Abstract
We propose a new historyfriendly approach to evolutionary socioeconomic dynamics based around competition between five ‘utopias’ as central ideas about which to order society: capitalism, socialism, civil liberty, nature, and nationalism. In our model, citizens contribute economic resources to support their preferred utopia, and societal dynamics are explained as a coevolutionary process between these competing utopias. We apply the model to analyze certain aspects of socioeconomic and political change in the US from the 1960s–present. We carry out a historyfriendly analysis inspired by such episodes as the outbreak of civil movements in the 1970s, the rise of neoliberalism in the 1980s, and the channels through which America has engendered an ‘age of fracture’. Further applications for empirical and theoretical research are suggested.
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Notes
This particular set of five is somewhat arbitrary – there could be more or fewer. Our economic actor/citizen is (directly or indirectly) affected by the state of all of the subsystems but, as citizen, our agents seek to promote one of these subsystems in preference to others.
It is difficult to calibrate and measure the “level of effort” in effective terms, since it is composed of observable (time, financial and material resources) and nonobservable (e.g. personal abilities, effort, skills, connections, knowledge) variables.
See the initial intrasubsystem shares in Table 2 with a low value for \( {\ s}_{20}^M \); this implies that the neoliberal mass can develop in its niche with almost no direct challenge from closemoderate positions; they perceive a very low negative externality from \( {\ s}_{20}^M \).
See the MisesKeynesian debates on the viability of socialism, e.g. Paul Samuelson’s failed predictions of the future of the Soviet Union in the first edition of Economics.
Note that there are a few constraints that must be taken into account when changing the values of the parameters in Table 3, namely:\( {\sum}_i{s}_{i0}^{\pi}=1 \) for all π ∈ Π, and \( {\sum}_{\pi \in \Pi}{\gamma}_0^{\pi}=1 \). To ensure that the restriction \( {\sum}_i{s}_{i0}^k=1 \) is maintained when adding a certain (positive or negative) value δ to the default value \( {\left({s}_{j0}^k\right)}^{DV} \) of any parameter \( {s}_{j0}^k \), we subtract δ/2 from the default value \( {\left({s}_{i\ne j0}^k\right)}^{DV} \) of the other two parameters \( {s}_{i\ne j0}^k \). Similarly, when adding a certain (positive or negative) value δ to the default value \( {\left({\gamma}_0^k\right)}^{DV} \) of any \( {\gamma}_0^k \), we subtract δ/4 from the default value \( {\left({\gamma}_0^{\pi \ne k}\right)}^{DV} \) of the other four parameters \( {\gamma}_0^{\pi \ne k} \) so that the restriction \( {\sum}_{\pi \in \Pi}{\gamma}_0^{\pi}=1 \) is maintained. This procedure implies that the range of admissible values that can be explored for a particular \( {s}_{j0}^k \) is often smaller than [0,1], since we must also honor the conditions \( {s}_{i\ne j0}^k\ge 0 \). To be precise, the admissible range when changing a particular \( {s}_{j0}^k \) is \( \left[0,\kern0.5em {\left({s}_{j0}^k\right)}^{DV}+2\cdotp { \min}_i{\left({s}_{i\ne j0}^k\right)}^{DV}\right] \). The same argument applies for \( {\gamma}_0^k \) and the conditions \( {\gamma}_0^{\pi \ne k}\ge 0 \). The admissible range when changing a particular \( {\gamma}_0^k \) is \( \left[0,\kern0.5em {\left({\gamma}_0^k\right)}^{DV}+4\cdotp { \min}_i{\left({\gamma}_0^{\pi \ne k}\right)}^{DV}\right] \).
Only values of α and β that make 0 ≤ x _{ i } ≤ 1 are admissible.
The effect of changing the value of α is merely a change in the time scale. This can be easily proved analytically conducting a change of variable t ^{∗} = α · t. The lowest value of β that we have checked is 10^{−5}.
As explained before, any change in a parameter \( {s}_{i0}^{\pi} \) or \( {\gamma}_0^{\pi} \) forces us to alter the value of other parameters to ensure that the constraints\( {\sum}_i{s}_{i0}^{\pi}=1 \) for all π ∈ Π, and \( {\sum}_{\pi \in \Pi}{\gamma}_0^{\pi}=1 \) are preserved.
Note, however, that this does not imply that strategy 3 will be wiped out in the Replicator Dynamics. Weakly dominated strategies in the Replicator Dynamics may remain present forever. In this particular case, strategy 3 obtains a strictly lower payoff than strategy 1 at any point in the interior of the simplex, but the dynamics may lead the process “quickly” towards the boundary s _{3} = 1 − s _{1}, where the selection pressure over strategy 3 disappears.
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Acknowledgements
We would like to thank Daniel Chirot, J. Stan Metcalfe, Scott Montgomery and Richard R. Nelson for their very helpful comments on previous versions of this work. We also thank two anonymous referees.
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Supplementary material: https://luisrizquierdo.github.io/utopia
The reader can replicate all simulation results presented in this paper by using the computer program provided in the supplementary material. This program can be run using NetLogo (Wilensky, 1999).
Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and ComputerBased Modeling, Northwestern University. Evanston, IL., open source software available at http://ccl.northwestern.edu/netlogo for free.
Appendix
Appendix
In this appendix, we present further insights on the intrasubsystemic dynamics of the model, and on the way these dynamics coevolve giving rise to the overall dynamics of utopia competition. The exhaustive mathematical exploration of the model goes beyond the scope of this paper. Nevertheless, we want to highlight here some possible lines of progress in the formal exploration; likewise, we present certain results which clarify the mechanisms supporting our socioeconomic insights in Section 4. We do not incorporate these results in Section 4 because, perhaps, they might interrupt the historyfriendly style of discussion of the paper.
As we show in this Appendix, it is interesting to note that, although we have presented the model as a coevolution framework that contributes to evolutionary political economy in line with population dynamics thinking, we can use machinery from evolutionary game theory to better understand the dynamics and the results. This is a typical way to proceed in population models (see Weibull 1995; Hofbauer and Sigmund 1998; Sandholm 2010). Thus, in this appendix, we show, firstly, how the intrasubsystem dynamics can be decomposed for future analysis in two extreme subgames and infinite mixes of these subgames. This procedure allows us to better understand the role of parameter φ in the model and in our results (persistence of various coexisting utopias, etc). Afterwards, we consider these insights to reflect on the overall replicator process (expression (3) in Section 3) which is interlinked (in a bidirectional way) in the model with the distinct intrasubsystem replicators (expressions (1) and (2) in Section 3, and the bidirectional links with expression (3)). We present new simulations as supporting material for the socioeconomic interpretations in Section 4. The appendix also helps us to pose possible future developments (departing from the current model as a benchmark) as we explain in Section 5.
Insights on the dynamics of the model
Decomposition of the intrasubsystemic dynamics
Note that the payoff for each level of contribution (eq. (1)) can be written as follows:
Thus, at the intrasubsystem level, eq. (2) can be seen as the replicator dynamics of a population game where players are randomly paired to play a 2player 3strategy game where the payoff matrix is:
Let us consider the extreme values of φ. For φ = 0, we have the following game (henceforth SG1, for subgame 1):
Given that x _{1} < x _{2} < x _{3}, strategy 3 is dominant, and evolutionarily stable. Thus, the point s _{3} = 1 is asymptotically stable and the system converges to it from any initial condition with s _{3} > 0.^{Footnote 14} The speed of convergence will be faster the greater the value of \( {\gamma}_t^{\pi} \). Figure 11 below shows the phase portrait of the dynamics of this game in the 2dimensional simplex.
For the other extreme value φ = 1, we have the following game (henceforth SG2, for subgame 2):
In SG2, strategy 3 is weakly dominated by strategy 1.^{Footnote 15} It is not difficult to prove that the rest points of the replicator dynamics for SG2 are:

1.
All points in the line s _{2} = 0 (and s _{3} = 1 − s _{1}).

2.
Point: s _{2} = 1. This point is unstable, as it is invadable by strategy 1.
Figure 12 shows the phase portrait of the dynamics of this game in the 2dimensional simplex.
Therefore, in terms of our model, when φ = 0, and citizens (within their subsystems) are purely partisans (in the sense that they just care about the rise to prevalence of their utopia, without paying attention to possible opportunistic behaviors by their peers in (1)) then, said subsystem tends (in isolated conditions) to a maximum average degree of citizen contribution. On the contrary, when permeability is absolute (as given by φ = 1 in (1)), then citizens perceive (or take advantage of) possible opportunistic behaviors and the subsystem tends to stabilize (in isolated conditions) in the lowest degree of citizen contribution. Of course, we have a continuum of possibilities between subgames 1 and 2, but we can infer that the lower the value of φ in a subsystem, we should tend to obtain higher average levels of commitment in said subsystem. Likewise, when φ is high, then low levels of commitment in the subsystem, or fluctuating paths driven by the ongoing revision of strategies, are expected. In any case, notice that when we couple the subsystems (considering (1), (2) and (3) together in Section 3), then the shares of the subsystems in society also evolve, and the effect of φ in the payoffs gets mediated by endogenously changing subsystem shares, and intrasubsystem behaviors. This much more complex situation is the one we see below.
Insights on the overall dynamics
Taking into consideration the decomposition shown in the previous section, and assuming φ > 0, note that the dynamics of subsystems with very low share \( {\gamma}_t^{\pi} \) are driven by SG2, so in such vanishing subsystems eventually strategy 1 becomes dominant, strategy 3 may hold some minor share, and strategy 2 effectively disappears. In the general case, the dynamics of subsystems with a nonnegligible share \( {\gamma}_t^{\pi} \) will depend on the value of φ.
Low values of φ
As pointed out above, in subsystems with low share \( {\gamma}_t^{\pi} \), SG2 drives the dynamics, so eventually strategy 1 becomes prevalent, strategy 3 may hold some minor share, and strategy 2 effectively disappears.
In subsystems with high share \( {\gamma}_t^{\pi} \), SG1 drives the dynamics, so strategy 3 is clearly favored, and the greater the value of \( {\gamma}_t^{\pi} \), the faster the convergence to strategy 3. A greater share s _{3} induces an increase in \( {\gamma}_t^{\pi} \), thus creating a selfreinforcing dynamic.
Which particular subsystem(s) will end up with a significant share \( {\gamma}_t^{\pi} \) will depend on initial conditions. A high value of \( {\gamma}_{t=0}^{\pi} \) and, particularly, a high value of \( {s}_{3, t=0}^{\pi} \) will be key. As a representative example, consider Fig. 13, where φ = 0.03.
High values of φ
As in the previous case, in subsystems with low share \( {\gamma}_t^{\pi} \), SG2 drives the dynamics. The analysis of the subsystem(s) with significant share \( {\gamma}_t^{\pi} \) is more complicated, as both SG1 and SG2 influence the dynamics. As an example, consider the case where φ = 0.8 and there is a subsystem with \( {\gamma}_t^{\pi} \) ≈ 1. This game shows cyclic dynamics, as can be seen in Fig. 14 (where x_{1} = 0.3, x_{2} = 0.45, x_{3} = 0.6). Figure 15 shows the overall dynamics of a simulation run where the Market subsystem prevails, and its intrasubsystemic dynamics are cyclic.
A final example
In intermediate situations where both SG1 and SG2 play a role in the intrasubsystemic dynamics of some subsystems, the overall dynamics can be very different from the extreme cases outlined above. As a final example, consider a model with x_{1} = 0.3, x_{2} = 0.45, x_{3} = 0.6, φ = 0.16, and two subsystems with \( {\gamma}_t^{\pi} \) = 0.5. In this setting, strategy 2 is dominant, and the associated intrasubsystemic dynamics can be seen in Fig. 16.
Figure 17 shows the overall dynamics of a simulation run where the conditions outlined above are approximately met.
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Almudi, I., FatasVillafranca, F., Izquierdo, L.R. et al. The economics of utopia: a coevolutionary model of ideas, citizenship and sociopolitical change. J Evol Econ 27, 629–662 (2017). https://doi.org/10.1007/s0019101705077
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DOI: https://doi.org/10.1007/s0019101705077
Keywords
 Utopia
 Citizen
 Subsystem
 Political economy
 Coevolutionary modeling
JEL classifications
 B52
 O57
 P16
 P51
 Z10