Rational sharing and its limits
First Monday

Rational sharing and its limits by Wai-Yin Ng



Abstract
People differ in their willingness to share, as well as their reasons to do so. An open collaboration community of willing sharing members thrives on a virtuous cycle: increased sharing often offers stronger reasons for more people to share. However, it may also decline when the cycle goes the opposite direction and turns vicious. What determines the dividing line? We offer insights into this important question based on an analytic understanding of the concept of rational sharing, which is sharing for net gain in personal utility. In a nutshell, a community thriving on rational sharing is essentially an economic system, a platform for creating mutual benefit through exchanges.

This analysis is based on our prior work in statistical modelling of peer–to–peer systems. There are two salient features. First, the shared content is modelled as a mixture of different types of goods. Members’ sharing is pooled and organized into supply, which in turn is brought to match with demand from the members themselves, and a wider community also in the case of open access. The importance of the goodness of match between supply and demand is therefore apparent. Second, incentive schemes are modelled simply as dependence between the quality of service a member sees and the level of sharing. Being simplistic, it points to an interesting generic observation: no incentive is strong enough to break the catch–22 situation during startup unless some seed content is present.

We are not suggesting rationality as the only conscious basis of sharing for individuals. Quite the contrary, we gauge the limits of rational sharing thereby, and identify when and how non–rational bases of sharing is needed. For instance, high quality open access Wikis we witness today would not have been sustainable if sharing had been purely rational, as meaningful reward in quality gain has to be reserved for enticing rational members.

Contents

Introduction: Open sharing, rational sharing
Sustaining content and membership: Between virtuous and vicious cycles
Marginal rates of content and membership changes
Variety in content and variety in behaviour
A basis for rational sharing
Rational sharing limits growth
Incentive scheme and rational sharing
Learning effects and social effects
Concluding remarks

 


 

Introduction: Open sharing, rational sharing

Openness has multiple meanings. Here we consider two specific ones. First, an open community allows people to join or leave as they wish. Second, joined members pool their stuff together which the community offers open access to all. We shall address such a community simply as an Open Sharing (OS) Community. The stuff they pool together for sharing may be information as in Wikis, resources as in GRID computing, or both as in peer–to–peer file sharing. In general, we shall address the pooled stuff as the community’s content.

For simplicity, we assume people prompt the content continuously for their changing demand, and jump in and out of the community rapidly as they are satisfied or frustrated with the results. For a file–sharing community for instance, it corresponds to people logging in once they desire some file, and logging out immediately as what they desire is not found. Also, when a member leaves, the community’s content is always compromised. Even for a Wiki which records all contributed writings, a leaving member would cease to write and edit for it. Content accumulation rate as well as quality improvement rate are reduced. If members continue to leave, the community may be at stake. The compromised content frustrates many prompting members, who would leave immediately and lead to further content compromise, and membership loss. A vicious cycle thus sets in.

What’s desirable is obviously the opposite of such a vicious cycle: as new members join and the content is enriched, it attracts more members and enriches its content further. In this way, the dynamical changes of the community’s membership and content feed upon each other. Under what conditions would a virtuous cycle occur? When would a vicious cycle set in instead? What determines the dividing line between the two? These are the questions that we studied previously in (Ng, Lin and Chiu, 2005) and (Ng, Chiu and Lin, 2005) by means of an analytical model of an OS community.

Drawing upon insights from our previous works, here we focus on people’s sharing behaviour. Folk wisdom praises member’s social spirit of generosity and altruism as necessary for a community to prosper. On the contrary, self–interest would breed free–riding behaviour that restrains from sharing. Such selfish interest, or rationality in economic term, should always be checked. Reputation systems such as those of Amazon’s or eBay’s that reward sharing, or BitTorrent’s tit–for–tat choking strategy (Cohen, 2003) that penalizes mean uploaders, are incentive schemes that serve such purpose. However, our previous work finds that self–interest and sharing are not necessarily incompatible. Instead, a rational basis of sharing behaviour is possible for an OS community. Furthermore, rational sharing may suffice to sustain such an OS community without resort to a social spirit.

This article describes rational sharing and how it may sustain an OS community. Our goal is not suggesting rationality as the only conscious basis of sharing for individuals. Quite the contrary, we want to gauge the limits of rational sharing thereby, and identify more clearly when and how non–rational bases of sharing, such as generosity and altruism, are indispensable for good openness.

 

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Sustaining content and membership: Between virtuous and vicious cycles

We first give a primer of the model of OS community developed in Ng, Lin and Chiu (2005) and Ng, Chiu and Lin (2005). The original model is analytic and describes the statistical mechanics of the join/leave behaviour of a large population. Here a qualitative description would suffice.

Equilibrium of high membership with rich content is obviously a desirable state for an OS community. Stability is essential in the face of many sources of fluctuations in the real world. As members may change in behaviour, the content also fluctuates in amount and quality. A stable equilibrium relies on sufficient restoring forces as the community shifts away from its equilibrium state. Growth of an open sharing community is naturally checked when the population is finite. The richest possible content they may share would also be finite. The single key to stability is therefore whether a random, perhaps accidental, reduction in membership or content would be checked by a restoring virtuous cycle.

Figure 1: Phase plane of an open sharing community

Consider charting the dynamics of an OS community on a graphical plot of content (Y) versus membership (X), an X–Y phase plane as in Figure 1. Both X and Y are proportions of their respective maximum values, and between 0 and 1. As people prompt the content continuously and jump in and out of the community rapidly, a statistical equilibrium may be expected. If a given level of content would satisfy people’s demand with probability p say, it would draw a membership of the same proportion on average. Obviously, empty content satisfies nobody. A richer content always sustains a larger membership. As a result, the trace of all such statistical equilibrium points would run from the origin in the bottom left towards the upper right corner. If all content together would satisfy all people always, the trace would end at the upper right corner.

If, at some point of time, the community finds itself with a rich content even with a low membership, somewhere in regime I say, a virtuous cycle may be expected for two reasons. First, as even a small proportion of the population already share a rich content, it is good evidence that the population comprises people who are ready to share. Second, as the majority of the population is still outside, the influx of new members from them, drawn by the content, would easily offset the outflux of any current members who are frustrated. A net growth in membership may be expected. Regime I therefore belongs to a growth zone.

If the community finds itself with a sizeable membership but relatively poor content, somewhere in regime II say, a vicious cycle would be expected instead, the reasons being converse of the two reasons above. Regime II therefore belongs to a shrinkage zone. In fact, the equilibrium trace is the dividing line between the growth zone on its left and the shrinkage zone on its right. If the community evolves and crosses the equilibrium trace at some point, its change would reverse in direction. Restoring forces on either side would tend to stabilize it at that equilibrium point in a statistical sense.

There is a second important dividing line, situated in the shrinkage region. If the community finds itself with content so poor for the current membership that the resulting vicious cycle may reduce it all the way to zero without ever crossing the equilibrium trace. If Y T is the threshold proportion of content that is just insufficient for a full membership (X=1) to cross the equilibrium trace, the trajectory traced by the vicious cycle from (1,Y T) towards the origin would give this second dividing line. The region below this line would be a death zone. The community is doomed whenever it finds itself in it.

 

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Marginal rates of content and membership changes

As an OS community evolves, content and membership always change in the same direction. However their marginal rates of change would vary, being dependent on the sharing behaviour of the population. The relative rate of content and membership changes would also govern the direction of its trajectory on the X–Y phase plane. For instance, if the relative rate is 2% content gain per 1% membership gain at a certain point, the trajectory would move at a slope of 2%/1% = 2. A high value reflects a high level of sharing. For a given community, we may trace all its average trajectories by following the relative rate directions over the entire phase plane. In the case of a budding community beginning its life near the phase plane origin, a high level of sharing is necessary for it to avoid the death zone and grow with a high enough slope towards a sustainable equilibrium.

Since the content is upper bounded, decreasing marginal rate in content gain would set in sooner or later. The relative rate, and the trajectory slope therefore, would tend to decrease as the content increases. The trajectories in the growth zone would always bend towards the equilibrium trace sooner or later. A higher level of sharing implies a steeper trajectory that bends later, towards an equilibrium with richer content and higher membership.

Also, the marginal rate of membership change would diminish as a trajectory approaches the equilibrium trace on either directions. It simply implies that change slows down when the community gets near a stable equilibrium, whether while growing or shrinking.

 

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Variety in content and variety in behaviour

So far our description is about the average case. The real picture is statistical with much random fluctuation. The X–Y trace of a changing community fluctuates about the average trajectory. The amount of fluctuation is crucial, especially in view of the death zone. Accidental death may happen if random fluctuation is large enough to shift a trace into the death zone. Naturally, we assume death to be irreversible. Random fluctuations in the good directions never compensate enough for those in the bad directions that increase the risk of accidental death. Large random fluctuations can be fatal.

The amount of fluctuation is dependent on how much variety there is, for which there are two important sources. First, when people vary in their sharing behaviour, the content level may vary even for a given membership size. Second, when the content comprises a large variety of different things, the proportion of satisfied demand, for a given total content level, would also fluctuate. Therefore, both variety in behaviour and variety in content would increase the risk of accidental death of an otherwise sustainable community.

Also, when people’s demand may vary over a wider variety of content, the proportion of satisfied demand would actually reduce on average, for the same reason that the hit rate of a fixed–size Web cache reduces as the Web increases in size. This directly reduces the relative rate of content and membership changes. For a small community near the origin of the X–Y phase plane, it may never sustain any growth as a result. Too much variety when the content level is low is not good. A community with more focused content would be more viable.

 

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A basis for rational sharing

We are now ready to examine rational sharing by means of the OS community model.

A rational self–interested member would see benefit in satisfied demand, and cost in sharing. Such a member would be willing to share more as long as it leads to marginal benefit that more than compensates for the marginal cost. The key quantities are again the marginal rates. When the community is in the growth zone, an increase in sharing by any member would see multiplying effect in the content level due to the prevailing virtuous cycle. The enriched content should satisfy his demand more. The marginal rate of cost–benefit change for a member may be called the community’s response to his sharing. Following the classical economics approach, we may assume a utility function that measures the value of different cost–benefit combinations for a rational member. Furthermore, the slope of the indifference curve at a cost–benefit level gives a marginal rate of substitution, namely, the threshold benefit needed in exchange for a unit cost with no net utility change. A rational member would increase sharing as long as the community’s response to his sharing is larger than his marginal threshold benefit level. In equilibrium, he would be sharing at the level where the two are equal.

The rational sharing level for a member therefore depends on two factors: his own utility and the community’s current content. A member with a low marginal threshold benefit tends to share more. Conversely, free–riding without sharing would be rational for one whose marginal threshold benefit is above the current community’s response. As long as the population has sufficient people with marginal threshold benefit levels that are low enough, a virtuous cycle may be driven by sharing behaviour that is purely rational and self–interested.

 

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Rational sharing limits growth

As the community grows in membership and content, the marginal rate in content gain would decrease sooner or later, and decrease community’s response to sharing. As a result, the rational sharing levels of the population would decrease, and limit the community’s growth. Furthermore, utility functions tend to exhibit decreasing return too, for the psychological reason that a typical person would demand more than before, for the same utility increase, when he is rich. Both effects reduce the rational sharing levels. The growth trajectory of a community is bent more, towards an equilibrium with less rich content. The equilibrium therefore sees less satisfied demand. An alternative interpretation is that the service level has to be restrained, so as to preserve room for good community’s response to entice sharing.

As rational sharing levels decrease, the equilibrium trace itself is shifted also, and towards the right. The same equilibrium content level requires a larger membership to sustain. Such a larger equilibrium membership comprises members who share less on a rational basis, perhaps including many free–riders, for whom the community’s response is below the threshold benefit they need for sharing at all.

 

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Incentive scheme and rational sharing

Any incentive scheme can be a two–edged sword, in two different ways. First, it is a two–edged sword for the community. An incentive scheme rewards good behaviours and penalizes bad ones at the same time. Second, it is a two–edged sword for the system: implementing an incentive scheme is always costly, which may result in net gain as well as net loss even when the community as a whole behaves better as expected. While eBay obviously needs a sophisticated reputation system to reduce costly frauds, Amazon would perhaps neither need nor afford anything much more complicated than the simple positive reviewer ratings. For instance, adding negative ratings may improve the overall quality of reviews, but there may be fewer reviewers and less traffic as a result.

A self–interested rational population can be tricky to incentivize, since an incentive scheme may alter their responses only indirectly through altering their cost–benefit calculations. When an incentive scheme is introduced to a community already sizeable in equilibrium, the resulting change may be carefully observed. Any undesirable changes may be reviewed and the incentive scheme revised if necessary. The case for a budding community during start–up could be much more risky. An incentive scheme may be an overkill before any growth allows sufficient observation.

For a budding OS community, an incentive scheme may indeed be unfavorable towards sustainable growth (Ng, Chiu and Lin, 2005). Consider the general case when a member’s demand for content may be satisfied to a controlled degree, in the time taken, the level of details of the reply, and so forth. A typical incentive scheme may set an individual service level, namely, the degree of satisfaction, according to the member’s level of sharing. For such an incentive scheme, we have derived an analytic result which implies two important necessary conditions for the community to grow. First, free–riding has to receive strictly lower service level, otherwise no rational members would share and the virtuous cycle needed for growth would not happen. Second, there needs to be some content even when membership is negligibly low. The necessary virtuous cycle needs a kick, which has to be some content to begin with. This would be a paradox, a catch–22 situation, for a community that relies solely on sharing for content. Before any member shares, there would be no content. Without content, no rational member would care to share. A common solution would be to jump start the community, one way or the other, with some seed content, perhaps contributed by a fellowship of enthusiastic non–rational members. It is indeed the case for many online communities of hobbyists, developers, hackers, etc. For communities with commercial sponsors such as eBay and Amazon, the seed content comes naturally from the sponsors themselves.

 

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Learning effects and social effects

Free–riding is an emotional term, and free–riders are sometimes penalized, even shut out altogether. In a BitTorrent file sharing community, any member who saves all bandwidth for downloading would be “choked” and receives no transmission from other members. This is reasonable when bandwidth resources being shared are rivalrous goods in nature. Bandwidth being used is bandwidth locked and not available until the user releases it. Free–riding consumes valuable resources otherwise available to well–behaved members. For community whose content is less rivalrous, free–riding may be more tolerable. When the content being shared is primarily information which may be replicated rapidly with little or no cost, the real cost of free–riding hinges on whether any underlying resources being used are constrained.

In practice, allowing people to free–ride may be necessary for the growth of a good community as they that helps draw new members by words of mouth. Also, free–riders themselves may learn to value the community more over time, so much so that some of them may share eventually. People’s cost–benefit profile often changes for the better as they learn. When they know better about good content, becoming more familiar and dependent on it, they would benefit more. When they become more skillful and resourceful, sharing would cost them less too. Sooner or later, they may find it beneficial to share on a rational basis, if not simply because they want to. Open content projects such as Wikipedia are excellent examples in this regard. Many contributing users of Wikipedia begin as read–only users who learn their way towards writers and editors.

Apart from learning effects, social effects also adds drive to OS communities, especially those in which like people collaborate. Many developers may be drawn to online open source communities for the opportunity to interact with fellow developers whom they may be hard to find in their everyday lives. Source codes may function in an open source community like beer in a pub. In the mean time, open source software users benefit from the community the way beer traders do from the pubs. More generally speaking, social effects stem from basic human nature. The open phenomena today are largely social phenomena arising out of our basic social instinct. While rationality alone may be sufficient sometimes, it is impossible to account for the extent of openness we witness today.

 

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Concluding remarks

It is certainly good news that an Open Sharing community is sustainable even if sharing is purely rational. It should help settle some skeptics, and save worries of sympathetic onlookers. Much classical works of economics assume self–interest rationality and still manage to offer a solid foundation for many human institutions of competing interests. It should not be surprising that open collaboration and access find rationality to their advantage too. Also, Benkler (2004) offers another an alternative analysis to show that certain goods are inherently sharable. A personal computer is inherently sharable in that it has to be bought in whole, and costs the owner nothing more in sharing excess capacities which are otherwise not used. Carpooling is another obvious example.

The main purpose of this article is to focus our attention on the limits that rational sharing poses. Within those limits, incentives are already built–in and stem from people’s sel–-interest. Beyond those limits, an open community may be more vulnerable, and its prosperity becomes reliant on either incentive schemes that expand those limits, or non–rational positive drives of the members. The contribution of a social spirit of generosity and altruism may be appreciated and analyzed more properly in this light.

We want to conclude with an interesting insight from our ongoing work. In principle, design of any incentive scheme requires a proper accounting of the costs and benefits of any action. When the content comprises a variety of stuff, such as the many different pieces being shared in a music file sharing community, the contribution of any piece should be calculated with respect to the drive of the virtuous cycle it causes. This depends on how many new members the piece appeals to, as well how many more new members are appealed to by the pieces that these new members will share, and so forth. If a virtuous cycle tends to bring in stuff of the same sort, it would appeal only to the subset of population interested in it. The resulting growth would be limited. Therefore, our guess is that members actually contribute more when they share a variety of different stuff, driving a virtuous cycle that appeals to a wider proportion of the population. In Ng, Chiu and Lin (2005), we simulated a stylized model of a population with content comprising two sorts of stuff. When members share the same sort of stuff they demand, two communities, each sharing one sort, would result. When they share in a mixed manner, even for the same quantity of sharing, the single community that arises can be much larger than the two communities combined. End of article

 

About the author

Wai–Yin Ng received his B.A. in 1985 (specializing in control and operational research) and Ph.D. in control engineering in 1989, both from the University of Cambridge, and is associate professor in information engineering in the Chinese University of Hong Kong. His current research focus is in complex networks, a young vibrant science concerned with connectivity, complexity and emergent phenomena in both natural and artificial systems. Within and beyond a university profession, he is interested in education, human intelligence, open communities and interdisciplinary communication.
E–mail: w.ng [at] acm [dot] org

 

References

Yochai Benkler, 2004. “Sharing nicely: On sharable goods and the emergence of sharing as a modality of economic production,” Yale Law Journal, volume 114, pp. 273–358. http://dx.doi.org/10.2307/4135731

B. Cohen, 2003. “Incentives build robustness in BitTorrent,” Proceedings of the First Workshop on the Economics of Peer–to–Peer Systems (Berkeley, Calif.); and at http://www.bittorrent.org/bittorrentecon.pdf.

W.–Y. Ng, W.K. Lin and D.M. Chiu, 2005. “Statistical modelling of information sharing: Community, membership and content,” Performance Evaluation, volume 62, numbers 1–4, pp. 17–31.

W.–Y. Ng, D.M. Chiu and W.K. Lin, 2005. “Club formation by rational sharing: Content, viability and community,” Internet and Network Economics (Proc. First International Workshop, WINE 2005, Hong Kong), pp. 161–173.

P. Resnick, R. Zeckhauser, E. Friedman, and K. Kuwabara, 2000. “Reputation systems,” Communications of the ACM, volume 43, number 12 (December), pp. 45–48. http://dx.doi.org/10.1145/355112.355122

 


Editorial history

Paper received 1 May 2006; accepted 17 May 2006.


Contents Index

Copyright ©2006, First Monday.

Copyright ©2006, Wai–Yin Ng.

Rational sharing and its limits by Wai–Yin Ng
First Monday, volume 11, number 6 (June 2006),
URL: http://firstmonday.org/issues/issue11_6/ng/index.html





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