# Nonlinearity makes people do strange things

Control engineers know that non-linearity causes problems – the rest of the world could maybe take note…

## What is non-linearity?

Non-linearity is where the response of something is out-of-proportion with the change that’s just been inflicted on it. If you tweak something and get a huge change all of a sudden, that’s non-linear. Light switches are non-linear – there’s a small change to the light switch, but the light changes abruptly. A dimmer switch is linear – you turn it a bit, the light changes a bit. Turn it a lot and the light turns a lot.

## Controlling

If you want to use that knob to control something, it’s an awful lot easier if the response is linear. Imagine trying to control the speed of a car if the throttle pedal responded non-linearly. You press the pedal more and more, the engine does nothing, and the suddenly as you cross some invisible point, the engine bursts to life and you scream ahead!

Control engineers (some of whom designed the engine management system in your car) take great pains to keep everything as smooth (ie linear) as possible.

## So what about the rest of life?

Now you’re wondering what the “rest of the world” I was talking about has to do with a relatively obscure engineering discipline?

Say you wanted to “control” something like the performance of your sales force. Or some money managers… Maybe you’d say “if you do this well, you get this much bonus”.

That’s a non-linearity right there. Small change at the input (between meeting the target and just missing), potentially huge change to the output (the bonus payment). This will encourage weird behaviours – towards the deadline date, a salesman who’s nearly met his target will cut a different deal to one he would’ve done at the start of hte month. Possibly to the detriment of the long term interests of his company. But to his personal gain short-term. Or a banker might be encouraged to take a riskier bet on some market or other, because she knows it will looks good towards the measures that her bonus depends on. Not necessarily in the long-term interests of the company. Or possibly the country… Taxation can also produce these sorts of behaviours – if there’s step changes (like to a 50% tax rate at a particular income), people will suddenly feel it worthwhile to try and avoid that last bit of tax. Whereas a continual change, or even a pure flat rate, will provide less incentive, as there aren’t opportunities for big “savings” for a relatively small amount of effort.

I’m not convinced by bonus schemes as motivators at the best of times, but a linear scheme, where the return is stricly proportional to the gain you’ve given the company, preferably over the long-term, will (IMHO :) provide much more sensible behaviour.

Maybe those specifying bonus schemes as a method of “control” (although I’m sure they’d it hate to be described as such) could learn a bit from control engineering?