[mwebb]

..."Does it reduce compression?

Actually it would increase compression by allowing more mixture into the cylinder to be compressed, but that is offset somewhat by the dilution of that mixture with a basically inert exhaust gas component.
"...

adding INert gas to the combustion air fuel mixture Reduces displacement and compression because
the INert gases are INert they do not react with anything they act like a big cushion or spring filling up space that normally would be filled by the air fuel mixture
so the effect is , there is less air fuel mixture in the same space .

which
reduces displacement and reduces compression While EGR is active only

these are the facts.
=======================
it appears that this poster feels that the same amount of air fuel mixture is present with the INert gases
in combustion ,
but that is not possible . the INert gas present displaces an equal amount of air fuel mixture

remember ;
EGR works by DILUTING the air fuel mixture in the combustion chamber with INert exhaust gas .

because the air fuel mixture has been diluted , the engine has less power
so
the driver steps down farther on the throttle , opening the throttle a bit so the engine produces the same power as without introduction of INert gases
which improves VE volumetric efficiency and REDUCES suction throttling losses
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to sum up
EGR displaces dilutes air fuel mixture with INert exhaust gas
yet the same total volume of gas at the same pressure fills the combustion chamber
which
reduces combustion temperature
reduces NOX
and
reduces the available space in the combustion chamber by partially filling it with INert gas , (reduces displacement)
which also reduces peak combustion pressure and compression