Question: Electric fans are often controlled by a knob which the user turns to power the fan on or off, and control the fan's speed.

On a lot of fans, the knob goes immediately from the off position to the highest speed, followed by the other speed settings in descending order. 

For example on the picture below, you can see the knob going from the off position ('0') to the highest ('3'), and then the other two in descending speed order ('2', '1').

![box fan top](https://i.stack.imgur.com/B4xgB.jpg)

Why is that?

Answer: 
I'm so tempted to suggest that they did analytics and found that the fastest speed is the most popular, and the slow one the least. But that's nothing more than a guess.

Although I'm not a motor expert, from a quick research this is what I understood. I'm pretty sure this is correct, but to get a definite answer, I guess the post is more appropriate in the electronics forum.

I'm really simplifying the explanation, which anyhow requires some understanding of electronics.

Anyhow:

Motor Technology
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Inductance
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Electric motors' key principle of operation is based on inductance. That is, a current flows through a coil to create a magnetic field, and magnets within this field start spin, being attached to a central pole. (It is also possible to have the coil on the spinning component and the magnets fixed.)

As with other inductive setups, once the moving components start spin they create what is known as *Back EMF* - a force opposite that of the force that caused the movement. In electrical terms, the more back EMF, the more resistance the inductor presents in the circuit.

Single Coil Designs
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While the fan is at rest, there is little resistance in the circuit. Thus, the circuit draws a lot of current, which may 'fry' the fan - various components can overheat.

The sooner the fan starts spin, the quicker the resistance rise, and the current consumption drops.

So quick starting of the rotation is beneficial here.

Multi Coil Designs
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Another type of design involves an even number of coils arranged in a circle around the spinning pole.

With this design, a different pair of coils are triggered in concession, depending on the angle of the spinning part. This requires a controller that can sense the angular position of the spinning component. This is done sensing the resistance of each coil. But if the back EMF is too low (due to slow rotation) the controller can't sense the position of the fan, which yields jittered behaviour.

Here again, there's a need for quick start.

As you can see, either designs would benefit from a quick start of the fan. Thus, the fastest mode is the one next to the off position.
My guess is that...

Imagine you have to operate the device in darkness (no light environment) or someone with visual difficulties, placing the off setting next to the highest allow the user to know they've switched off the device.

See it this way, you are at position 2, your intention is to switch off the fan, you knob in the "0,1,2,3" setting, you will not be able to tell immediately if you are at the 1 position or off position as the fan is turning at a similar pace. (Slower but unable to identify easily). 

Whereas, by placing the setting as "1,2,3,0", you will be able to tell immediately if you are at position 3 (faster and louder noise) or at position 0 (significantly slower and lesser noise). Thus, user in dark places can "feel" the setting without looking at the knobs. 

Don't shoot me if I'm wrong, this is just my guess. Cheers. =)