How to choose wire size for an air conditioner?
You do not indicate so I wonder if you have considered the cable run length.

Why would you like a thinner cable, if it is to save cost then the length is likely subtantial and therefore more of a reason to use thicker conductors.

Also the electricians are aware that compressor devices have very large inrush currents that are supported by thicker cables. 

EDIT:
I found this mentioned in an Off grid guide by JayCar.
Australian Standard AS4509.2 states a surge factor of 7x the continuous power should be used for electric motors, water pumps, fridges, air conditioner, and washing machines. A surge factor of 3x should be used for kitchen appliances and other electronics equipment, and surge factor of 1x for resistive loads. 

Another more interesting document on Cold Load Pickup Issues also shows similar inrush current figures.
Similar tests were conducted with on a ¼ HP refrigerator motor.  The test results showed an average inrush current of 15 amperes and a maximum of 18 amperes.  The average inrush was 7.5 times the steady state run current of 2 amperes.  It took 483 milliseconds to reach the steady state condition.   The test after a 25 cycle interruption produced lower inrush current and shorter times to reach steady state, 6 – 17 amperes and with 217 milliseconds to reach steady state.      

Also tested was a 3 ton air conditioner.  The momentary interruption test and the cold load pickup test showed an average inrush current of 90 amperes which lasted for 117 milliseconds.  The inrush current was 7.26 times the steady state run current of 12.4 amperes.  The steady state value was reached in 267 milliseconds.