Community Uniformity Border Index for Exposure

Community Uniformity Border Index for Exposure (commonly abbreviated as CUBIX) is a proposed measure to determine the fairness of an electoral map (or a group of electoral districts) where first-past-the-post or ranked-choice voting method is used, or any method which results district-based representation for single/multi-representative districts. It incorporates factors like shape of border between 2 districts and the difference in partisanship and demographics in order to measure the intensity of gerrymandering of districts in an electoral map generally done by governments and election commissions to grant unfair benefits to certain individuals, political party(ies) or group(s).

The index was proposed in a research paper titled "Towards a Comprehensive Scale for Measuring Partisan Gerrymandering: Integrating Demographic Uniformity and Border Effects" published by Oxford Journal of Student Scholarship in March 2026 by author Shourya Phadnis.

Mathematical definition

$CUBIX=\frac{\sum _{(i,j)}\{L(i,j)\cdot [{\omega }_{dem}\cdot {\mathrm{\Delta }}_{dem}(i,j)+{\omega }_{part}\cdot {\mathrm{\Delta }}_{part}(i,j)]\}}{\sum _{(i,j)}L(i,j)}$, where

• $i$ and $j$ are any 2 distinct bordering districts in the electoral map (though there is no problem in letting any 2 districts $i$ and $j$ as $L(i,j)$ for any non bordering district is zero, making the entire term zero. Summation includes all combination of 2 bordering districts (or all combinations of any 2 districts) mapped by the electoral map.
• $L(i,j)=\frac{\text{Length of border between the two districts }i\text{ and }j}{\text{Sum of perimeters of the two districts }i\text{ and }j}$
• ${\mathrm{\Delta }}_{dem}(i,j)=\text{Difference in percentage of any binary demographic data between two districts i and j}$

Here, the demographics may include age, race, gender, nationality, income, level of education, etc. (For example, if district 1 has 83% white population and district 2 has 78% white population, the difference is 5% of the population taking population of both districts in account. Hence, with respect to white and non-white race groups, ${\mathrm{\Delta }}_{dem}(1,2)=83\mathrm{\%}-79\mathrm{\%}=4\mathrm{\%}=0.04$ )

• ${\mathrm{\Delta }}_{part}(i,j)=\text{Difference in percentage of partisanship favourable to an ideology/group between two districts i and j}$

Here, partisanship is calculated by percentage of voters of a political party in the electoral districts, which may be calculated by taking an arithmetic mean of all elections happened in the district in a particular time frame (say last 8 years) taking equal weightage or giving more weightage to nearer elections, or by a public survey, or by any method as the observer may seem fit.

• ${\omega }_{dem}(i,j)\text{ and }{\omega }_{part}(i,j)\text{ represent the weightage given to demographics and partisanship in the area consisting districts i and j}$${\omega }_{dem}(i,j)+{\omega }_{part}(i,j)=1\text{ and }{\omega }_{dem}(i,j),{\omega }_{part}(i,j)\in [0,1]$

The weightage must be given carefully. The region where the weightage is to be given must contain districts $i$ and $j$ entirely and exclusively (unless the same amount of weightage is to be given in the entire electoral map if it contains a state or geographical region where society gives partisanship and demographics uniform (which does not imply equal and can be very distant from equal) weightage. If the observer fees that partisanship also includes demographics its weightage, he/she may prefer to keep ${\omega }_{dem}(i,j)=0$ and ${\omega }_{part}(i,j)=1$.

It must be noted that CUBIX is index of an electoral map (of a state or territory), not of a district.

Recognition

The following awards were conferred upon the author Shourya Phadnis for the research paper by Oxford Journal of Student Scholarship.

Winter 2026 awards

Award	Distinction	Rank	Medal
Distinguished Analytical Contribution Award	Highest distinction	1	Gold
Outstanding Paper Award	Distinction	2	Silver

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