Good question. Assessment of these critical mass i economics and social systems is often complex as many variables contribute to change in these systems. In addition, sensitivity, resilience, and transformability of systems play a role in what these critical thresholds are. A historic analysis of particular case studies might be useful in answering such questions

Difficult question. I think there is no exact theory. In some papers on politology the goal is to predict voting. There are different types of agents, with strong and weak preferences towards a party or social objective. A party can easily win few % of strong followers, but a lot of investment in marketing has to be done to win people with weak preferences. That is why money often make politics.

In the case of critical situation (like revolutionary situation) the things may go different. I think that there is critical mass of active people who can ignite the rest of the mass for social motion. But there should be objective conditions like critical impoverishment of population (see the works of V.I.Lenin about revolution)

Even though I'm not sure that I exactly understood what you are refering to; I think that if you are looking for possibilities to modelling social phenomena such as solidarity (which might also be described with reference to social capital) it is worth having a closer look at concepts from social network analysis.

Good morning Timothy O Randhir,

I totally agree that, to propose a model of social change (in particular, community) is necessary to start from a historical analysis historical analysis of the factors responsible for changes. The paradox seems to occur only here: times are totally different from those traveled by the human society so far. If we think about it, the culture is different, not to mention if  the wonders of the internet ... that turned Earth into a small global village. The challenge, in terms of solving the problem, seems to occur just by radical changes in society.

Dear Volker G. Täube,

I find it very interesting Your opinion. Trying to get documents about the social networks I found some interesting information about community Methernitha in Linden, Switzerland. Unfortunately, there are very few information about this community, so I can't understand the mechanisms of functioning and possible replication in other areas.

Ronald Inglehart has been working with the World Values Survey since the 1970s. It is a survey instrument that is repeated every 5 years or so and encompasses a large number of societies. In Modernization, Cultural Change and Democracy, he and Christian Welzel examine the link between what the call post-industrial values and the ability of a society to sustain a democratic government. They do not give a precise answer to the percentage of people who hold [pst-industrial values in a society needed to make this transition, but looking at their tables, it appears to be 30% to one third. Whether that would hold for other kinds of social change is uncertain. 

Thank You, David Schak!

Thank You, Yuri Yegorov!

Thank You, Yuri Yegorov!

Use insights from sociophysics and econophysics-of tiping points, and momentum.

http://gps.ijl.univ-lorraine.fr/webpro/berche.b/Seminaires/TalkKrakow.pdf

http://arxiv.org/pdf/1006.0928

http://jasss.soc.surrey.ac.uk/9/3/reviews/edmonds.html

Critical mass is an important milestone for any company. Critical mass is an ever changing target and not a constant one time only goal. The challenge is to keep updated with current definitions and recognize the point where the business has reached a self-sustaining and stable state. Obviously achieving critical mass does not happen on a prescribed timeline and it can vary between companies even if they are in the same industry. Collective action usually depends on a "critical mass" that behaves differently from typical group members. We simply assume that individuals take account of  how much others have already contributed in making their own decisions about contributing to a collective action.

Your question, it seems to me, relates to estimation. This implies some statistical approach. This, in turn, requires data. So you need some feature of social change that occurs over and over. I suggest neighborhood change.  Suppose that a society has two well defined groups of urban residents. These groups could be religious, ethnic, tribal, recent v. long-term residents, whatever. Then you need a theory of neighborhood change from one group to another. Next you need to gather data that support a test of your theory. Finally, you need a statistical test of your theory. Let me know when and if you are ready for these stages of your research.

Dear Peter, I think that the issue of critical mass is a strongly non-linear phenomenon. We may think about it from the perspective of dialectical materialism, as a transition from quantity into quality. We have many of such phenomenon in nature: landslide, when the slope has critical angle for wet substance, explosion of atomic bomb, emergence of epidemies, etc. Statistics may be not the proper instrument for such studies when we have no background theory. Simply because these are relatively rare phenomena, and we cannot collect good statistics for transition. It is much more difficult than to collect statistics for equilbrium state, below the critical mass.

Critical mass is important for emergence of some actions or even firms, when we have scale economies. For example, young and not rich people want to rent a bus for some travel, but cannot afford its rent if their number is below critical mass, let say 10.

I think that the key methodology is derivation on non-linear dynamical systems that model those phenomena. Parameters of those systems can indeed by estimated using statistics. For example, average number of contacts per person, % of situations when his/her opinion was changed under external influence, etc.