4ohm, 8ohm speakers and output power

I was thinking that if the speakers are rated using Volt instead of Watt then the imdedance will be taken into account.

For example if both are rated as 88db/2.89V/meter then they would play to the same loudness. The 4ohm speaker will just draws more current and therefore double the input wattage.

BUT I STILL think if they are using wattage as a reference then the 4ohm must be able to play louder given the same input wattage. I still don't see it any other way.

Sean: Let's say that the sensitivity is rated using 1W as a reference which says that given an 1W input, both speaker can generate both 88db of sound at 1meter distance. And of course as you said, speaker impedance was taken in account which means that the amp has to apply a higher voltage to generate the same amount of power to a 4ohm speker as opposed to a 8ohm.
(Assume also that the 4ohm speaker always has its impedance lower than the 8ohm speaker in all frequency band from 0 - 22khz)

I guess we can agree that there can be no argue about the rating of the speaker and how it was measured. So let's ignore how efficiently the amp can generate power, and assume that somehow we manage to double the power when we drive the 4ohm speakers, then I don't see how the 4ohm speaker cannot be played louder than the 8ohm speaker.

The only factor that we don't know is that sensitivity may not be linear which means that higher Wattage the 4ohm speaker somehow is less sensitive than the 8ohm speakers but that is another set of specs all together.