yeah, that that's sortedness. Why might lower levels of sortedness be desirable for a population? I think there's basically three arguments or three clusters of arguments. The first is that sorting is real. That's there's a stream of literature in political science that's the consensus seems to be that what has happened in The US in particular over the last few decades is not so much that the population is polarized on any particular issue dimension, but that it's sorted into two increasingly homogeneous groups. Issue political affiliations and issue positions have become increasingly correlated with one another, and there's different sources of evidence for this increasing yeah. Basically, you can directly measure correlations between issues positions. There's geographic sorting as well if so where you live can be considered just another attribute of any of individuals. This is a paper from last year showing county level geographic sorting in The US over a long period of time where there there is data. And in 2016, sorting where data was available is higher than it's been since the the the civil war, approximately speaking. There's also, as a like, a model of politics sufficient to explain other empirical trends such as an increase in the difference in approval ratings for political leaders, a decrease in split ticket voting, sort of shifting the the stamp campaign strategies from conveying to convince other sided voters to campaigning to mobilize base. And with the additional sort of minor assumption that it's easier to like someone the more you have to come on with them, increases in effective polarization. There's also more normative arguments. So one is that high levels of sorting are bad and increases sort of the ability to accurately pigeonhole or stereotype people. It decreases political representation of nuanced cross cutting positions. If if the political elites are all sorted, then there's only representatives for the the highly sorted groups. There aren't representatives at the the more nuanced positions that might take aspects of both groups or neither. And there's also work in conflict studies that shows that countries where attributes like religion and ethnicity and geography more sorted at greater risk of civil war than than countries where those attributes are more independent of one another. That's just correlational analysis, obviously. There's also in the the opposite direction arguments that unsorting is a good thing. It increases the number of surprising validators, which is a term for people who hold uncommon combinations of perspectives such as, I don't know, Democrats who are anti migration or, yeah, pick pick your topic of choice. But, basically, in terms of you've been trying when you're trying to reach people, having someone who they normally agree with on everything, express a perspective that doesn't normally go with that cluster of beliefs, tends to be more palatable and, more successful at, sort of allowing people to think more openly about about about new perspectives when we encounter someone who we mostly agree with, express something that we find sort of surprising and perhaps on that perhaps don't agree with, we tend to think, oh, maybe I should give that more thought rather than, oh, I don't need to worry about that. They're they're just a a sort of part of the app group. I can disregard anything, I think. Unsorting also increases the extent to which any majority will have something in common with a minority which reduces risk of sort of majoritarian tyranny, and it increases week or long tires almost by definition in a population which has been trained to improve economic outcomes for people. So there are reasons why unsorting or lower level of sorting might be a thing. There's also sort of more qualitative evidence, I think, from various sources in the the canon of political and democratic theory. A few of those are listed here. Not all of these are necessarily normative arguments, but I think they're evidence that the degree of sortedness is a sort of core property of societies that's worth monitoring and and and thinking about. And and some of these are more explicit normative arguments that lower levels of sortedness are a good thing. Why might high levels of sortedness be better? Or why shouldn't we try to unsort groups of people? The first argument is that perhaps it's too neutral a goal. As I I sort of flubbed the example early about surprising validators, but you can unsort people basically by moving or or convincing people to move from more common to less common combinations of of attributes. So that might be convincing people who you agree with on everything to take an extreme case or you think are right about everything to adopt a perspective which you disagree with normatively or otherwise, and presumably that's not something that you would advocate for. There's also cases like q and on could be argued to be bridging in that it attracts people from both sides of political spectrum, so it would probably reduce sorting overall. The the the sort of q and on group helps helps bridge and reduce sorting across the two two political clusters in The US, but maybe that's not something that that we should be advocating for. So it's it might be too neutral. It might also be absurd if you take it to the extreme. In the extreme case, all attributes are sort of perfectly probabilistically independent of one another. That that it's a bit absurd if you if you think about what that means. So it's not clear that this should necessarily be used as a objective function. The it's it's possible that if you're trying to intervene to reduce the level of sorting, that there there's more or less ethical ways to go about doing that that respect autonomy and so on. And finally, there's an argument which I I don't think is particularly strong, but it appears in the literature, which is that high levels of sorting make politics more simple and legible, particularly to people who don't wanna spend a lot of time thinking about it. If in highly sorted world, there's two very clear alternatives. It's quite easy to pick which one pick pick a side. In a highly unsorted world, the the situation is a lot more messy and probably harder to make sense of if you're not thinking about it all the time. So, yeah, that's another argument why, like, levels of sorting might not be desirable. So the next section is about mechanisms by which populations sort and unset. The I think there's this is an exhaustive typology. There's basically three mechanisms. The first is what has been called in the literature conversion, which sounds like it seems, but it's basically just any process by which people change the the groups that they're a part of. So and I think any of these sort of phrases at the bottom of the slide, which hopefully at least some of those are sort of recognizable to you. I'm happy to talk about any of them in more detail. But I think all of these are basically talking about unsorting by conversion, And these are all concepts that are sort of emerged in peace building and conflict management and so on. Complicate the narratives is a peace building strategy, which focuses on sort of amplifying so called contradictions or, people who hold combinations of perspectives that are sort of surprising. And I think, to to go back to one of my motivating questions, diverse approval, that sort of pattern of interaction where you have people who would normally disagree with one another or normally be quite different from one another, but finding some sort of convergence around an idea or perspective, I think the the reason why this has been used so widely might be well, one of the reasons it might work if it works is that it basically contributes to unsourcing by conversion. As a pattern, it sort of picks up these uncommon combinations of perspectives in in a population. And by sort of directing attention towards those, it encourages people to move more in those directions. And there there's lots of reasons or mechanism by which people might change their perspectives. There's a at least here, but there's basically a huge number of results from psychology and social learning and so on that when we're exposed to ideas more frequently, we tend to gravitate and become more aligned with those those ideas and perspectives. I'm thinking mainly here about the sort of online social media recommended systems context, but you can think about this in any sort of governance system that directs attention towards certain perspectives or proposals or ideas. The the second mechanism by which the level of softness in a population changes by adding or removing groups or correspondingly dimensions in the probabilistic model. I I think cases of sort of humanization, which might come about through intergroup contact, would be an example of this. There's quite a robust body of evidence suggesting that contact between people who might who have sort of prejudices towards one another in non conflictual settings can lead to reducing that prejudice. And I think that basically happens by adding extra groups or dimensions which correspond to basic things like, what do you like in person? Where do you shop? What sports teams do you work for? That kind of thing. And yeah. So I think that's an example of unsourcing by by this mechanism. The third mechanism is, entry or exit of people from the system, which can happen naturally over time through migration or generational change. Also, if you're viewing this from some sort of online community, account creation or deletion. And finally, two sort of technical properties of sortedness as a a a property which might make it feasible to sort of, intervene upon. And these both correspond to more formal theorems, but I'm just gonna sort of talk through intuitively what they mean here. The first is that you it's possible, like, theoretically to reduce sortedness globally by intervening locally, predominantly with only local information. So if you're some sort of online community or an online platform, you've got a a user base that looks something like this. You don't know if the whole population looks like a scaled up version of what you you can see or if it is actually something more complicated with other overlapping groups. It it doesn't matter what the the whole population is. You can just unsort or in in principle, if if you can reduce the level of in the community that you have influence over, then that is not going to make the situation worse overall. It's still gonna contribute to reducing sorting the the the whole population level. This is in contrast to polarization, which because it's only one dimensional, if you're only looking at a sort of subset of population that sits along the line and you move people close together, it's not possible to know if you're consolidating a single faction or moving multiple factions close together. And so either improving or worsening polarization. And then the the second sort of technical property is that is, in a formal sense, orthogonal public opinion because it's a property of the dependency structure between attributes rather than the sort of attribute positions themselves or the size of the membership of groups. It's, again, in principle theory, possible to reduce sortedness or change the level of sortedness without changing the number of people who are members of any particular group or the distribution of opinions over a particular policy issue. And I think this might make it or the the yeah. There's there's different things you could do with that information. One would be just to sort of have confidence that when you're if you're advocating for lower levels of sauciness, you're not advocating for manipulating the public sphere in a sort of material substantive way. You can sort of conceptually separate public opinion or the size of political stakeholder groups from what the the change that you're you're advocating for. And then more technically, you could build systems or mechanisms which explicitly try to have no incentive to change public opinion or the size of groups or so on, but sort of more, yeah, targetedly and more directly focus on on affecting. I'm going to finish quite abruptly there, but but sorry. Yeah. This diagram we had earlier, but I I didn't emphasize that the so the size of the groups doesn't change at all, which emphasizes the point I was just making. I'll finish there. Very happy to take questions. But, yeah, this is ongoing work. I'm I'm still sort of involving my ideas about all these concepts, so very happy to take feedback and, yeah, discussion. Thanks.

I I guess my my personal motivation is just trying to improve the clarity and precision with which I'm thinking about things. But I think it can be generative as well. So yeah. Even just talking this through with people helps raise ideas, at least for me. I think thinking through this sort of, like, those three classes of mechanisms by which you can sort of intervene, I I think the the sort of diverse approval pattern is basically the, like, the technical operationalization of the of conversion, but the other two is room to sort of think through how do you how do you operationalize those in code. Yeah. I'm not sure if I've got a very clear answer, but feel free to

No. No. No. I think that's that's possibly fair. I I had a point. I don't sleep on my mind. Oh, yeah. I I I think, well, also the your your point about sort of needing to overpower existing tendencies within the system, I think maybe the goal is not to sort of absolutely decrease sorting in any sort of huge way, but it is just a design mechanisms that sort of counteract natural tendencies to to sort. Yeah. I think that's a bit of a better way of phrasing it. Thanks.

Okay. Luke, thank you. That was a great presentation. The kind of question I had, and this is maybe something that

I don't know how good a question this is, but it was what what was

on my mind. To what extent is the process of sorting, like, fundamental or the default unless steps are taken to prevent it? Is the process of sortation neutral, and it only occurs in the presence of actors that push it one way or the other? Is there can we say, you know, psychologically, the tribal instinct will push us towards sortition unless steps are taken in the opposite direction? It's almost like a like a law of thermodynamics type thing where you must prevent it, or is it neutral and, you know, people will act in one way or the other to to further their own goals? What's your thinking on that?

I think it really depends on the setting. I'll I'll just say to start with to my knowledge, I think is something slightly different. Is well, not slightly, something something a fair bit different. Statition refers to sort of randomly selecting people in a sort of jury like style for the government's bodies. This is the the idea of sorting or partisan or ideological sorting, which I think is different. But, yeah, I I think that, like, there would be so many different causal pathways and mechanisms by which this happens. In The US, the literature sort of talks about the political elites sorting first. It's in their sort of self interest to simplify and the the space of politics and sort of cluster people into into two groups. And then that sort of slowly trickles down to the general population through media and that that kind of thing. Media organizations will have an incentive to sort of build a brand around a particular group and that sort of reinforces existing actions. But, yeah, I I most of this talk and and my thinking has been around sort of describing a state of things rather than a dynamic process beyond the sort of mechanisms I outlined. And I'd like to do a lot more to figure out what what are the the processes by which this changes

Sure. So the first point also, community notes on Twitter, for those who don't know, is like a a crowdsource fact checking tool. If you opt in to be part of the program and you see a tweet that you think is misleading, you can contribute a note or suggest a note that adds context to the tweet or corrects the false information and so on. But those notes aren't showing publicly straight away. They're only showing publicly if they're rated as helpful by other people in the program who are basically from both sides of politics in The US. X or Twitter doesn't collect that information explicitly. They sort of learn where people tend or the patterns of how people tend to vote and assign some number along a one dimensional spectrum, which just so happens because of the nature of the population and the voting patterns to correspond to politics in The US. And then they get they they only show notes that are rated sort of consistently highly and are not slanted heavily in either direction using that that model. Polis is a bit more complicated than that. It's doing multiple things at once, but they have a measure called group informed consensus, which if you sort of rank the statements that people have contributed by that measure, it it's basically ranking the most cross country or most the the statements that generate the approval or support from diverse groups at the top and those that are more partisan or fictional further down. I'll I'll mention also there was a in one of the Frances Houghton Facebook papers, there was reports of experiments at Facebook where they used this sort of that they called it diverse positive motifs, motifs being patterns of interaction. But they basically showed that when you rank comments using the principle of placing those at the top where the elicit sort of positive engagement from people who are sort of normally diverse in their their patterns of engagement, that that correlates quite strongly with following community guidelines and being thought valuable and high quality by the users and and so on. So, yeah, it's been used in at least those three contexts. The second question. Oh, yeah. How how can you use this? Or so this is all sort of very high level and a bit speculative because it's very hard to, I don't know, prove absolutely that that recommended system causes sorting, say. But I think, intuitively, it seems quite plausible that the whole sort of, I don't know, collaborative filtering style logic, which even though it's not used so much explicitly anymore, it's still the same basic principle. It's still there where you're showing things that people who like the stuff that you like have also liked. That seems to be something that would push people into the highly sorted groups because you're just sort of reinforcing, okay, you're you're like these people in this way. Let's make you more like those people in these other ways that we think will keep you on the platform. Whereas if you use something more like diverse approval as a as a logic, that's counteracting that tendency. It's still showing you stuff that you like, but it's emphasizing or prioritizing stuff that you like that most people like you don't like. And that seems to be something that would counteract the the sorted sorting. Yeah.

Collaborative filtering is it was like the early approach to building recommender systems where you basically have a matrix of items and the people and the ratings of people and items, and you try and fill in that matrix in such a way that you you show people stuff that people like them also liked that they haven't seen yet.

I I'm not familiar with it, but I think I get the gist of it, and it sounds super relevant. Yeah. My my guess would be that that's sort of one of the common mechanisms by which sorting takes place. But, yeah, it's the first I'm hearing of hearing of that word, so I'm not sure I can speak.

Yeah. So this is sort of the more theoretical line of research, and I'm doing more empirical stuff as well trying to evaluate sort of bridging in right vendor systems. But in in this sort of more theoretical front, I thought that that this talk is based on a paper that I'm writing up at the moment, and it's all all yeah. It's a little bit too much. Sortedness is the the thing with capital t's, and I'd like to sort of complexify it a bit. And in in particular, some feedback I've got from other forums is that well, yeah, that sorting is it it's probably an important property, but it's not necessarily the thing that causes unproductive conflict. There's places in the world that are fairly highly sorted that are quite socially cohesive at the same time, at least don't seem to have huge issues with political division. So maybe there's something to do with the way sorting interacts with the governance mechanism and some decision making mechanisms in a in a community that makes it more or less problematic. Maybe there's more sort of granular information about the the hypergraph that is lost when you just convert it to a a spatial model. That's yeah. I'd also like to think more about that. I've yeah. I've been talking about this with as well, and he's also suggested that that there's I don't know. The the goal is not so much to reduce sortedness, but to have some sort of optimal degree of the cohesiveness of groups. They're they're they're too cohesive, then you get high levels of sorting and conflict in intergroup conflict. But if they're they're not cohesive enough, then you don't sort of get the productive community effects of community. And so you need some sort of middle ground or or some sort of process for managing and veering too far in either direction, which yeah. I I think there there's more complexity there rather than just saying, oh, there's some optimal level of sauciness in the middle that you have to try and maintain. There's other other formalisms that are a bit more complex that capture that better.

That's a really interesting question. I'm not sure I've got a great answer. I think yeah. Most of the literature that that I found in political science was focused more on explaining or trying to quantify sorting or explain sort of normatively why it's high levels of sorting is bad. There's less on the process by which it happens, I think, or at least it is not referenced under same keywords. So, yeah, I would very much like to know more about that. But I'll I'll let you know. Yeah.

Yeah. I again, I'm not sure I can point you anything to anything, but the term surprising validators was, I think, coined by Cass Sunstein, and he's got a few articles about it. And I'm sure it it he didn't sort of invent the concept. He just sort of gave pity name to it as far as I know. I'm sure there's a bunch of work in sort of peace building mediation, facilitation literature on more actual case studies of this at a at some more fine level. But, yeah, I I don't have anything I can put you to other than.

If you just go to my website, lukethorben.com, it's got my email address there, and it's probably best. Okay. Amazing.