Weighting the Data

In order to make disparate raw data comparable and most useful, it is relativized through a system of normalization and non-linear aggregation. These procedures are explained below.

Score Normalization

Since the range of Indicators are measured in diverse ways, the algorithm required a method of normalization such that each Indicator could be scored on a common scale.

For example, ‘Unemployment’ is generally measured as a percentage of eligible individuals who lack employment; thus, a lower percentage is desirable. By contrast, ‘Life Expectancy’ is typically measured in years, where a higher score is desirable. Thus, normalizing Indicator scores involves mathematically translating these raw values onto a 0-100 scale, where 0 is the worst possible value and 100 is the best.

Constraint of Linear Aggregation

Forms of linear aggregation allot equal weight to each part comprising the whole (such as the average or mean); thereby failing to reflect the complex relationships between Indicators and Considerations. For example, while a high score should be an indication of effective performance, aggregating scores linearly (where each is weighted equally) can obscure outlier scores, such as particularly well or poorly scoring Indicators.

To promote clarity and accuracy in exploring community performance of the 35 Considerations, CitiIQ employs non-linear aggregation to combine Indicator scores and to accurately highlight the “gaps” which may otherwise be overlooked.

The following figure illustrates the bias linear aggregation can introduce into a model. The linear score is calculated by averaging the four scores and the non-linear score is calculated on a weighted basis.

Normalization Formula

One of four different approaches may be taken to normalize an Indicator depending upon its characteristic as follows:

Linear

Used when there are defined maximum and minimum values that the Indicator can take. The raw value is scaled proportionally between these values, as shown in the graph.

Exponential

Used when there is a precise minimum value the Indicator can take, but no defined maximum amount. As shown in the graph, when the raw value of the Indicator is small, the scaled value increases rapidly, but as the raw value becomes larger and larger, the scaled value gets closer and closer to 100.

Sigmoid

Used when the maximum and minimum values of the Indicator are not defined. The graph tends towards 0 for small raw values, and towards 100 for large raw values, but most of the change occurs within a smaller range of values.

Bell Curve

Sometimes there is an ‘ideal’ value for an Indicator, and anything larger or smaller is not as good. In this case, the bell-curve graph is appropriate, where the shape is determined by the standard distribution parameters, the mean and the standard deviation.

Non-Linear Aggregation

The CitiIQ algorithm employs several forms of non-linear aggregation.

Firstly, an Indicator will most likely influence more than one Consideration; however, may not influence each Consideration to the same degree. For example, the Indicator ‘Greenhouse Gas Emissions’ informs the 3 Considerations “Energy Supply”, “Resilience” and “Green Space”. As the following diagram indicates, this Indicator carries a different weight for each Consideration, reflecting the known strength of its relationship to each Consideration.

Secondly, in the same way the top of a pyramid is only as secure as it’s lower layers, so a city’s measure of wellbeing depends firstly on the primary Dimensions. A community may have a high score for “Signature + Identity”, but if the scores for “Water Supply”, “Food Security” or “Shelter + Housing” are low it does not have a high measure of wellbeing. As a result, only when the primary Dimensions of wellbeing are satisfied, do the other Dimensions factor meaningfully into the score.

The CitiIQ algorithm presents a more accurate critique of the priorities necessary to improve a community’s wellbeing.

The following visualization demonstrates an example of how the 35 Considerations, the 5 Dimensions and the City as a whole might be scored for a particular community:

The following figure illustrates the total CitiIQ score.

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