Question

Is kinetic energy conserved in the Compton effect ?

Answer 1

I would say conserved

Answer 2

In the derivation of the Compton effect equation conservation of energy is assumed.

Answer 3

Medals?

Answer 4

In the process of Compton scattering, a photon gives up some of its energy to an electron.
Since photons have zero rest mass, all their energy is kinetic.
The kinetic energy gained by the electron is equal to the (kinetic) energy lost by the photon and so the answer to your question is yes, the kinetic energy is conserved in Compton scattering.