Why is the Earth's magnetic field stronger than its neighbors? [Edited] I've learned that the Earth's core is hot due to decay of radioactive elements, causing the liquid part of the core to stay liquid. This was stated as an explanation to why the Earth has a strong magnetic field.

Assuming the rocky planets were formed roughly the same way (planetoid collisions etc.), why was Earth the "lucky winner" of abundant radioactive elements, while Mars &amp; Venus were left with much less, causing their cores to solidify, their magnetic fields to weaken, their water blown into space, and their fate sealed to become arid desert and boiling inferno, respectively?
I've learned that the Earth's core is hot due to decay of radioactive elements.


This is unproven, non-standard geophysics. There are several arguments against this. One is that all of the long-lived radioactive isotopes are isotopes of uranium (two isotopes, 235U and 238U), thorium (232Th), and potassium (40K). The problem: Uranium, thorium, and potassium are strongly lithophilic ("rock-loving") elements. These elements dissolve very nicely in molten rock, but not so much in molten metal. The presence of long-lived radioactive isotopes is enhanced in the Earth's crust, slightly depleted in the Earth's mantle, and by all rights should be strongly depleted in the Earth's core. 

Another problem is that any significant amounts of uranium and thorium in the Earth's core have been ruled out due to neutrino detectors. Potassium-40 has not been ruled out because the neutrinos from 40K decay are too low in energy to detect, but that brings us back to problem #1.

The only hope for this conjecture is that potassium somehow becomes siderophilic at high pressure. There are some experimental results, most of which are highly controversial, that this might be the case.

Yet another problem is the conjecture of high radioactivity in the Earth's core was motivated by explaining the Earth's magnetic field. A number of recent papers say that there is zero reason for this motivation. The Earth's magnetic field is fully explainable without resorting to the chemically unsupported hypothesis that 40K somehow becomes a siderophile at high pressure.