Cosimo Chiera and Tom Edwards, "Impacting Neighbourhoods: Mathematical Measures"

Conference paper presented at Urban Life Together: Inhabiting Our Neighbourhoods, October 17-18, 2014, Urban Seed. Published online November 12, 2015.



Neighbourhood and community interventions represent an important positive influence on our society. However, the current funding climate requires that interventions mimic business plans in so much as proposing clear objectives, methods and metrics through which a project can be evaluated. This approach, while being seen as providing due diligence for funding organisations, is often at odds with the community-centred approach of contemporary interventions and the organic nature of community change. Nevertheless, the authors propose a simple mathematical model using a limited number of variables which may assist community organisations to: (1) a priori predict the degree of change likely in an intervention; and (2) assist in a post-hoc evaluation of the project. The Victorian Children’s Koori Court is used as a case study to validate this model and show how it may be applied to other community interventions.


Background and Model

Philanthropy is a growing concern in Australia with the peak body Philanthropy Australia increasing in membership from 477 in 2012 to 715 by the end of 2013.[1] In addition, various government departments, both State and Federal, make funds available for a range of projects designed to increase the social capital of Australia. However, funding bodies rightly need to do their due diligence, and this requires those applying for funding to clearly state the purpose of the project, often with predicted outcomes, use a validated methodology and, following completion, provide an extensive evaluation. The last of these is increased in importance if ongoing funding is to be sought.

However, community interventions are typically organic: growing and changing with the needs of the community who, through an action-learning model, take ownership of the intervention. That this is so often makes such interventions difficult to design and evaluate. To this end it is vital that the community sector have access to tools which will help them: (1) better to express their ideas to funders; (2) to predict outcomes; (3) to assist in working efficiently during project implementation by making timely “course corrections”; and finally (4) to evaluate projects in light of the stated objectives. To achieve these goals a simple mathematical model is proposed.

In brief, we propose that project performance can be evaluated as a trajectory on a two dimensional mathematical sheet represented in three-dimensional space. As such only three variables are required to encapsulate the main features of this model. Arising out of a psychological worldview they are: (1) r0 as the initial “resistance” the community has to change; (2) the duration (d) over which the project will occur; and (3) a measure of the relative threat (T) vs. control (C) the community feels (see Figure 1).[2]


Figure 1: The model represented as a two-dimensional sheet in three-dimensional space. Changes in r(d, T, C) are seen as a consequence of changes in its contributing variables being duration (d) and threat vs control (T – C) and the initial condition of community resistance (r0). Note that when (T – C) exceeds the ‘Order one’ (O(1)) by one or more orders of magnitude the model is considered to be unstable and may be akin to aberrant behaviour. This is represented by the plateau seen above.

Mathematically this sheet is defined by:

From this model we can map trajectories onto the mathematical sheet described in Figure 1 above. In doing so, each trajectory describes the progress and outcome for a community intervention given either: (1) the weight placed on each variable during the intervention’s design; or (2) after the intervention’s completion, the weight of each variable observed and mapped for evaluative purposes. For example, given a community with a moderate resistance to change and an equal duration for two interventions we can map their respective trajectories (see Figure 2). In brief, the “negative trajectory” in Figure 2 demonstrates the failure of the intervention because either the threats the community faced were so large, and/or there were insufficient control elements put in place by the intervention’s designer. By way of control elements we refer to those aspects of the project which build personal autonomy and self-esteem as well as community cohesion. By contrast, the positive trajectory in Figure 2 represents a successful intervention outcome as, in this instance, the project designer most likely focused on the inclusion of substantial control elements which empowered the community and overwhelmed any threats which may have been present.


Figure 2: Two trajectories representing a successful community intervention (positive trajectory) and an unsuccessful community intervention (negative trajectory). In these instances the relative levels of threat vs control were fundamental in producing the opposing outcomes.

From this model it is also apparent that if community resistance is high and project duration brief then particular emphasis must be placed on implementing control elements if positive change is to occur. Alternatively, if community resistance is reduced or duration extended then control elements should still be included in the intervention to bring about positive change, but their emphasis need not be as great. As such this model speaks to what is possible given a particular community, the ability of the intervening organization to bring sufficient resources to bare, and project duration.

However, this model also predicts some less intuitive outcomes. For example, while high levels of threat are likely to adversely affect the community over time the complete removal of threat may result in a community which feels freed of any onus of responsibility leading to either social breakdown or unconscionable conduct towards other groups.

We see this situation where control overwhelms threat (C >>T) most plainly in the modern celebrity. As social restraint diminishes (T is small and C is very large), we see more and more outrageous and socially disruptive behaviour. As such, we observe that when freed from the normal threat of social chastisement people believe themselves to be “entitled” or “grandiose,” and behave accordingly. At a community level this may be observed in a variety of ways including poor social cohesion through to institutional discrimination.

Taken together, optimum outcomes occur when control elements in the environment outweigh threat elements by only a small amount, say no more than 10% of the larger of the two values. It is as if this relationship produces a community motivated for change.

A Demonstration of the Model

To demonstrate the value of this model in a real world, if not local, context, let us look at an evaluation of the Victorian Children’s Koori Court (CKC). The Children’s Court of Victoria states that the purpose of the CKC is:

… to address the over-representation of young Koori people in the criminal justice system. By involving the Koori community in the court process through the participation of Elders and Respected Persons the Koori Court aims to reduce offending behaviour and reduce the number of young Koori people being sentenced to a period of detention.[3]

Established in 2005 the CKC has been rolled out to nine sites in Melbourne and across regional Victoria, demonstrating its success. However, it is not good enough simply to acknowledge the success of the CKC by noting its persistence and growth over the last nine years, nor to validate the work of the CKC by making vague statements about the value of therapeutic justice— although these are true of themselves—we require metrics. Usefully the CKC has been thoroughly evaluated and these evaluations published. For example, Borowski evaluated the outcomes of 62 offenders who appeared before the CKC in its first two years of operation (2005–07) and tracked these individuals for between 6 and 30 months.[4] Four key findings can be identified from his work. First, a “very low” failure to appear rate. Second, a “very low” rate of breaching court orders. Third, a recidivism rate of approximately 60%, which is comparable, if not slightly less, than other studies assessing similar defendants in the traditional court system. Fourth, that for recidivists their subsequent crimes were typically only of equal of lesser severity than the original crime dealt with in the CKC. In trying to measure the degree of success of the CKC in its first two years of operation it is reasonable to measure each key performance indicator on an ordinal five point scale: very low success, low success, average, high success and very high success. In doing so the first two key performance indicators could conservatively be rated as highly successful, the third as average and the fourth as again highly successful. Therefore, overall the CKC may be regarded as a highly successful community intervention.

To determine if our mathematical model will demonstrate similar findings let us first understand how we might evaluate the three variables of initial resistance, duration and threat vs. control. Taking initial resistance first, Borowski noted that, at face value, a substantial recidivism rate and that approximately 50% of CKC defendants had prior involvement with the Department of Human Services (DHS).[5] With respect to criminal matters approximately 40% of CKC defendants had prior convictions while approximately 40% had prior warnings or diversions, leaving only 20% without prior police or judicial involvement. Such data would suggest these individuals to be highly resistant to change. However, we must also note their ages as typically between 15 and 19 years old at the time of their CKC appearance. Given their youth it is reasonable to suggest that they may be less resistant than adults. As such we suggest that the defendants studied had an overall “medium” level of resistance. The second model variable, duration, is given as 1.5 years as this represents the average between 6 and 30 months of observation by Borowski.

Finally, to threat vs. control as the third variable. The CKC represents an interesting model of court practice where control elements significantly outweigh threat elements. For example, it is a sentencing court and thus does not practice in the typical adversarial manner. Sentencing is designed to be therapeutic, not punitive. The atmosphere of the court is relatively informal with all parties sitting around a common table. Moreover, the defendant has their own lawyer and other Indigenous workers may also be present. The court also promotes Indigenous culture through a smoking ceremony and the use of Indigenous art. Curiously, the presence of elders or respected people as part of the court may be viewed differently by various defendants. In some instances they may act as a control element providing support, for others they may cause shame and thus be viewed as a threat. Nevertheless one clear threat element remains within the CKC: the Magistrate who remains in charge of sentencing. Nevertheless, the CKC prefaces control over threat by a large degree. Taken together we can now plot a trajectory on the sheet described in Figure 1 and determine the likely success of the CKC given our model. In summary, for mid-level resistance and a high degree of control the trajectory at d = 1.5 years agrees with our assessment and the assessment of others that the CKC is a highly effective community intervention (see Figure 3).

Figure 3: A validation of the model using the CKC as an example. For a medium level of initial resistance and when control elements significantly outweigh threat elements then at a duration of 1.5 years a high level of success is observed for the CKC.


Taken together this model suggests a number of important consequences for those doing community work. First, it is now possible to model various intervention designs to determine which will be the most effective given the community profile, duration and available resources. In addition, this model allows an intervention’s trajectory to be plotted such that at different time points along the trajectory, say d = 0.5, 1.0, 1.5 and 2.0 years, one can evaluate project success and make any required “course corrections.” Finally, the model allows one to understand if the intervention’s proposed outcome has been reached. If so, a strong argument can be made to a funding organization for ongoing support. Taken together, this simple model allows those doing important community work to now utilize metrics to secure funding and manage scarce resources to maximize change.


[1] Philanthropy Australia, “Annual Report” (2013), (accessed November 18, 2014).

[2] Tom Edwards and Cosimo Chiera, “Personal Narratives: A Mathematical Model for Their Behavior with Cross-disciplinary Implications,” Storyworlds, under review.

[3] Victorian Government, “Koori Court,” Children’s Court of Victoria, 2012, (accessed November 18, 2014).

[4] A. Borowski, “Indigenous Participation in Sentencing Young Offenders: Findings from an Evaluation of the Children’s Koori Court of Victoria,” Australian & New Zealand Journal of Criminology 43, no.3 (2010): 465–84; A. Borowski, “Evaluating the Children’s Koori Court of Victoria: Some Key Findings” (Occasional Seminar, Australian Institute of Criminology, 2010), (accessed November 18, 2014).

[5] Borowski, “Indigenous Participation in Sentencing Young Offenders,” 465–84; Borowski, “Evaluating the Children’s Koori Court of Victoria.”


Image: Cosimo Chiera and Tom Edwards