I don't really understand why people suggest "sistering" joists. I graduated from university with a Bachelor's degree in Mechanical Engineering and the design of beams is part of the course work that every mechanical and civil engineering student takes.

Instead of sistering floor joists, I'd suggest that you talk to any architectural or structural engineering firm about ADDING wood to the bottoms of your existing joists.

If you can use a glue that forms a bond that's as strong or stronger than the wood the joist is made of, then you can ADD wood to the bottom of a joist to make it stronger. That is, you can turn a 2X8 into a 2X10, or a 2X8 into a 2X12 for that matter. All that is necessary is that the glue you use and the wood you add be as strong or stronger than the wood you have now.

If you were to use a construction adhesive like LePage's PL Premium to glue and screw two pieces of fir 1X2 together (side to side), and once the glue sets up you were to take the screws out and bend that 2X2 beam until it breaks (by using a car jack, for example, to apply tremendous force), and you find out that it broke in the wood, not at the glued joint, then you have proved that the glue is stronger than the wood. If the glue is stronger than the wood, and the wood you add is as strong or stronger than the wood you have, you can do nothing but strengthen the joist by adding wood to it ANYWHERE. There rest of this post will be about where you need to add it for maximum effect.

Travelover was correct in saying that the height of the joist is one of the most important considerations to the rigidity of a joist, and he was correct, but the length of the joist is equally important. Apart from changing the cross section of the joist to make it look more like an I beam than a rectangle, or changing the material the joist is made of (magically changing the wood into steel, say), the height of the joist and the span of the beam are equally important in determining how much a beam deflects under any given load.

This web page gives the basic formulas for determining the deflections of beams:

Deflection of beams
For a solid rectangular beam like a floor joist, the ends of the beam are supported at both ends. Neglecting gravity, the joist will deflect the same amount if it's supported from below and a weight is rested on it, or if it's prevented from moving upward, and a vertical upward force is applied to it:

In the above drawing, the gray triangles are the supports and are assumed not to move. A force is applied at the center of the beam and the deflection of the beam is calculated as:

deflection = F*L*L*L / 48*EI

where

F is the force applied

L is the span of the beam, which is the distance between supports

E is the "Modulus of Elasticity" of the material the beam is made of. This parameter takes into account that a fir joist will bend less than a spruce joist, and one made of solid steel will bend even less. This web page gives the values of E to be used for Southern Yellow Pine, Douglas Fir, Hemlock and Spruce for various grades of these woods. For steel, use E = 30 million psi. Steel is about 15 to 20 times as stiff as wood. So, just be aware that the Modulus of Elasticity, "E" is the parameter that accounts for the strength of the material the beam is made of, and the value of E won't change unless you replace the joist or beam with one made from a different material.

http://www.southernpine.com/speciescomparisons2x6.shtml
I is the Moment of Inertia of the beam, which takes into account it's cross sectional shape. This parameter takes into account that a round solid steel bar will be stronger and bend less than a hollow steel tube of the same diameter, or that a square hollow tube will be stronger and bend less than a round hollow tube of the same height. The mathematics in the equations developed to predict beam deflection presume that the beam is a bundle of fibers. When the beam bends, those equations predict that the fibers on the top and bottom of the beam will be in compression and tension, and the fibers in the middle of the beam won't have any stress on them at all. Consequently, it's the material that's furthest away from the middle of the beam that's in the most tension and most compression and helps the most in resisting any bending of the beam. This is exactly why an I beam (with it's top and bottom flanges) is very much stronger than the same beam with those top and bottom flanges removed. And, it's also why the same 2X12 can be used as either a very rigid floor joist or a very bouncy diving board depending entirely on it's orientation relative to the applied force. So, just be aware that the Moment of Inertia, "I" is the parameter that accounts for the shape of the beam relative to the applied force.

For a solid rectangular beam (like a joist), I is calculated from the formula:

For a round beam, like a round pry bar, I is calculated from the formula:

So, just for argument's sake, let's plug the formula for I for a rectangular beam into the formula for a beam's deflection under a concentrated load at mid-span of the beam:

We have:

deflection = F*L*L*L / 48*EI

substituting I = b*h*h*h / 12, we get

deflection = 12*F*L*L*L / 48*E*b*h*h*h

or, deflection = F*L*L*L / 4*E*b*h*h*h

Now, if you sister the joists, all you're doing is effectively doubling the width of the beam, b. The result, predictable from the formula above and from common sense, is that the deflection of the sistered beam will be half of what a single beam is under any given load.

But, if you start playing with the h (height) of the beam, or the L (span of the beam), then you get much greater changes in the rigidity and deflection cuz these terms are CUBED in the formula for deflection.

So, for example, if you were to cut a hole in the basement floor, pour a reinforced concrete footing, and sit a jack post on it to support a beam supporting the floor joists in the middle of their spans, you'd effectively cut the span, L, in half. The result would be that the floor deflection would be 1/2 cubed, or 1/8 of what it was before.

Similarily, if you doubled the height of the joists, h, you'd also get 1/8 of the deflection you had before.

If, for example, you used PL Premium to glue and screw some fir strips 2 inches high by 1 1/2 inches wide to the bottoms of 2X10 floor joists, then the reduction in the deflection in the floor would be:

(9 1/2 * 9 1/2 * 9 1/2) / (11 1/2 * 11 1/2 * 11 1/2) or (9.5 cubed)/(11.5 cubed)

or 0.56, or you'd have only 56 percent of the deflection you had with the 2X10's.

That is, by adding 2 inches of wood to the bottoms of 2X10 floor joists, the deflection of the floor is 56 percent of what it was before, or approximately the same amount as if you'd used vastly more wood to sister each joist. And, strengthening the joists by adding wood to them completely avoids all of the potential additional work involved in running electrical wires and such through the sistered joists.

Aslo, that above estimate of reducing the deflection of the floor by 56 percent is based on turning the 2X10s into 2X12's. You COULD glue 2X4's edge-to-edge to the bottoms of the joists for a much larger increase in rigidity, or even glue them on to make the bottoms of the joists resemble the bottom half of an I beam (which would allow you to use shorter screws. Both of those gameplans would result in an even larger increase in rigidity of the joists, and therefore less deflection of the floor.

But, the above is not really strengthening the subfloor, as the post is entitled. It's strengthening the floor joists that support the subfloor. It could be that the inspector was saying that there's too much flexing of the subfloor between the joists. In that case, strengthening the joists won't address the problem he's complaining about. AND, it's based entirely on the assumption that you can find a glue that'll form a bond that's as strong or stronger than the wood you're gluing to. I really don't know whether PL Premium is, but it'd be an easy matter to test it.