Opinionista Clinton Nortje 6 November 2019

Why maths is important to politics

The Institute of Race Relations’ views about Broad-Based Black Economic Empowerment have come under public scrutiny and the institute has been accused of being ‘tone-deaf’. A matric-level maths problem might help us understand their position.

Maths regularly proves that our intuition is just plain wrong. The infamous Monte Hall problem is a commonly quoted illustration of this fact.

The problem is named after the host of the Let’s Make a Deal game-show, where contestants were given the choice of three doors, one of which concealed the grand prize. Let’s say a car.

After choosing the door that they thought the car was behind, the host would eliminate one of the other two doors. The contestant was then given the option of sticking with their original choice or changing their mind.

Intuitively, most people think that it makes no difference whether you stick to your original choice or change your mind – 50/50, right?

Wrong.

Maths proves without a doubt that sticking with your original choice would give you a 1/3 chance of winning the car while switching gives you a 2/3 chance of winning. You may be screaming at the screen right now but trust me, it’s true. Google it.

A similar debate rages around transformation in South Africa, and specifically, the Institute of Race Relations’ (IRR) views on empowerment.

The organisation’s world view has recently been placed under significant public scrutiny which, given their vocal criticism of the DA as well as their seemingly linked membership base, is entirely warranted. However, the dominant narrative that the organisation’s position on empowerment is racist, or at the very least “tone-deaf” to the issue of race seems to be without merit.

If I take a charitable view of this narrative, then perhaps the misrepresentation is not deliberate, but rather a case of human intuition being at odds with mathematics as was the case in the Monte Hall problem.

My understanding of the IRR’s position is that they do not deny that poverty disproportionately affects black people in South Africa, and they do not deny that apartheid and colonialism played a big role in how poverty disproportionately affects black people.

So far so good.

They also believe that empowerment and transformation are best achieved through individual upliftment and not by using race as a proxy in the way that Broad-Based Black Economic Empowerment (BBBEE) policies do – it is at this point that many commentators throw up their arms at the seemingly incongruous statement.

It is clear that poverty and inequality affect black people more than white people, so why wouldn’t you use race as a proxy. Must be a desire to protect privilege, right?

Not really.

When you look at the maths behind this, it paints a different picture. Consider the following word sum (matric learners are doing it, so can you.): You have 100 pairs of socks in a wash basket (80 blue and 20 red) and a total of 75 pairs of these socks are dirty (70 blue and 5 red), and you can only wash 15 pairs of socks at a time. Your goal is to make sure that all of the blue dirty socks are cleaned in as few washes as possible.

How many washes would it take to make sure that all of the blue socks are clean if you: Identify all dirty socks and begin to wash them in batches of 15; select 15 random blue pairs of socks to wash at a time, and return them to the wash basket when cleaned and repeat the process.

In option A, we would have a 100% probability that all blue socks are cleaned after 5 washes. As a bonus, all of your red socks will also be clean.

In option B, we are not guaranteed that we are washing only dirty socks, so let’s set an arbitrary acceptable percentage of dirty socks that we would like to be washing in each cycle at 80% (12 pairs of dirty socks out of 15 chosen).

On our first wash, things look good – because 70 of the 80 socks are dirty, you have an 89.22% chance of selecting at least 12 pairs of dirty socks. If we assume that we keep managing to clean 12 pairs of socks on each cycle, by the time we have completed three cycles, we have a 0.36% chance of selecting at least 12 dirty pairs of socks. In fact, there is only a 27.6% chance that even half of the socks we are washing are dirty.

Doesn’t seem that efficient, does it?

In the above example, we can think of the 15-sock limit as the amount of opportunity that exists at any given time.

Option A can be thought of as upliftment policies based on individual circumstances that the IRR seemingly promotes and option B as BBBEE policies that focus upliftment on the group of people that are most affected by inequality and poverty.

When you evaluate these concepts mathematically, it seems to suggest that tackling the problem of redress is counter-intuitively best tackled by ignoring race and focusing on the actual circumstances of individuals.

This may not fit the dominant narrative, but it is hard to argue with the logic. You may not agree with the IRR, but dismissing this particular position as racist or tone-deaf is just lazy. DM

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