“the average bus-passenger is on a bus that’s much more full than the average bus” Paradox

Following on from me discovering the yogi berra paradox for the first time a few weeks ago, today I discovered another paradox which I feel stupid for not knowing about before now. This one doesn’t seem to have a proper name or anything more about it online, but I think it’s really interesting and quite relevant to transport planning.

It’s basically what it says on the tin. Consider a town that has 5 buses: 1 bus carries 40 passengers, while the other 4 buses only carry 2 passengers each. The average bus patronage is 9.6 people per bus (48/5).

But yet almost all the passengers are on a bus with 40 people. Each one sees this many people on their bus {40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 2 2 2 2 2 2 2 2}, of which the average is 33.7.

So transport planners will calculate the average as 9.6 people per bus, but the average bus user sees 34 people everytime they catch the bus. Bus users could be forgiven for thinking that the buses are busier than they really are. And if the transport planner talks to an average bus user, they may find a disconnect in how well-patronised each thinks the buses are.

This principal doesn’t just apply to buses either. Motorists will probably think of roads as busier than they really are because most of their observations are happening at busy times. Cyclists may think cycleways are busier than they really are. However you choose to get around, there’s a chance you think more people also do it than really do.

And it extends outside of transport too: shops, restaurants, cafes, pubs, parks, libraries, swimming pools. All places where you tend to see them when they are busier than average. Even stadia…

PS I think the reason this doesn’t seem to have a name or any references is that it’s really just a variation of the Friendship Paradox, which states that “most people have fewer friends than their friends have, on average“, because you’re less likely to be friends with the people who have fewer friends. As with the bus example, and all those other examples, it’s ultimately a form of sampling bias.

But it’s always good to be conscious of our own sampling biases.

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