What's the best way to get your idea accepted?

We recently had a client ask us to help them with a problem.  The problem is that they believe one idea, but a lot of people believe a different idea.  “Help us,” they asked, “get our idea accepted by the other side.”  No small task, right?  Like any good agency, we tackled the problem strategically and then developed a (what we thought was a pretty good) tactical plan.  We executed and started tracking the analytics and discovered, rather quickly, that our predictions were off – way off.  The campaign was meeting its goals, but through unintended areas of influence.

We predicted X for tactic 1 and it came back Y.  We predicted A for tactic 2 and it came back B.  On and on it went – so much so, that it appeared that our very basic standard model was flawed.  Turns out, it was – at least for this particular case.  It’s always challenging to apply a model designed for one strategy to something new.  What worked as a model for reaching potential customers didn’t work so well for public relations.  I know that seems obvious, but considering the public relations was for a product, we thought it would at least be close.

Everything worked out pretty well in the end, but the analytic nerd in me needed to solve why our predictions were so far off and how we could correct for the future.  I’ve been kicking this around for awhile, and thanks to Yub Wang, Gaoxi Xiao and Jian Liu, we may finally have an answer.

Wang, Xiao and Liu have authored a paper entitled, “Dynamics of competing ideas in complex social systems.” Their excellent paper addresses the idea that individuals accepting an idea may intentionally or unintentionally impose influences in a certain neighborhood area, making it less likely or even impossible for other individuals within the area to accept competing ideas.

Depending on whether such influences strictly prohibit neighborhood individuals from accepting other ideas or not, we classify them into exclusive and nonexclusive influences, respectively.  Their study reveals, for the first time, the rich and complex dynamics of two competing ideas with neighborhood influences in scale-free social networks: depending on whether they have exclusive or nonexclusive influences, the final state varies from multiple co-existence to founder control to exclusion, with different sizes of population accepting each of the ideas, respectively. Such results provide helpful insights for better understanding of the spread (and the control of the spread) of ideas in human society.

Ideas spread in human society through education, public media, religious practices, literature publications, propaganda, rumors, etc. While some ideas can easily spread out with virtually no resistance (e.g. the education of fundamental science in primary schools), others may have to be in face of competition. The competition can be mild or even hardly noticeable, such as those between different opinions in rumor spreading, or rather fierce, e.g. some violent conflicts between different religions in human history.

While the spread of an idea with no competitors, which to a certain extent is analogous to the spread of an infectious disease, has been extensively discussed, studies on dynamics of competing ideas are largely in absence. In fact, even the existing work on the spreading of multiple competing viruses/pathogens is very limited.

The majority of the existing work is on analyzing competing viruses in well-mixed populations, with no detailed modeling of the interactions between individuals. It is only in recent years that a few detailed studies have been conducted on interacting viruses with the aid of graph theory, considering cross protection where individuals infected by one agent are immunized to the other; propagations of two agents in two overlay networks; and a special case where agent A induces agent B which in turn suppresses agent A.

In social science, various voter models have been proposed for studying the dynamics of two different opinions. Typically, it is assumed that each voter may discard his own opinion and accept one of his randomly selected neighbors’ opinions instead. Such models help explain the co-existence of different opinions. Yet the assumption that each individual has to accept one of the two opinions at any single moment (S/he cannot be left idle) makes such models quite specific for studying voter behaviors only.

They argue that the spreading of competing ideas is very different from the spreading of competing viruses. An important feature of idea spreading is that an idea can typically generate some ‘influences’ in a certain neighborhood area. Individuals in the area may not necessarily accept the idea, yet while under the influences, the chance that they accept a different competing idea is usually lowered, or even eliminated in some extreme cases.

Such a feature does not exist in most virus spreading cases and, to the best of their knowledge, has never been systematically studied in existing sociology research either.

In this paper, the authors focus on studying the effects of such neighborhood influences.  Specifically, they consider two representative types of neighborhood influences:

Knowing that a close friend has accepted an idea may not immediately or finally make us accept the same idea. However, it usually lowers the chance that we accept a different idea, at least within a certain period of time. Since the influence from the friend in this example does not eliminate the possibility that we accept a different idea, we term it as nonexclusive influence. An interesting observation is that when under non-exclusive influence, people sometimes may finally accept multiple different ideas, say, by taking them as valid and valuable insights from different points of view.

In a region ruled by extremists, people may be prohibited from accepting any other idea, or be deprived of access to any competing ideas altogether. When such control is strictly implemented, the chance that people accept a different idea may be virtually zero.  They term such cases as exclusive influence. To evaluate the effects of exclusive and non-exclusive influences in idea spreading, the authors consider three different cases with two competing ideas where both ideas have non-exclusive influences; both have exclusive influences; and the two ideas have non-exclusive and exclusive influences.

Considering that many social networks closely resemble scale-free networks with power-law nodal degree distribution, they focus on studying the spreading of two competitive ideas in scale-free networks.  For the spread of two competing agents with cross-protection in scale-free networks, it is easy to figure out that the two agents can always co-exist in the steady state (although a strict proof has never been published in any reference to the best of their knowledge).

Specifically, when two competing agents spread out in scale-free networks following the susceptible–infected–susceptible (SIS) scheme, at any single moment neither of them can infect all the high-degree hub nodes, unless we assume that at least one of them has nearly infinite transmissibility. It is known that in sufficiently large scale-free networks, leaving a non-zero percentage of hub nodes unprotected causes persistent existence of infection.

Therefore, the two agents definitely co-exist in the steady state. For two competing ideas with exclusive and/or non-exclusive neighborhood influences, however, the dynamics is much richer.

Specifically, the main conclusions of the study can be summarized as follows:

For competing ideas both with non-exclusive influences, they may have multiple coexistence states: the final states of the two ideas with comparable transmissibility and strong neighborhood influences are determined by their initial densities, while the idea with a relatively higher transmissibility can easily suppress its competitor to a low level.

For two ideas both with exclusive influences, they can never stably co-exist in scale-free networks regardless of their respective transmissibility. The possible outcomes can be classified into founder control, (where the final winner is determined by the initial densities of the two ideas) or exclusion (where one idea steadily drives out the other).

For two ideas with non-exclusive and exclusive influences, respectively, the one with exclusive influence has a chance to drive out its competitor altogether. However, this is guaranteed to happen only if its transmissibility is high enough compared to that of its competitor. Since it typically takes non-trivial effort (energy) to have exclusive influence in a neighborhood region, which may consequently lead to a lower transmissibility, it may not be a favorable strategy to try to have exclusive influence. In fact, for both the cases of non-exclusive influence versus non-exclusive influence and non-exclusive influence versus exclusive influence, when subject to limited resources, it helps enlarge the size of acceptance at steady state by focusing on increasing the transmissibility of the idea rather than weakening the neighborhood influence of the competitor.

Theoretical analysis and numerical simulations verify the above conclusions in random scale-free networks.

From an agency perspective, the formulas they provide may be very useful in predictive modeling in determining influence of ideas and concepts, especially from a social media or public relations perspective.

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