The Pareto effect in tipping social networks: from minority to majority

This manuscript presents a literature review on social norm diffusion/contagion on social networks, and whether a critical mass similar to a Pareto effect is observed. The manuscript makes a relevant and important contribution to the expanding literature on social tipping by aggregating the available empirical evidence on tipping dynamics. I also appreciate that authors clarify and describe tipping-related concepts and terms in Section 2, yet I believe that manuscript would benefit from a more condensed version of it.

My main concern is how “social tipping” is implicitly defined in the manuscript, and that it is not clearly aligned with the real-life examples of what social tipping in the climate change and sustainability context entails. For instance, the manuscript focuses on social networks and complex contagion, but does it mean that all social tipping process, such as rapid reduction of EV battery costs, coverage of climate change in the school curricula, as identified in the authors’ own paper from 2020, have to include contagion dynamics through a social network? Even if we can rightfully represent many of those in networks, do we have to? Is the presence of a network structure necessary condition for tipping?  How does this relate to the existing social tipping and “positive” tipping literature that does not necessarily focus on networks? Answering such questions would improve the manuscript.

Relatively minor comments:

Lines 75-88 : This paragraph does a fair job in listing the objectives, yet they sound a bit too ambitious. For instance, “we identify critical factors influencing tipping processes in social systems” is eventually only limited to a handful of studies included in your review on social networks, therefore I suggest to reformulate these objectives more consistently with the actual methods and results.

Figure 1a:  I don't find this figure very clear especially considering the accompanying text. If the “shaded area represents the domain where the system exhibits a nonlinear response” would any nonlinear curve above the y=x line mean "tipping"? How about the zone below the line? It might also include very nonlinear changes.

Line 121-122: “where roughly a 20% change in a system control parameter results in an 80% change in the system state at equilibrium”. I am not sure if this is the right formulation of your idea. What happens as lambda moves from 0.1 to 0.12, which is a 20% change in the control parameter?

Line 126-127: “the shown Pareto CDF depicts a scenario in which a minority of actors have convinced a large majority to switch to another social norm.” I think it doesn't show that one, because the y axis is F when t goes to infinity, the final state. When lambda=0.8, we end up at >0.8 and no tipping occurs. The pareto cdf line covers many different scenarios not necessarily those where a minority convinces the others.

Figure 1b: Appreciating this plot of tipping dynamics over time, yet it is the typical s-curve of transitions/innovation adoption. Could you expand on what makes it “tipping”? Furthermore, it is not clear on the figure what the tipping threshold is, as suggested in Box 1.

Line 182: Using cascade and social tipping interchangeably. “Cascade” has been used (in the GTPR) recently to refer to the tipping dynamics in different systems affecting each other, both for climate tipping points and positive tipping points. This terminology choice might be confusing for the readers.

Figure 3: Not clear what the x- and y- axes represent.

Line 368: 21 papers were discarded because they did not include complex contagion. It would be useful to mention what they included instead.

Table 4: Very useful table summarizing the  reviewed studies. To strengthen the conclusions of the manuscript, we need to know more about these studies, though. Could you specify sample size/network size, geographic location, what the nodes and edges are, socioeconomic and demographic background etc.?

Figure 6: Very informative figure especially because it distinguishes between model-based and empirical studies! The sample size is confusing, though, since the caption says that it includes 87 papers and the text earlier mentioned the eventual # of studies in the review were ~30. Please clarify. It raises the question of what made the empirical studies with a similar lambda around 20% but not tipped (bottom left). This figure could have been improved in a bubble chat format, where the dot size refers to the network size in each study. “Population size” came up as one of the most important drivers in Fig.4, and we do observe its relevance. For instance, the global percentage of vegetarian population is 20%, but no tipping is observed.

Line 518- Evidence of critical mass: For the empirical studies covered in this paper, it would be very informative for the strength of evidence whether they are in lab settings or in a real-life experimental setting or contain large-scale data?

Line 531-533 “For modellers…” : Could you expand on “validation across modelling approaches” for computational efficiency? There are examples of system dynamics models which do not use a complex contagion and threshold approach, but show that the inflection point of the norm adoption function (the counterpart of the cdf of the probability of an agent adopting a norm for the fraction of agents who already adopted it) is the most important driver of large scale change in the diet context. How do we for instance cross-validate those? https://www.nature.com/articles/s41893-019-0331-1           

Line 542: Undermining what you did.

Minor comments:

Line 45 “mechanisms. In which…” please watch the grammar.

Line 174 Please clarify what “systems-dynamics” is, since it is not a commonly used term.

Line 338: Which “Ref”?

I suggest to put table captions above the table, since it is a more commonly used convention.

Line 497: table x

The first paragraph of Section 5: I suggest to divide this paragraph and several others, since they are too lengthy and contain more than 1 argument, main point etc.