The mechanics of the deflection of ukulele tops is a complex subject, but we can probably make some gross simplifications for discussion purposes. The amount a material deflects under a given load is inversely proportional to its elasticity coefficient. Assuming you wanted to build a cedar ukulele whose top would deflect the same amount as the same ukulele built of mahogany, you could compare the coefficient of elasticity of one vs the other. Then, you would make the thickness proportional to that.
The properties of various woods are given
here.
Cedar's modulus of elasticity seems to vary between 5,200 (Eastern white) and 8,000 (yellow). Western red cedar is about 6,500. The modulus of elasticity for mahogany varies between aproximately 8,000 and 10,000 from the tables. If we use the number for WRC and average out the mahogany, we would use 6,500 and 9,000 to get a ratio of 9/6.5 = 1.38. In other words, mahogany is about 1.38 times as stiff.
So if we wanted the top to deflect the same amount for a given string pluck, we would make the WRC about 38% thicker. For a 0.06" mahogany top, the equivalent WRC top would be 1.38x0.06 = 0.083. That would be my guess. This ignores the fact that you might want the cedar to deflect more to take advantage of a louder sound, and ignores properties such as density, which probably affect brightness etc. I might be tempted to go lower than 0.083 just to see what happens, but then I would not be too disappointed if the resulting instrument sagged after awhile.
We could refine these calculations by considering how much strain it would take to permanently set the wood, and look at elasticity in more than one direction of the wood fibers, but it starts to get complex. A copy of "
Left Brain Lutherie," might come in handy for people who think such thoughts. Unfortunately, I don't own a copy.
If any of this is nonsense, blame it on the earliness of the morning (never do math early in the morning, especially on tax day).