# The challenge of equifinality to modelling opinion dynamics # 1 Introduction The often-unpredictable dynamics of public opinions, their hatching from private ideas and thoughts that then spread across billions and billions of brains until they flood and reshape the political landscape like tempest waves, are increasingly captivating our public discourses and our minds. Especially democracies, who by their nature draw a lot of their legitimacy and policy decisions from public opinion (cf. Chu et al. 2008; Noyon et al. 2020), have been struggling during the 21st century with rapidly diverging and shifting opinion landscapes and a subsequent rise in polarization and populism (cf. Falkenberg et al. 2023, p. 9). As political division deepen and public trust in institutions erodes (cf. ibid.), understanding how – especially radical – opinions are formed and disseminated has become an urgent topic in both public and academic debates. Yet, the study of public opinions and their dynamics is a notoriously difficult field of inquiry, where scientific models are still often immature (cf. Smaldino 2023, p. 118) and studies often fail to deliver valid results – e.g. in election forecasting (cf. Grimmer et al. 2024, p. 18 - 19). These difficulties arise from multiple sources: opinions are cognitive artifacts that emerge from interactions between complex minds, making them largely invisible to direct measurement (Smaldino, 2023, p. 118-119). Furthermore, empirical data on public opinion is often deeply distorted. There is a gap between what people think, and what research can measure they say or write that they think – often leading to surprises, when people reveal their real preferences e.g. by voting differently than polls would have predicted (cf. Grimmer et al. 2024, p. 18 - 19). This gap seems only to get wider, as self-selection, gate keeping and the rise of AIs on social media paired with human retreat from it, distort the quantifiable opinion landscape. But except of the recently added layers of complexity and speed through Social Media and AI, and especially due to the devouring of the former by the later leading to an increasingly dead internet (cf. Walter 2025, p. 239 – 240), this fundamental practical challenges to the study of public opinion are rather well known and have been of central interest to researchers from the fields of communication, propaganda and media studies since their modern articulation by Lippmann (cf. Lippmann 1922). Or in other words: there is a lot of noise, and more of it than ever, so it’s becoming harder and harder to dissect and distinguish what influences and shapes public opinion – but neither the noise, nor the need to cut through this noise are particular new to the research of public opinion. But: Because of these mounting empirical challenges, researchers have increasingly turned to formal models as new tools to cut through the noise and to capture underlying mechanisms. However, these computational approaches face their own limitations. As Smaldino (2023, p. 146) notes, formal models of opinion dynamics remain weakly integrated with theories of cognition, social behavior, and evolution. A fundamental and often underappreciated challenge in this field is _equifinality_—the issue that multiple distinct causal mechanisms can lead to the same observed outcome. This issue has been at the heart of recent debates, such as those surrounding the filter bubble hypothesis versus negative influence effects (Cottee, 2022; Smaldino, 2023, p. 120). This paper sets out to articulate, clarify and analyze the challenge of equifinality to public opinion modeling, exploring its significance and influence on model creation and validation. By examining the epistemic difficulties that equifinality introduces, this paper assesses the limits of modeling approaches to public opinion by deeper theoretical integration and philosophical reflection. # 2 Defining equifinality ## 2.1 Origin and Definition in General Systems Theory “Equifinality is the idea that a particular pattern in data can be generated by multiple, mutually exclusive mechanisms”, writes Smaldino (2023, p. 306), but the idea is deeper and encompasses two distinct, though closely related concepts: one from systems theories and one from modelling. To gain a clear understanding of equifinality, both concepts will be outlined. The general concept of _equifinality_ was first used by german biologist and vitalist philosopher Hans Driesch at the beginning of the 20th century. Driesch argued that biological beings display an inherent teleology (goal-directed force), somehow being guided by a mystical final cause towards final states from different initial conditions. He coined this capacity _equifinality_, interpreting it as evidence of entelechy or vitalism - a view that life has irreducible goal-driven principles, which couldn’t be explained by science and physical laws (cf. von Bertalanfyy 1988, p.40, pp. 131 – 133). The term equifinality was then successfully appropriated by Ludwig von Bertalanffy in his _General Systems Theory_ as rebuttal to vitalism (cf. von Bertalanfyy 1950). He adopted and reformulated the e_quifinality concept_, stripping away the mystical overtones and explaining it as a natural result of open systems maintaining steady states (cf. von Bertalanfyy 1988, p.40, pp. 131 – 133). This the first concept of interest for this paper. Von Bertalfanny formally defined this concept pf equifinality as property of a system, as follows: Every system of elements _Qi(x, y, z, t)_ is equifinal in an subsystem of elements _Qi,_ if the initial conditions _Qi0 (x, y, z)_ can be changed without changing  the value of _Qi (x, y, z,_ _)_ (cf. ibid. p. 132). ## 2.2 Equifinality as a property of Open Systems In closed systems, such as Newtonian physics problems, final states can be precisely determined by knowing the initial conditions. For example, in a planetary system “the positions at a time _t_ are determined by those of a time _t0_” (von Bertalanffy 1950, p.25). The systems in this typical physics textbook problems do not exchange energy or matter with their environment – or in the case of planetary systems, the environment of the galaxy is so vast and of low impact, that on the timescale of human civilization it might as well not exist (yet). These systems are therefore displaying _uniquifinality_, ergo have predictable and deterministic equilibria given their initial state. Since key functions of the closed system’s elements are by definition constants, (e.g. the total mass or energy in the system), the final state of the closed system will tend toward an asymptotic value determined by those constants. Furthermore, a closed system, will in the long run - following the second law of classical thermodynamics – inevitably reach a predictable, stable state determined by maximum entropy or disorder(cf. von Bertalanfyy 1988,  pp. 132 – 133). But: With biological beings (and many other systems) we are not dealing with closed systems, but with dynamic _open systems_. These systems are not self-contained and externalize entropy by exchanging inputs and outputs (ergo energy and matter) with their environment and react to external inputs over time. In such systems, multiple different initial states and trajectories can lead to the same final state, often a structurally determined homeostasis or equilibrium, which the system achieves by balancing inputs and outputs to maintain its order — displaying equifinality and explaining the (false) impression of finality of biological beings (cf. .ibid.). This has profound implication: While we might calculate the trajectory of an apple falling down a tree, when we know all the initial conditions, like the distance to the ground and the gravitational force determining the acceleration (cf. Flannery 2013), the initial conditions alone are not enough to calculate the behavior of open systems, as the systems are not only determined by them. As an example, take the average blood sugar levels of a human. If we wanted to calculate the average blood sugar levels of a person, it would be of little use to do this based on the initial conditions, ergo, the amount of sugar he or she consumed. This is because the blood sugar levels are less determined by the amount of sugar consumed, but by action of hormones like insulin and glucagon, which will break down ingested sugar or draw it from reserves in the tissue, to achieve blood glucose homeostasis (cf. Jiang & Zhang 2003). By just monitoring the sugar intake of a human, we couldn’t calculate his or hers average blood sugar levels, as those are – excessive or deficient consumption behavior aside – more determined by genes and the functionality of the pancreas, ergo the structures of the system and its ability to selfregulate by drawing energy from other systems, as if the system gets out of balance, the system will incentives itself – ergo the human – to get something to eat or treatment. This all without the need to have a supernatural vitalist factor and without breaking laws of thermodynamics (cf. von Bertalanfyy 1950, p.25). Equifinal states are also observable in social and cultural systems, which consist of several beings –  e.g. population dynamics as described by the Lotka-Volterra Predator-Prey Model (cf. Smaldino 2023, p. 15) or social learning strategies (cf. Barrett 2019, p. 130) show some equifinality; though equifinality changes again its shape slightly, when moving from smaller systems that are trying to maintain homeostasis, to societal systems, as those often are not moving towards an equilibrium, but are adaptive. ## 2.3 Equifinality in Complex Adaptive Systems When we are looking at highly complex systems like human cultures and the transmission of ideas and opinions within them, we are not only dealing with merely open systems – we are dealing with complex adaptive systems. The concept of _complex adaptive systems (CAS)_ goes beyond open systems and is based on the insight, that certain complex systems, which consist of many components or agents – like human societies, economies, informational networks, brains, ant colonies, to cite a few popular examples – not only react to environments to maintain an homeostasis or equilibrium, but also adapt to it and exhibit distinct emergent properties or features (cf. Holland 2005, p. 1). These are, following one of the pioneers of CAS Theory, John Holland, mainly four: _Parallelism, Conditional action, Modularity_ and _Adaption / Evolution_, which all combined lead to non-linearity and a wide range of other subsequent common properties like open-endedness (cf. ibid. p. 1-7). As CAS are open-ended and change or evolve almost constantly as a response to changing conditions, often dramatic through lever points, there are no final states or equilibria to them, except as part of (temporary) subroutines, which can be described as open systems within the CAS (cf. ibid. p. 6-7). For example, take a biological being, like an individual Dinosaur: the Dinosaur is an open system, which tries to maintain a certain stable state of energy and matter to stay alive. 66 Mio. Years later the Dinosaur is dead and earth is populated by humans (cf. Vaughan 2025),the open system got replaced by others. But the complex global ecosystem of planet earth, where plants put oxygen in the air, and animals roam the lands, hunters hunt prey and so on, this complex ecosystem still exists, though it adapted a lot to external and internal changes and replaced many reptilian subroutines through mammal ones. The ecosystem is best described as a CAS, and individual are being usually best described as instances of open systems. Subsequently, equifinality can only be attributed CAS as a temporary pattern – or a constantly changing pattern. E.g. to survive and procreate, individual beings as open systems exhibited different strategies and features a few million years ago than most living beings do today, as changes in oxygen levels and temperatures made certain previously equifinal strategies non-funtional anymore. E.g. flying insects the size of today’s dogs, which once roamed the earth, don’t exist anymore as the possible size of insects is strongly limited by the atmospheric oxygen levels, which have dropped from 30-35% to merely todays 20% over the last 300 Million years (cf. Chapelle & Peck 1999). So to reach the same goal – to remain equifinal – species changed, or rather, through grind of evolution and the deaths of the less fit, survivors of changing environments became new species. The function remained, but the state changed – unlike with open systems, where functions change to maintain a certain state. To sum it up, **equifinality in CAS is conditional and often realized at the level of function or pattern rather than exact state****.** An unlike for open systems, equifinality is not a defining feature, but rather a conditional and shifting byproduct. ## 2.4 Equifinality as non-identifiability in modeling When creating theories and explanatory models of real-world phenomena, researchers are often troubled by another – though closely related – phenomena also called by some _equifinality_, though it being a slightly different concept than that from general systems or complex adaptive systems theories. This is the concept Smaldino is referring to, when he writes of equifinality as “the idea that a particular pattern in data can be generated by multiple, mutually exclusive mechanisms” (Smaldino 2023, p. 306). This concept of equifinality, where “a given set of observed patterns or outcomes can by produced by multiple distinct explanations” is also known under the equivalent but rarer terms of _nonidentifiability_, _nonuniqueness_ and _multi-realizability_ (Williams et al. 2020, p. 3). This kind of equifinality arises especially in cases, when limited knowledge of the processes modelled and limited empirical data, make calibrating the model challenging and leave many parameters free (cf. ibid.). This concept of equifinality is also the one, which troubles modeling complex adaptive systems – and therefore social processes – the most, as it might lead to models which seem to explain empirical phenomena very well by fitting our data, despite being completely wrong. ## 2.5 Equifinality defined To summarize this chapter: _equifinality_ as a term refers to two distinct but related concepts: 1) The first concept of equifinality comes from general systems theory: When we observe and measure several instances of system _R(y)_ at t0 and at tn, and when different values at t0 lead repeatedly to the same values for _R(y)_ at tn, we have equifinality, in the sense of an open systems structures and mechanisms leading it to convergence at a stable state again and again. On can visualize the concept as a convergence of data points over time to the same values: ![[Pasted image 20250316124806.png]] This use of the term _equifinality_ can described by the old idiom: (Almost) all roads lead to Rome. 2) The term equifinality as it is used in modelling complex adaptive systems describes than the issue: When we are already in Rome, how do we figure out, how someone got here? Even when we know their point of origin, there are countless equally possible ways they could have used to get to Rome, that you could generate an endless amount of plausible but wrong explanations. Or in stricter terms: When we observe and measure a single instance of a CAS _S(y)_ and we got empirical data for _t0_ and _tn_, there a several possible pathways, which given the data, are all more or less equally good in explaining how the data for _S(y)_ at _tn_ emerged – but only one can be right. ![[Pasted image 20250316124823.png]] Both terms are insofar describing similar phenomena, one as a system property, and the other one as a property of explanations regarding systems – both caused fundamentally by the same issue: the contingency and opacity of our reality and the subsequent many possible ways things can happen and can be explained. # 3 Equifinality in models of public opinion dynamics ## 3.1 Public Opinion Landscape as a CAS In general, public opinions and their dynamics, can most effectively be described as parts and examples of complex adaptive systems (CAS). Only certain parts of the public opinion landscape, e.g. where institutions and social structures enforce consensus formatting e.g. opinions being debated and integrated into the decision- and lawmaking of a democratic parliament, could be described as open systems. The public opinion landscape, as the set of all opinions held and expressed by the agents of a defined population e.g. a society, is a complex adaptive system, as it shares all the four main features of such systems, as they are defined by John Holland (cf. Holland 2005, p. 1 – 2): 1)         _Parallism:_ Public Opinion consists of a large number of agents, that interact by sending and receiving signals and information. These agents, members of a particular society, furthermore interact simultaneously e.g. each minute, approx. 251.1 Mio. Emails and 18.8 Mio. Textmessages are sent (cf. Domo 2024), all of them being a small part of a digital and analogue information exchange among all of humanity, all contributing a bit to shaping opinions. 2)         _Conditional action:_ The dynamics of public opinions are conditional on received signals, in abstract terms, they are following an IF/THEN structure. Human agents adjust their views based on the information they encounter—whether from own experience or transmitted through conversations, media exposure, internet etc. For instance, if an individual repeatedly encounters news articles and memes suggesting a financial crisis, they may adjust their opinions and consumer behavior accordingly. This one could describe as an IF signal: _if economic downturn_, leading to a THEN act: _adopt negative economic sentiment_ _and spread doomer opinions, e.g. encourage everyone in the family whatsapp group to hoard gold and ammunition_. This conditional response mechanism enables opinion feedback loops, where reactions to information further shape the information landscape, leading to reinforcement effects and subsequent shifts in collective attitudes e.g. _bank runs and stock market collapse._ 3)         _Modularity:_ Public opinion does not operate as a monolithic entity but consists of smaller, interlinked components—subgroups of individuals sharing certain views, ideological subcultures, or communities centered around particular issues. These modules, akin to subroutines in computational systems, allow for flexible and context-dependent opinion dynamics. For example, political parties and civil society often exhibit modular structures where individuals can align with different issue-based positions. This modular structure enables the recombination and evolution of viewpoints, as individuals form new opinion coalitions in response to emerging issues  (cf. Holland 2005, p. 1 – 2). 4)         _Adaptation and evolution:_ Public opinion changes over time, with shifts often following patterns of adaptation rather than random fluctuations. Opinion dynamics respond to external stimuli - e.g. crises or changes in media institutions - through mechanisms akin to evolutionary selection. This is most notably seen in how the change of media technologies, changes not only the accessibility but also the content of the media, or as Marsh McLuhan exaggeratedly put it: The medium is the message (cf. McLuhan 1994, p.7). As the opinion landscape is a CAS, we can expect both kinds of equifinality to be relevant here. ## 3.2 Mechanisms for opinion shaping ### 3.2.1 General Mechanisms used in modeling In general, when using agent-based models to formalize and simulate opinion dynamics, there are two main ways agents form their beliefs 1)         _From social influence._ Most opinion model research focuses on how humans influence each other through propaganda, marketing, social interactions, media exposure, propaganda, and group dynamics. Three core mechanisms of social influence are often discussed and modeled: a.         _Positive influence._ “When agents interact, their opinions become more similar to one another” (cf. Smaldino 2023, p.120). b.         _Bounded confidence or biased assimilation_ (cf. ibid.). c.         _Negative influence._ Agents who differ, grow dissimilar after interacting (cf. ibid.) 2)         _From experience._ Agents experience and interact with their world, e.g. a human experiences a painful disease and subsequently adapts a more cynical and negative opinion of the world. Or a scientist like Kopernikus observes the motion of planets, and adapts an opinion on the position of the earth in the universe, which is different from the opinion most other people have. In reality, belief formation is often a mix of experience and social influence, but most models simplify this process by treating environmental interactions as static or uniform.   ### 3.2.2 Equifinality in opinion convergence: An illustrative thought experiment Equifinality is a challenge already when considering these mechanisms, as for example both positive influence and biased assimilation on one hand as well as experience on the other can be equifinal explanations and mechanisms for opinion convergence - in both ways, as we defined equifinality in the previous chapter. Take as thought experiment, that we are group of research studying opinion dynamics in a group of peers, for example a small, rather isolated village. On our first day _t0_ arriving in the village _T_, the mayor of the village proposes in the council of the village the idea of building a new bike lane going through the village. Immediately, we conduct opinion polls on this topic _b_ in the village _T_ to measure the first gut reaction of opinions to this proposal and find that for _T0(b)_ we find a wide range of nuanced opinions among the 50 villagers, more or less following a normal distribution. After some time _tn_, e.g. a month or around 700 hours, we return to the village and conduct once again opinion polls to create a data set on _T700(b)_ . Now we find, that the villagers after discussing and thinking about the idea for month, converged more or less around a somewhat neutral consensus, that the bike lane should be build. Now we try to create a model to explain, how this convergence of opinions happened. #### 3.2.2.1 Bayesian Agents Our first idea is, that we treat all villagers as rational Bayesian agents, as they all are somewhat rational and share the same environment. After they first got the idea proposed by the mayor to build a bike lane, their initial gut reaction we polled at _tn_ was a Bayesian prior, but after this, they started to pay attention to their villages traffic and think about how the bike lane might impact the village, gather information and conducting Bayesian updating (cf. Smaldino 2023, pp. 232 – 234). As the villagers are all rational Bayesian agents in our models, interacting with more or less identical data, over time Bayesian updating led all the villagers to approximate the same opinion, which approximates objective reality (cf. Martins 2021). The village achieved enlightenment so to say, arriving at rational, reasonable conclusions, as they are reasonable beings. So, them having all the same opinion after a month is the result objective truth and reason. We simulate this (see for code appendix figure 3) – and indeed, the simulation fits our two data sets _T0(b)_ and _Tn(b)_: ![[Pasted image 20250316124904.png]] #### 3.2.2.2 Positive Social Influence But what, if our Bayesian model isn’t right? What, if the villagers aren’t that enlightened and scientific minded, but just – as they all live in a small village and see each other everyday – extreme people pleasers, very focused on social harmony and having a consensus? The real world and reason don’t matter as much, as social cohesion. So we create a new model, now every time the villagers interact with each other and exchange opinions they slightly adjust their own opinion to the other persons opinion. Over time, as all the villagers talk to each other during the course of the month, their opinions converge at a consensus. This model too does fit our two data points. ![[Pasted image 20250316125008.png]] #### 3.2.2.3 Social Contagion But what if the discourse for the village works way differently: There is one very, very good argument for a specific opinion on bike lanes – and once you have heard it, you will adopt the opinion 0 an try to tell other people about the argument, though with some reduced effectiveness, as each newly convinced person, is slightly worse a retelling the original argument as convincingly as the first person, who came up with it. So the opinion b = 0 spreads like a virus, which gets less effective over time – it’s a viral meme with some decay in relevance. We plot this model, and indeed, it too will more or less fit our two datapoints: ![[Pasted image 20250316125026.png]] #### 3.2.2.4 Coercion by the mob While contemplating whether our villagers are Bayesian agents or people pleasers or just susceptible to rhetorics, we hear a rather wild story: The village is controlled by a powerful mafia clan, which really likes the idea of building a bike lane, as they own the only construction company in the village – also, the head of the clan does really enjoy going on bike tours. So, every day the mobster snatch on average two villagers, threaten or bribe them, to adopt the positive opinion on the bike lane 0. This is a rather strange story but let us code it as a formal model anyway. It too fits: ![[Pasted image 20250316125055.png]] ### 3.2.3 Reflecting on the models from the thought experiment While all four of models here are very simple and the research scenario from our thought experiment a highly simplified strawman, they nevertheless illustrate equifinality as a challenge to modelling opinion dynamics very well, as they exhibit both forms of equifinality in several ways: 1)         As our data set is very limited, all four models are equifinal in the sense of non-identifiability as they are all equal in explanatory power – they all fit the data, all produce the convergence on one opinion in our fictional data set from _T0(b)_ to _Tn(b)_. From the models and the limited data alone, all models are equally strong and we can’t identify the true model. We see in the models that the pathways between the identical data T0(b) and Tn(b) evolve differently, as e.g. Bayesian agents adjust their opinions gradually, while agents coerced by the mob do it abruptly. If we had more empirical data and the opinion distributions between our first day and the finale state, we could easier exclude certain explanations – e.g. we could exclude the mob coercion as an explanation if we see more gradual changes fitting the other models. 2)         All models except for the model of _positive social influence as people pleasing_ (3.2.2.2), are equifinal like an open system is in the sense of General System Theory. If one changes the initial condition or distribution of opinions at t0 in the second model (3.2.2.2), the consensus while change rapidly. So, using von Bertalanfyys original definition (cf. von Bertalanfyy 1988, p.40, pp. 131 – 133), the model of 3.2.2.2 is not equifinal in its function. But the other models are – no matter, what opinion the agents did hold at t0 – if they are Bayesian agents, they will converge on objective reality; if there is a viral great argument, everyone will get infected or convinced at the end; if the mob runs the village, everyone will be coerced to adopt opinion of the mobsters. 3)         Is the village an open system?, is a urgent research question resulting from the models and their data fit within our thought experiment. If the village is an open system, opinion convergence may be driven by structural constraints rather than by a specific underlying mechanism e.g. one could argue, that an village is an open system, which can only survive in the long term, if all inhabitants agree on the most important issues and maintain social cohesion – how this cohesion is achieved, doesn’t matter, as an cultural CAS (e.g. population dynamics like migration across several villages) might create evolutionary selection pressures, leading to the self-destruction of villages without cohesion in the long run. This social cohesion might be facilitated differently in different villages or times. Ultimately our thought experiment highlights the challenge that equifinality presents in modelling opinion dynamics and the need for more empirical data, as incompleteness invites for equfinality in explanatory power of model. While our models differ in their underlying mechanisms, they all lead to the same fitness to our fictional limited empirical data. This demonstrates the fundamental issue of equifinality of non-identifiability in social modelling, where in theory multiple distinct causal processes can generate identical empirical patterns. Moreover, the nature of the system itself—whether it behaves as an open or closed system or a complex adaptive system or how it is shaped by a larger CAS—further complicates interpretation. Without additional data and constraints – e.g. more tracking of individual opinion shifts, experimental interventions, or larger datasets that capture more _tn_ and variables for _T_ – equifinality may lead us to very wrong conclusions on the nature of the village e.g. it being run by the mob. What can be done about this? It is especially necessary to keep in mind, that models are just maps and not the territory of our world – and to be useful, we need to integrate formal models with extensive empirical validation to among other challenges, reduce the possibility of explanatory errors caused by equifinality. ## 3.3 Temporality and Equifinality in Opinions in CAS As pointed out already in in 2.3 and hinted at in the previous section, equifinality in CAS is a rather unstable phenomena, often only a temporary pattern or subroutine within the CAS (cf. Holland 2005 p. 6-7). When trying to model opinion dynamics, this leads to three fundamental challenges: 1)         _Temporal instability of equifinal equilibria processes._ Equifinal outcomes from open systems within the CAS may emerge at certain points in time, but these equilibria are often transient and subject to disruption by new influences, new agents structural shifts, or feedback loops within the system. Examples for this are from biology, dinosaurs getting replaced by mammals as the agents within the CAS ecosystem. Examples for public opinion dynamics, are in general the disruption and reshaping of discourse by new media technologies, which lead to paradigm shifts in gate keeping, opinion leader hierarchies and flow of information. 2)         _Temporal instability and equifinality of models due to evolution_. CAS are adaptive and open-ended (cf. Holland 2005, p. 1-2), meaning the processes we model and measure can shift within our dataset without us noticing, leading to equifinal explanations for phenomena with a temporal dimension. What may have been a dominant causal mechanism at _tn_ may become irrelevant due to structural changes in the system at _t_n+1. This poses a challenge for validating models, as a once-accurate model may fail and be dismissed in a different timeframe, even if it was correct at an earlier stage. 3)         _Parallelism_. A defining feature of CAS is their parallelism (cf. Holland 2005, p. 1-2), which can cause equifinality both in processes as in explanatory models. As many agents and processes run in parallel within a CAS, processes which would be mutually exclusive otherwise and might be explained by mutually exclusive models, might run in parallel, contributing together to a final state. This in result creates two problems: for one, data, which seems to contradict itself, and correct models, which might seem to paradoxically explain sometimes the data and sometimes not. ## 3.3.1 Example for temporality and equifinality: Drivers of radicalization Recent debates on public opinion dynamics have centered around the causes of public polarization and radicalization. During the last few years in these debates, the theory of selective exposure – also known as the filter bubble or echo chamber hypothesis – has been one of the most popular and influential explanations, yet recent studies are pointing to contrary evidence and suggest a different theory, mainly ones of confrontation as negative influence (cf. Cottee 2022; Törnberg 2022). Though most serious researchers of public opinions are aware of the complexity of their shaping, for the purpose of the argument and to illustrate the challenge of equifinality in an accessible manner, we will briefly contrast and strawman the two explanatory approaches to the phenomena of radicalization at the center of this debate. The goal is to show how equifinality in CAS adds a temporal challenge of equifinality to modeling public opinion dynamics, assuming they are part of a CAS. ### 3.3.2 Two opposing theories of radicalization #### 3.3.2.1 Selective exposure For last few years, the dominant hypothesis to explain rising polarization, has been selective exposure, amplified through social media and partisan sorting, leading to individuals isolating themselves on social media and their real life into so called filter bubbles or echo chambers consisting of like-minded peers (cf. Törnberg 2021, p.2). This selective, self-enforcing exposure to like minded individuals is said to lead to the clustering and polarization of society into groups moving toward more and more extreme positions (cf. Törnberg 2022, p. 1 – 3). #### 3.3.2.2 Confrontation Recent data and research suggest that this popular theory of selective exposure doesn’t seem to match empirical data. Recent data on the contrary suggests, that true echo chambers are rather rare and most radicalization steams from negative influence – being exposed to the opinions of political adversaries, makes people more radical in their own world views (cf. Cottee, 2022). ### 3.3.2.2 Reflections These two theories propose fundamentally different mechanisms for how social environments (especially on social media) contribute to opinion polarization, to explain the same empirical phenomena. Therefore, they are initially equifinal in the sense of both being models, which seemingly fit the data. But here in their validation there are challenges stemming from the equifinality challenges outlined above, which I will illustrate by thought experimental explanations or concepts for the sake of argument, as empirical verification is beyond the scope of this paper: _Temporal instability and equifinality of models due to evolution_: The reason, why newer empirical data discredits the filter bubble or echo chamber theory, might be not that the theories were wrong initially, but that they are no longer true as the system evolved. Maybe filter bubbles were the right explanation for radicalisation a decade ago – consequently, the media systems adapted to this issue: social media companies tweaked their algorithms to expose users to more opinions from outside their bubble, and people by a need for Bayesian truth seeking started to look for more contractionary data etc.. But as humans got accustomed to their social media front pages giving them confirmation, which felt good, they now are enraged by being constantly confronted with different opinions. So the system overcorrected, and now exposure to the Other is fostering radicalisation. Both explanatory models are right – just for different points of time. The main issue here is, that if such a shift in the underlying causal mechanism occurs, it might not be apparent in data sets but make empirical validation of models really hard. _Parallelism_. It could be, that both models are right – within specific clusters of the CAS of opinions. It might be, that they act equifinal: While some people become radicalized by being in extreme echo chambers of reinforced radicalization, others might abandon balanced opinions and become radicals due to being exposed to opinions they strongly disagree with. E.g. someone in a right wing extremist group chat, might turn a radical right winger due to being exposed to a lot of right wing content. While someone else, might turn a radical left wing due being disgusted by right wing memes in their social media feed. Contradictory data might be explained by the equifinal processes running in parallel as distinct subroutines of the opinion landscape CAS. ## 3.4 Implications The case of radicalization illustrates how equifinality in public opinions as CAS manifests as  temporal instability and parallelism of explanatory models. Equifinality as a challenge highlights the limits of deterministic explanations in social science—public opinion dynamics are shaped by complex interactions between cognitive, social, technological, and institutional factors, which can’t be as easily modeled as closed systems from physic textbook problems – though some people try to do it in the emerging field of sociophysics (cf. Schweizer 2018). This has several implications: Obviously static models based on a single causal explanations are unlikely to capture the full complexity of opinion dynamics, but they might be considered pieces or maps for certain processes – which might actually explain processes at certain times or places within the CAS, even when they seem to contradict the data initially.  Given that multiple distinct mechanisms can lead to the same observed outcome, traditional validation techniques may struggle to determine which model best explains the data or should be used to make predictions. This has also real world consequences, as generalizing findings across different time periods or social contexts becomes difficult, as a model that accurately describes opinion dynamics at one point or place may fail at another due to shifts in underlying causal mechanisms or equifinal structures. This is especially consequential in regards to policy interventions, as the example of radicalization shows, as opposite processes, which might be seen as a remedy to a problem might actually just make it worse e.g. exposing people to more different opinions to get them out of radicalizing filter bubbles, might radicalize even more people. To address this, future research should prioritize longitudinal studies that track opinion changes over many time tn with a wide range of opinions captured, rather than relying on static snapshots. Adaptive modeling approaches, where models can evolve in response to shifting causal mechanisms, must be pursued further, as they are still underdeveloped and underused. Ultimately, opinion formation in CAS is not governed by a single dominant force. Instead, different mechanisms can be active at different times and in different contexts, and models must be dynamic enough to account for these shifting realities. This of course leads to other trade offs, as models need to be simple enough as well to be useful, but many models in parallel might bring here a completer picture (cf. Smaldino 2023, 318). # 4 Conclusion As outlined in this paper, equifinality represents a pervasive challenge to the study of the dynamic landscape of public opinions. Within open systems, equifinality stems from the structural capacity of these systems to self-regulate, allowing them to converge on similar end states despite having different initial conditions. This basic insight, captured in General Systems Theory, takes on new complexity in Complex Adaptive Systems where agents and institutions evolve and adapt in parallel, producing outcomes that are dynamic rather than fixed. In such contexts, final states or equilibria and the processes causing them may be only temporary subroutines in an ever-evolving opinion landscape. Turning specifically to public opinion dynamics, the problem of equifinality emerges in two main ways, which again branch out into several derived and subsequent problems. First, distinct causal mechanisms can each produce identical or near-identical opinion distributions in a population from the same initial conditions. As a result, researchers may confidently fit a model to empirical data, despite being completely wrong. Second, these mechanisms themselves may shift or co-exist parallel in different segments of a population or at different points in time, making it difficult to generalize models. Empirical data alone cannot unambiguously identify which underlying processes shape observed opinion dynamics. As illustrated by the example of radicalization, even contradictory explanations, like the selective exposure of filter bubbles or the negative influence of polarizing confrontation, can each account for rising radicalisation in different contexts or time periods. From a methodological and philosophical standpoint, addressing equifinality demands more robust approaches to model building and validation. Equifinality in all its forms also demonstrates the limits of purely formal approaches. Academics and policy makers should approach the issue therefore with some humility, as it appears unlikely that the challenge posed by equifinality can be entirely solved. Taking the challenge of equifinality seriously subsequently might facilitate our understanding of the many paths by which opinion are being shaped. This might help us to develop more nuanced insights into how public opinion emerges, transforms, and occasionally converges in a world that will remain complex, adaptive, constantly shifting and opaque until entropy might completely disintegrate the closed system, which is our universe, but that distant future is probably as much beyond the horizon of human civilisation as it is beyond the scope of this paper. # Bibliography Axelrod, Robert (1997): The Dissemination of Culture: A Model with Local Convergence and Global Polarization. In _The Journal of Conflict Resolution_ 41 (2), pp. 203–226. Available online at http://www.jstor.org/stable/174371. Bertalanffy, Ludwig von (1950): The Theory of Open Systems in Physics and Biology. In _Science_ 111 (2872), pp. 23–29. Available online at http://www.jstor.org/stable/1676073. Bertalanffy, Ludwig von (1988): General system theory. Foundations, development, applications. Rev. ed., 10. print. New York: Braziller. 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