Does inequality slow everyone down?

Has a trial on London Underground escalators uncovered a mathematical formula to reduce inequality? They discovered that organising the transport system around a few who want to go further and faster than everyone else holds back the many.

The protocol on the London Underground has always been to stand on the right of an escalator so people in a hurry can walk past you on the left and get to the top quicker.

This works OK on short escalators. But on long, steep escalators the results are surprising. Fewer people are inclined to walk up long ones, so the benefits of getting some to the top faster diminishes.

The London Underground ran a trial in December, which I found out about via blogger Jason Kottke.

Researchers asked commuters at Holborn station to stand two abreast, and not walk up. They chose Holborn because it has one of the steepest escalators. At a vertical height of 24 meters, only 40 per cent of commuters would even contemplate walking to the top.

The results seem counter-intuitive: Standing still on the escalator was faster and more productive.

Operating the system for the few who wanted to run up had halved the capacity of escalators and created crowding at the bottom. Everyone but the few running up the outside went slower. Add to that the effect researchers called ‘the human ellipse’, where we don’t like standing adjacent to someone on the same stair, and we prefer a stair between us — above and below. The ‘stand aside’ system was grossly inefficient.

An escalator that carried 12,745 customers between 8.30 and 9.30am in a normal week, for example, carried 16,220 when it was designated standing only. Getting people to stand on both sides meant 31 more passengers get on to the escalator every minute — an increase of 28%. At a vertical height of 24 meters, and walking on the left, the present system accommodates 81.25 people per minute. With both sides standing still, the escalator could carry 112.5 people each minute.

Everybody moves faster when the system is more equal.

But not everyone welcomed losing the choice to walk. “Can’t you let us walk if we want to?” asked another. “This isn’t Russia” “This is a charter for the lame and lazy!” said another. The pilot was “terrible”, “loopy,” “crap”, “ridiculous”, and a “very bad idea”. One man pushed a child to one side to get to the top faster.

My maths are not up to it, but can someone derive the algorithm from these figures, then apply it to inequality?

Assume vertical height is the accumulation of wealth, and for these purposes let the person standing still on the escalator represent the share of increasing GDP of working people. The few who run to the top are individuals who accumulate wealth fastest; making them increase their ‘vertical height’ at the same rate as others would be the equivalent of an redistributive tax on their wealth or income.

Using a model built from these assumptions, what could we say about the benefits for overall productivity in the economy of a more equal economy?

I think the analogy works: Most people can’t avoid the long queues caused by congestion on the escalators, just as most working people, by definition, can’t be the few who rush past to make it to the top. There is an effect on overall wealth production from some people taking a greater share than others. If you can calculate the size of the growth effect, and compare it to the incentive effects of working harder, you can probably derive the ideal tax ‘wedge’ — the optimal level of taxation in the economy.

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