How about considering Voltage to be whatever is indicated by a Voltmeter?
No way, Clarence! Read on...
I perform a lovely demonstration which clearly demonstrates that
the reading on a voltmeter is *not* unique. This seems to be the
best way to free students of the misimpression that an induced
emf is a potential difference.
I take two resistors (say a 1 kohm and a 2.2 kohm) and solder their
pigtails together. (At this point I hesitate to say "in parallel"
or "in series" - that idea is undefined in this case.) I take the
combination, spread the resistors apart so I can slip the pair over
the yoke of a dissectable transformer, and close the transformer up
again. Now take two voltmeters. Connect one across the 1 kohm
resistor. Connect the other voltmeter across the 2.2 kohm resistor.
If you do this in the most straightforward manner you will find the
voltmeters read the same value, 0 AC volts. Now turn on the primary
of the transformer. A current will flow in the (now series) pair of
resistors, say 1 mA flows. One meter will read 1 VAC and the other
will read 2.2 VAC, as predicted by one of the sacred Laws of Ohm.
But hold on a minute. Those two voltmeters are connected to the
same places! How can they have different readings?
Of course the answer is simple, and the students seem to grasp it
well enough.