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The magic of Zipf’s law can be used to tackle voter apathy

Dr Pali Lehohla is the former Statistician-General of South Africa and the former head of Statistics South Africa. Photo: Thobile Mathonsi

Dr Pali Lehohla is the former Statistician-General of South Africa and the former head of Statistics South Africa. Photo: Thobile Mathonsi

Published Nov 7, 2021


THE failures in local government are well documented in the reports of the Auditor-General and the lived experiences of citizens.

As the campaign for elections moved, citizens cut a grim picture as they sidestepped streams of sewerage and dirty water where water was available and long queues of empty buckets waiting for the possibility of water where taps have run dry. Now we have the results. Not only that, but we also know how they panned out.

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The electorate have given a clear message that elections are not about service delivery, but about the circus of the elected at the expense of the electorate.

These groups refused to go to the polls. They said they will not be part of the circus.

The sad part is that among those who participated, there are those whose desire is to continue the circus, while the others participated in the circus with the hope that things will change.

The message is very clear and is compounded by the space in which we are as a country and the globe. The model of democracy as we have interpreted and acted upon it is a farce. The question is how do we change it?

Before I get drained by my soliloquy, allow me to secure solace from the centre that I contributed to creating in 2010 as the Statistician General. This was the Centre for Regional and Urban Innovation and Statistical Exploration (Cruise) at the University of Stellenbosch.

The key focus for creating this centre was to ensure that as Statistics South Africa, we produced appropriate data that fundamentally respects spatio-temporal waves to go beyond the national level but expand to advise local government programmes.

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An intellectually stimulating subject that was taken by the successive cohorts was that of Zipf.

Dr Hlabi Morudu, who was in the first cohort on the MPhil programme, decided to look at Zipf’s law, to the excitement of Professor Mannie Geyer.

Zipf’s law “is an empirical law formulated using mathematical statistics that refers to the fact that for many types of data studied in the physical and social sciences, the rank-frequency distribution is an inverse relation.” In his paper, Dr Morudu explored how this law applies to the city hierarchy in South Africa and makes the following important observations which are relevant for societal renewal of vows to democratic participation.

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He notes vast differences among South African local municipalities. There are in this regard a small number of large municipalities (both in terms of population size and economic activity) and a seemingly disproportionate number of intermediate-sized and small municipalities.

He identifies the challenge that there is no clear systematic national approach to assess the distribution of core variables at municipal level in South Africa.

He concludes that the results indicate that the Zipf rank size rule distribution is applicable to municipal level population data in South Africa, but less so for Gross Value Added and municipal income.

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Dr Arul Naidoo, another of the members of the first cohort at Cruise, and I have been sharing notes on what we could consider as a modified Zipf. We focused on the results of the poll that each party obtained.

The results show that the runner up to the party with the majority polls is half the size of the first, the second runner-up obtained half the results of the second largest party, the third runner-up was half the third largest.

The magic of Zipf is that it has explained itself in ways that those who held their vote in protest have done so with such regularity that their actions generated halving the relative size in the sequence of size of polls of parties from the biggest polling to the smallest polling.

Hopefully Zipf may change our thinking and lead to better participation in claiming the democracy back from kleptocrats.

Dr Pali Lehohla is the former Statistician-General of South Africa and the former head of Statistics South Africa. Meet him @ and @Palilj01.

*The views expressed here are not necessarily those of IOL or of title sites.