# Sovereign Wikirating Index

 Wikirating needs somebody who wants to update the economic data for the SWI.

##  Criteria and Base-Data

The Sovereign Wikirating Index (SWI) uses the following five criteria (with weights):

The resulting value is scaled by multiplying it with a social factor, which is composed by the Human Development Index (HDI)[1], the Corruption Perceptions Index[2], and the Political Instability Index[3].

Each criterium is calibrated with respect to the relative minimum and maximum value of all countries. For some criterion a threshold value is defined in order to avoid distorted values.

Short Title Long Title Value Weight Real Min Real Max SWI Min SWI Max
HD Human Development Index Weighted index of development indicators 60% 0 1[scale 1] 0 1
CO Perceptions Index Index of perceived corruption 20% 0 10[scale 1] 0 1
PI Political Instability Index Index of political instability 20% 0 10[scale 1] 0 1
PD Public Debt Debt/GDP as %, reflects the economies ability to honour loans. 50% 0 15 90
AB Current Account Balance Current account balance as % of GDP, reflects foreign inflows and outflows. 20% -∞ -20 20
PG GDP Growth Domestic growth an an annual % 10% -1 -0.1 0.1
IR Consumer Price Index CPI as % 10% -1 0.02 0.2
UR Unemployment Rate Rate of unemployment as % 10% 0 1 0.03 0.3
R Rating Result of SWI calculation as % 0 1 0 1
1. 1.0 1.1 1.2 Raw Data of social scaling factors is divided by the Real Max value to normalize the input.

##  Formula

Definition Explanation
Let c be an element in the set of countries C:
$c \in \left\{ \mathbf{C} \right\}$
That means that every c is a country.
Let R be the vector of ratings, so that
$\forall c:\ R_c \in \left[0,1\right] \subset \R$
That means that Rc is the rating for the country c and every rating is ranging from 0 to 100%.
Let $\operatorname{dim}\left(v\right)$ be the dimension of v. The function $\operatorname{dim}$ basically counts the number of elements in the vector. In example, $\operatorname{dim}\left( R \right)$ is the total number of ratings and thus the number of rated countries.
Let $\operatorname{min}\left(v\right)$ the minimal, and $\operatorname{max}\left(v\right)$the maximal value of v. These functions find the smallest and the biggest number in a set of numbers, such as a vector. This is needed for normalization.
$\operatorname{norm}(v) = \frac{v-\min(v)}{\max(v)-\min(v)}$. We are defining a scale-normalizating function on an vector v.
Let $\operatorname{B}(x) = {\mathbf C} \times \left\{ \mathrm{HD, CO, PI, PD, AB, PG, IR, UR} \right\}$. x is a matrix. We define the base B of this matrix, so that it contains vectors with factors for individual countries in the direction xc, while the economic and social factors are in direction xi.
Let $s\in\left\{\mathrm{HD,CO,PI}\right\}$ and $e\in\left\{\mathrm{PD,AB,PG,IR,UR}\right\}$ s is an indexer for the social factors and e is the indexer for economic factors.
wHD = 60%, wCO = 20%, wPI = 20%, wPD = 50%, wAB = 20%, wPG = 10%, wIR = 10%, wUR = 10% Applying the weights. The vector wi contains the (scalar) weights for the individual economic and social factors.
$r = \left( x^s\,w^s \right) \cdot \left( x^e\,w^e \right)$ By using the Einstein notation, we weight and sum the social factors to get the scaling factor. We also weight and sum the economic factors. Then we multiply the two results.
$R = \operatorname{norm}\left(r\right) + \left(1-n \right)\cdot \left( 1-\operatorname{norm}\left(r\right) \right)$ We finally do some normalisation on the rating r, so that the resulting values are ranging from 0 to 100% and the values represent the performance relative to the other rated countries. The result of this formula is the SWI rating R. n is a vector that contains the number of given ratings for a specific country and thus the trust in the values.

##  Calculation

The actual calculation of the values is done with a spreadsheet (wr_swi_method+data_2011-09-26.xls).

### General Variable Modifiers

For example, the variable AB.

• AB = Number used in calculations for SWI.
• rAB = Raw or real value, actual data from source in whichever format it is acquired.
• wAB = Weighting value for the data.
• minAB = Floor value of variable, will cause ABC to equal 0 or 100 if ABC is below this value.
• maxAB = Ceiling value of variable, will cause ABC to equal 0 or 100 if ABC is above this variable.
• nAB = Number of ratings (for rating)

So for instance, if the real value (rAB) was 4 on a 10 point scale, this would be divided by 10 to create the value for calculations (AB) which, in calculations, is multiplied by the weighting (e.g. 0.5 for 50% weight.)