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A reduction of 3dB at any point in space is equivalent to halving the energy at that point.

But we humans don't perceive sound energy linearly, so half of the energy is not equivalent to half of the perceived loudness.

The usual rule of thumb is that it takes a reduction of 10dB (1/10th energy) for a thing to sound about half as loud, or an increase of 10dB (10x energy) for a thing to sound about twice as loud.

(This leads to all kinds of interesting problems with making things quieter or louder. It seems superficially implicit that moving from a 100-Watt amplifier to a 1,000-Watt amplifier would be strikingly-dramatic difference, but in an ideal world where everything else is the same then that change only makes things about twice as loud -- the same as moving from a 1-Watt amplifier to a 10-Watt amplifier.)