It has been proposed the Hubble tension can be solved if we assume our galaxy is located in a giant void (such as KBC). I am confused at this point. If we were living in a giant void, we should have measured the Hubble constant lower. Since when the light passes an underdense region it gets less redshifted. Less redshift means less expansion or lower Hubble constant right? But we are measuring it higher. So shouldn't we live in a more dense region rather than an underdense region, to explain the discrepancy? What am I missing here?
The "void" in concern is commonly referred to as "Hubble bubble". Below is explanation from wiki on Hubble bubble:
In accordance with the Copernican principle that the Earth is not in a central, specially favored position... If, on the other hand, Earth were at or near the center of a very low-density region of interstellar space (a relative void), denser material in a shell around it would strongly attract material away from the centerpoint. Thus, stars inside such a "Hubble bubble" would accelerate away from Earth much faster than the general expansion of the universe.
As you can see, the key to the "Hubble bubble" is the denser material in a shell beyond the bubble which pulls things within the bubble away from Earth faster. Apart from the technical minutia (for instance, where the heck is the edge of the bubble?), the "Hubble bubble" thesis is especially distasteful in abandoning the Copernican principle. But truth hurts, as aptly worded by Lizzo: maybe Earth just took a DNA test, turns out it's 100% the center of the universe.
Note that the "Hubble bubble" line of thought is to change the Friedmannian cosmology at low redshift (since local bubble pertains to the low redshift observations), while most of the other proposed fix to the 'Hubble tension' is to tinker with the early universe via fudging the high redshift parameters (like a bit more dark energy here and a touch of jalapeno there).