 maybe a few floors above us and yeah so yeah is it everything ready yeah okay perfect so I'm still on it can you can you speak hi can you hear me yes we can Alex perfect so all right so I shut my screen yeah if you can please I think I can we'll see do you see yeah we do we do we do so our Zoom speaker Zoom but closed-room speaker of today it's Alexander Stewart and he comes from the University of St Andrews and he's going to talk about models for the onset and resolution of effective polarizing all right thank you very much everyone I'm sorry I'm not down there in person I have been feeling very unwell last night in this morning and I was worried I had COVID I do not I should emphasize but I'm nonetheless not feeling great so I figured it was probably better for everyone if I stay up here and talk to you from a distance so yeah I'm gonna talk about some modeling work that I've done with some collaborators looking at the relationship between polarization and inequality so why talk about polarization it's a workshop in inequality and to some extent we've already answered that question we've had other talks that discussed polarization in some depth and I don't think it's necessarily a sort of counterintuitive idea that polarization and equality should be linked but I do just want to flag up one one strand of the empirical case for the relationship which is shown in the figure here can people see my mouse by the way yeah okay so this is taken from Nolan McCarty's book polarization what everyone needs to know and the models I'm gonna show you are done in collaboration with Nolan and some other people although of course the usual caveat applies that anything that sucks about them is my fault not theirs but what this figure here shows is in red we have the degree of polarization in the United States over the course of the century from 1917 to 2017 polarization here is elite polarization it's measured using the DW nominate metric which captures the extent to which political parties in Congress are polarized and plotted against it are both the genie coefficients in the United States in blue and the income share of the top 1% of taxpayers in green and what you see is that both polarization by these by this DW nominate measure and inequality by these two similar measures follow a u-shaped distribution in the United States over the course of that century now of course just because two things trend in the same direction doesn't mean they're causally related but it is very suggestive especially because there's good a priori reasons to think that polarization and inequality should interact with each other so what is what could be the causal relationship between polarization and inequality well inequality may cause polarization by exam is exacerbating tensions between groups with different levels of wealth polarization may increase inequality by preventing redistributive policy and when polarization leads to legislative deadlock is arguably it has in the United States over the past decades reversing it may become a necessary but not sufficient condition for tackling high levels of inequality so the work I'm going to show you is trying to unpack this relationship the dynamics that arise from this interaction between inequality inequality and polarization using mathematical and computational models the work I'm going to present is based mostly on these two papers and which if you want to I'm obviously not going to have time to go into infinite detail here so if you want to get into the details of these models I very much encourage you to look and of course site these papers and I'm not going to show I'm not going to show a great deal of data here because although I emphasized in my introduction introducing myself and my research that I'm very keen on collecting mechanistic models to data the data side of it is still sort of ongoing and so I will talk about future plans but not really any many results along those lines so my talk is going to be split into three parts time permitting in the first part I'm going to talk about models of mass polarization and in particular I'm going to focus on effective polarization as instantiated in as a form of loss of cooperation and then I'm going to talk about the relationship between risk aversion identity and sorting and I'll explain what what those terms mean in this context in a moment in part who I'm going to talk about the relationship between inequality and polarization I'm going to show that polarization can be sticky under some fairly simple assumptions and that when it is and that the polarization can exacerbate the effects of inequality and then finally I'm going to talk about the bit that everybody always asks when you talk about these models is alright so what what does that tell us about how we fix polarization and I'm going to talk about redistribution as a preventive but not corrective measure for fixing polarization and then I'm going to show briefly some new results on how we can use heterogeneity and influence to a modeling of a modeling of good behavior as a way to potentially reverse polarization so polarization in public discourse tends to refer nebulously to a wide range of interconnected phenomena we talk about polarization a lot but we don't necessarily obviously in this audience we do but in in general discourse we don't necessarily pin down exactly what we mean and so I'm going to talk about polarization and think about polarization in at least three interrelated but distinct ways the first way is I'm going to refer to a sorting which is clustering of people into competing groups typically aligned with a political identity antagonism between identity groups so this is known as effective polarization and is usually measured by asking for example in the US case Republicans and Democrats to rate their attitudes towards the political outgroup and their political in group on a zero to 100 feelings thermometer and looking at the difference between those two numbers and when the difference between those two numbers is large that means you like your in group a lot and you dislike your outgroup a lot and then of course the sense of polarization which we saw in the first slide in which distinct clusters of policy preferences arise in a group or population and I refer to this as ideological polarization so obviously all of those things interact with each other but they are also clearly distinct and of course it's also important to talk about who we're interested in being polarized so this could we could talk about mass polarization i.e. voters as opposed to political elites or we could talk about political elites and so in this talk I'm going to focus mainly on mass polarization and I'm mainly going to focus on effective polarization and sorting and I'm going to defer that there's any discussion of elite polarization and ideological polarization to discussion or to another time and what we're particularly going to be interested in trying to capture in these models and what's originally motivated these models is how things like inequality and more generally this term economic anxiety which is not a great term but it's a commonly used term how these this kind of idea of economic anxiety can lead to polarization and we're going to conceptualize polarization for the purposes of this talk as willingness to cooperate with political in versus outgroup so we're going to be interested in the population dynamics of polarized attitudes so we're inherently adopting a mechanistic worldview here i.e. we're thinking that ideas and attitudes emerge and spread in a population through a process that is less than rational i.e. we're thinking of the spread of polarization as something more like an epidemiological process as opposed to a decision-theoretic rational process and the mechanism of spread that we're going to focus on for the purposes of these models is utility based social learning so what do I mean by that? Well I mean something relatively simple we're going to assume that social learning occurs through observing and imitating others and that payoff-based or utility-based imitation occurs according to this function where the probability that a player i imitates a player j's strategy is equal to 1 over 1 plus e to the sigma wi minus wj where wi and wj are the utilities of the respective players and sigma is a global parameter that basically controls the strength of selection or the amount of noise in the imitation process so it's not super important that you i'm not going to dwell on the details of the math but it is i think useful for people who are familiar with these models to just see what we're assuming and the key thing that we're going to assume about the utility function is that it is non-linear and s-shaped and that's the and that it is and that utility of all individuals in the population arises both from their interactions their cooperative or not interactions with other people and also from some sort of underlying state of the environment so utility arises from multiple social interactions with during a given period of time and also the underlying economic environments and we assume that it follows qualitatively the form shown in this figure where when the underlying environment is is bad when you're down here where my cursor is then your utility is low and as the underlying environment increases utility increases and what the effect that this has is that when you are when the underlying environment is very good you're sort of risk neutral so you don't you know you neither risk tolerance or nor risk averse but as you start to approach this cliff here where your utility decreases rapidly with the underlying environments you become risk averse and then as you get down close to zero you become risk tolerant so that's just to do with the curvature of the utility function but this assumption that you took the level of risk aversion that's a population feels varies with the underlying environment is key for studying this question of how so-called economic anxiety and inequality interact with polarization in our model so that's the utility as I said utility arises from a combination of the underlying environments and from social interactions occurring between members of the population so we're going to assume that these social interactions take the form of cooperative cooperation in which individuals choose whether to interact with members of their in-group or members of their out-group with a probability p and if they do choose to interact with a member of their in-group then the success of that interaction that's sorry that interaction is successful with a probability qi to generate a benefit bi and it fails with probability 1 minus qi and for out-group interactions the probability of success is different it's qo and the benefit that you generate is qo and in particular what we assume is that when you choose to engage in out-group interactions those interactions are more risky but more beneficial so why do we assume that well this is basically a priori assumption that we assumed to capture the idea that polarization can in principle be generated by risk aversion by economic anxiety so in order for a risk aversion to generate high levels of polarization i.e. to generate a high level of interactions with in-groups as opposed to out-groups you need to assume something like this you need to assume that out-group interactions are perceived as more risky or are in fact more risky than in-group interactions and then so the level of polarization in our model is measured via this parameter p which is the each individual in the population strategy and we also make an additional assumption that in order for an out-group interaction to successfully occur both players have to be willing to participate in it i.e. if polarization is equal to or close to one for all members of the population then even if one individual decides to try not being polarized they won't get anywhere because of the members of the population that are not willing to interact with them so i've thrown a lot of information at you i hope it's not too confusing but this is the basic setup of the model which i just wanted to give you a sense of before i start to move on to some of the results i guess i'll kind of skip over the additional mathematical descriptions here because i want to get to the actual things that we find but we have this utility function which i showed you before and we parameterize it in a particular way that depends both on the underlying environment and the benefits that arise from these social interactions that i just described to you and then a particular individual's utility depends on their strategy individual i that has a utility wi that depends on their strategy pi and the probabilities of success and failure of interactions and of this utility function f and i'm not going to belabor that because i don't really have time to go into it so the basic thing to understand about this model is that if most players have high levels of polarization meaning p is equal to one or close to one interactions will tend to remain within group and that means that polarization is high because people don't attempt to cooperate with people outside of their political in group if most players have a low level of polarization p equals zero that means interactions occur commonly between groups and we think of polarization as being low and what we want to study is the population dynamics of this level of polarization p under different underlying environments theta so these social learning models are stochastic and complicated to analyze and we use a combination of agent-based modeling and adaptive dynamics to do so i'm again i'm not going to belabor that but i can return to it in the discussion if people are interested but what we find when we carry out this analysis that combines sort of adaptive dynamics analysis if that means anything to anyone and agent-based modeling yes ask a question just to clarify so when you imitate you copy also p yeah you copy p that's exactly right so the imitation process is the copying of another player's strategy and in this context you call it's it's p and i realize now that my notation is actually bad because i also use p to mean the probability of copying sorry about that but yes you copy p okay great okay so now now what we can do is look at the the dynamics of the the polarization the level of polarization p in the whole population as a function of the underlying which we call this the economic environment theta and so at the top on if you look at this figure on the right you see this is a sort of phase diagram i've labeled roughly the regions where the underlying utility function is risk tolerance risk averse or risk neutral respectively and what you see is that if you're in the risk neutral region you have bi-stability where both low polarization and high polarization is is stable so if you initialize your population in this white region here where my cursor is p will evolve down to zero if you initialize it in the blue region p will evolve up to one similarly in the risk tolerant regime you see that there's a there's bi-stability there's a very small region under these parameters in which if you start just up here where my cursor is p will evolve to high levels of polarization if you start in this big white region you'll evolve to low levels of polarization however if you're in the risk averse region the bi-stability disappears and you only evolve towards and i'm using evolve here to mean population dynamics change over time you only evolve towards p equals one i.e. you only ever evolve to high levels of polarization there's no longer any bi-stability why is that important well it's important because if we consider a time-varying economic environment so here in this figure at the bottom we have theta the economic underlying environment varying sort of sigmoidally um so initially the environment is good so we're risk tolerance and if we initialize our population this is the this is the level of polarization as a result of agent based simulations we initialize our population in the basin of attraction for low polarization you tend to stay there until the environment becomes sufficiently bad that you end up in the risk averse regime in which case you tend to evolve towards high levels of polarization and when you the system um when so when theta goes back up to high levels of um um this is to being a good environment again you don't go back to the low levels of polarization because of this bi-stability so you start off down here say but then the environment gets worse so then you end up following this arrow up here and then when the environment improves again you're still up here stuck in the stuck in the high levels of polarization um due to the bi-stability and so what you see in this model is first of all that polarization can arise from um essentially economic anxiety from risk aversion in certain underlying environmental states and that polarization is sticky in the sense that once it emerges in the population it doesn't disappear when the environment improves again and so this is obviously bad but um I think sort of an interesting um hypothesis about the nature it generates in the interesting hypothesis about the nature of polarization and the relationship between things like economic anxiety and polarization okay so so far we've made implicitly made some very simplistic assumptions about the nature of identity in particular that political in-groups and political out-groups are the only feature of identity that matters and that people make their decisions about who to cooperate with based on political identities this is obviously not reasonable uh and not a reasonable account um of reality and it doesn't allow us to study other forms of polarization than effective polarization such as sorting which as I mentioned is the sort of alignments between political identities and other forms of identity so in order to capture this we um made our model more complicated and allowed um identities to be multi-dimensional such that in-groups encompass multiple fat sets of identity possibly including political party but also including other features of identity that are not to do with politics could be race religion etc and what we study is and we assume rather that an individual strategy is not only their willingness to interact without groups so there's probability p but also their political identity so we allow them to both switch political identity and to switch their willingness to interact without groups now this gets rather complicated so I'm not going to go into it in detail but I do just want to flag up one particular result that we get when we once we make this complicated more complicating assumption so we keep fixed group identities such as race or religion allow party identities to change over time and we look at how both the level of sorting i.e the alignment between fixed features of identity and political identity change alongside the degree of effective polarization i.e the willingness to cooperate without groups and what we find is that in all of the regime's um risk tolerant risk averse or risk neutral the we will see evolution of high levels of sorting which is given so the here in all of these three figures we're showing um the the the possible trajectory is that the population can undergo the red dots indicate stable equilibria and so you see that sorting i.e the alignment between fixed forms of identity and political identity reaches high levels it's symmetrical because you we we don't assume any particular bias in one way or the other um and we also see we get this by stability in the risk tolerance and risk neutral regimes why is this important well the reason it's important is that it suggests and I don't really have time to go into the details of this but I'd be happy to discuss it with you is that as political identity becomes more salience in decision making at the expense of other forms of identity um what that means is that we will see increased levels of sorting um along such that political identities align with other forms of identity and that is precisely what we see in the United States over the course of more or less the last century depending depending on which of these figures you're looking at so here what we are showing is the degree of racial polarization as measured by um on the left here as measured by um the same kind of feelings thermometer type questions that define effective polarization so you ask people their opinions about racial outgroups and this is specifically showing the responses for white people in the United States about other racial outgroups over the course of sort of like 1960 to 2020 and we see that the expressed level of polarization racial polarization in this sense is decreasing over time but at the same time effective polarization is increasing and the degree of sorting i.e. the tendency of race to align with per political identity is also increasing and so what this suggests is that we're seeing political identity becoming more salient in the way that people think about themselves and think about others that's leading to greater levels of sorting and rather than actually say oh right whilst if you just looked at the left hand figure this would suggest a sort of positive world view in which the world is becoming less racially polarized what we think is actually happening here is that um racial political identity is becoming a proxy for race essentially and so the effective polarization is a sort of more acceptable way of expressing racial dislike which is great um okay so i've talked a lot about polarization and sorting affect polarization and sorting but this is a workshop on inequality so what about the relationship between polarization and inequality so we go what we're going to do now is take the same basic model that i've described to you again rather quickly and we're going to instantiate the idea of inequality by assuming that different subgroups of the population experience different underlying environments theta and we're also in order to study the relationship between polarization inequality and redistribution we're going to also assume that there's a possibility of redistribution via public goods at rate alpha such that the group um in the if we increase the amounts of redistribution we we improve the environments of the people experiencing the worst underlying environments and make and decrease the economic environments of the people in the good environments so the first question we want to ask is is this kind of inequality sufficient to generate polarization in our model and secondly we want to ask can redistribution make things better and i'm sort of giving away the answer to the first question by asking the second yes inequality can generate polarization in our model and then we're going to ask can redistribution make things better so to capture this idea of inequality and redistribution we assume that the underlying economic environment um theta depends on again i'm not going to go into this in detail but happy to discuss later um redistribution from these cooperative interactions between members of the population um plus a baseline environment theta zero minus a baseline environment theta zero so what we're doing what we then do here in this figure is compare the first of all on the left the level of polarization evolving over time in a scenario where there's inequality in the sense that some people experience a bad environment and some people experience a good environment um and we're comparing this to a scenario which has the same average environment but everybody faces the same you know if everybody gets the same theta and what we see is that polarization under inequality tends to evolve to high levels and much higher levels than we see when there is no inequality and even more striking if we look at the effects on utility under our model is so if you look on the left here initially where the difference in utility between the high quality environments and the good quality environment the red and the blue lines is very small but as polarization increases the people in the low quality environments gets increased in the low levels of utility whilst the people in the red environments end up once we reach equilibrium having kind of the same level of utility as they had to start with and the population average utility in the unequal environment versus the same faces the same average environment where there is no inequality has lower average utility so the effect of inequality here is to increase polarization and the effect of polarization is to increase the the manifested effects of inequality as understood through utility under this model and so this is capturing the idea of this feedback loop between inequality and utility as inequality and polarization where inequality exacerbates polarization and polarization exacerbates inequality of course there are other mechanisms for this but I think this is nonetheless an interesting way of looking at it in the space of mass polarization or effect of polarization so the way this happens just to give you a little bit of intuition is that the people in the low quality environments are experienced essentially a risk averse environment which leads them to adopt start adopting high polarized strategies but because of this process of social learning this quickly spreads to the whole population even though the people in the high quality environment are not really advantaged by adopting a risk averse attitude because they're fine and so you get this same kind of dynamic that we saw previously where once polarization takes hold it becomes sticky and it's not easy to reverse and this can happen if only a subset of the population become risk averse or economically anxious or whatever you want to call it okay so I have literally no idea how I'm doing for time by the way because I'm sick and I'm confused so people should please shout at me if I'm going on too long so I finally want to talk about the thing that I guess is the sort of important point so what lessons can we take from this kind of modeling for fixing polarization and what are we going to do in the future to try and understand address these questions better using these kinds of models so the first thing I want to note is that sufficient levels of redistribution meaning high levels of this parameter alpha that I mentioned before can prevent the onset of polarization in the low quality risk averse environment so if we haven't if we haven't initially unequal environments but we engage in redistribution such that environments become more equal between the two groups we see that as we oh I missed an N off the axis there but as we increase the level of redistribution alpha inequality declines and polarization declines and the average utility of the population increases in response so that's really kind of to be expected right if we I already showed you that if you start off with the same average environments without inequality you get less polarization than if you assume that one group has a worse environment than the other just a side note that if we include some form of dead weight loss due to taxation in our public goods model then this makes reducing polarization and notably harder to do so here on the left we see that increasing redistribution does decrease in equality by necessity but it doesn't do such a good job of reducing polarization when there is this dead weight loss due to taxation but that's a bit of a side note that I again happy to discuss towards the end so this redistribution is sufficient to prevent the onset of polarization in our model but it is not sufficient to reverse polarization because polarization is sticky and essentially the only way to reverse polarization under this model is to knock the population out of the basin of attraction for high polarized behavior high polarized strategies one thing that's sort of neat here in this model is that it sort of builds what emerges from it is the idea that a so-called you know shock and economic shock or some kind of other shock that such as a war or something which vastly decreases the utility of the population can actually be effective in reducing polarization and you can see this this figure isn't ideal for the points I want to make but I didn't have time to make a better one so here we have the baseline environment theta zero on the x-axis and the color indicates the size of the basin of attraction of polarization so where the darker the color the harder it is to reverse polarization and if the baseline environment becomes bad enough then you the basin of attraction for high polarization becomes sufficiently small that it's pretty easy to escape it and generate low polarization in the population and so if I just very quickly zoom back to this figure that basically what I'm saying is if the environment theta goes from kind of here you're up here at high polarization and the environment theta goes down here it's very easy to escape this basin of attraction because it's so small so that's one way of escaping polarization you in our model the only way of escaping polarization is to knock the population out of the basin of attraction for high levels of polarization and you can try to enact policies which essentially shrink the the size of the basin of attraction for high levels of polarization. One way that you can try to generate this kind of knocking the population out of the basin of attraction for high polarization is via so-called coordinated efforts in which you get enough people to start being unpolarized that basically you escape the basin of attraction for high levels of polarization. How could you do that? Well one way you could do that is by having elites who model good behavior and so we've started recently to look at the idea of influence inequality in which the population has people with heterogeneous levels of influence such that people with high influence will tend to be copied by people with low influence but will not tend to copy people with low influence and we show that this can be actually quite successful and again I apologize for the bad notation here I've repeated the use of gamma but the way to read this heat map is that when the proportion of low influence individuals becomes high enough and when the relative influence of the high influence individuals is high enough then the then you will end up getting low levels of polarization i.e you so in the blue region you tend to get you tend to be able to successfully reverse polarization quickly and the yellow region you tend to be able to not reverse polarization quickly and so what this is showing is that it is possible to model good behavior and push these dynamics out of the bad basin of attraction of high polarization provided the group of low high influence individuals is small enough and that their levels of influence are big enough okay so finally I just wanted to say a couple of notes about where we're going next with this work so we obviously haven't presented very much data here connected to this model and I would like to correct that so one thing that we're looking at doing and that we're piloting a version of this but it's not yet connected to polarization but what we're doing is um carrying out multi-scale public goods games in which individuals have to choose whether to invest in their local group or in a global group in this figure it's called Westville Eastburg and Allshire um so it's a regular public goods game where people invest if also yeah so it's a threshold public goods game excuse me if enough people invest then everybody gets a payoff within the group be it Allshire Westville or Eastburg or of course people can choose to defect and keep the coin what we want to do with polarization of course is to make these groups aligned with people's political identity and make the degree of that political identity sufficiently salient um or vary the degree of salient to that political identity in order to see how that affects their willingness to engage in um cooperation at different scales we're also measuring the extent to which people identify with different groups be it they're in group they're out group or the whole group using the dynamic identity fusion index and again that will be interesting to look at when the different populations different subgroups are divided according to um political identity um okay and that's all I have to say I hope that wasn't too confusing as I say I'm a little sick so I don't not totally sure whether what I said made sense but hopefully there's some interesting stuff there and I'm happy to discuss um I'd like to thank my collaborators and my funders and especially as I said at the start Nolan McCarty who is a political scientist and who is sort of the why why I'm happy to work on this um because I have a political scientist to talk to who who's willing to sort of like keep me grounded and not wander off into weird model worlds that doesn't connect to reality okay thank you very much okay so well there are a few questions so I keep track of you okay uh thank you really great talk great work I now I realize I read some of your papers and I really was very impressed by your work so cool stuff um yeah I've actually two questions um if I may um the first one is um so it's in in the model uh you you presented a very crucial assumption is that if people let's say from a low income group interact with people from a high income group that is a risky thing and it's even more risky if there's more inequality um and and how does that relate uh to say also the the economic benefits that you get particularly in an unequal society if you get the chance to interact so say you are poor and you get the chance to work for an employer who is rich so you have a job you make uh an earning uh as compared to and you are better off than other poor people who don't have a job and don't make an earning so that's a positive interaction say with a rich out group member so there must be somehow a trade-off somehow a balance uh or a trade-off between these things and I wonder how that figures into your modeling yeah it's it's really interesting actually so in the initial model we don't assume that the so what I was showing you here we don't assume that these groups are unequal in wealth we just assume that they having different identities is perceived or for some reason is in fact more risky now this is sort of why I got into the identity sorting stuff because what we assume is that different that wealth does not like inherently vary with political identity but it may vary with other facets of identity and then and so if what happens is sorting i.e political identities align with other facets of identity then you end up with a scenario like you describe in which um you have a wealthy group is perceived as the out group and the non-wealthy group is perceived as the in group so that doesn't answer your question but that's just to clarify the model um so the I guess I think that the there's a that what we've assumed is very simplistic there is there are some interesting studies that show for example um how people's attitudes vary when hiring someone from a different identity group so there is evidence for example that people are you know engaging racial bias in hiring and that sort of thing and I think that speaks to what you're describing if it's literally the case that there's just a rich group and a poor group like everybody in one group is rich and everyone in one group is poor I don't think I think you're right and you wouldn't sort of have this risk aversion that we're assuming but I think if on average one group is rich but the both groups are heterogeneous then what we're sort of assuming is that people within a given identity group who are rich will give the opportunities to the people who all who share their identity and they will perceive giving an opportunity to someone in the poorer group who also has a different identity as risky does that make sense yeah I think so yeah maybe short second no okay as okay where no I save it for later I save it for later okay thanks a lot thank you no I'm going to ask you something Andrew I mean would you feel okay just having one more question taking a break now and then continuing later would it be okay for you or yeah I may even talk to here and later yes no no I'm just saying it because I mean well also for logistic reasons but then since then we have more discussion so just one more question you can take a break and rest a little and then we go back okay okay so one more yeah just like and so Eduardo and then Alexander I just need to talk enough to the camera focus on me here so thank you for the talk so in particular going through these distinctions about polarizations I always found that very confusing I learned a lot and that's my questions just to see if I understand because the identities you had where always a binary decision or a discrete set of options so while I could think about examples where the opinion or a stance on a political issue could be better modeled by maybe a real variable I just want to to clarify from you whether this is indeed a different type of problem or you can map this to the things you did and if it is a different type whether you think that is different dynamics or if that aspect is relevant or the discreteness is not important yeah thank you I think the discreteness is important and it's sort of important for the definition of sorting so that isn't to say that you can't have sorting along lines of continuous identity just as you can have sort of bimodal policy preferences when policy preferences are continuous but that is obviously much more complex to model and we haven't done it yet but I think that you're right that it's an important thing to think about and actually one of the things I'm very interested in doing which is semi-related is to connect these kinds of models more explicitly to both opinion dynamics of the type that we heard about in some of the previous talks and also a more sort of nuanced model of identity dynamics itself so where its identity is continuous and where you can feel more or less attuned to a particular identity in response to both your opinion and your economic environments and all that sort of thing so I think it's a really important point but I don't really have a lot of intuition about how it will change the results at this point. Yes it's more of a reminder but then we'll come back for the discussion so just before the so let's perhaps thanks again Alex.