The principle of guidance is intellectual convenience and not natural fact.
This position has been misunderstood by many of Poincare's expositors.
They have muddled it up with another question, namely that owing to the inexactitude of observation it is impossible to make an exact statement in the comparison of measures.

It follows that a certain subset of closely allied congruence relations can be assigned of which each member equally well agrees with that statement of observed congruence when the statement is properly qualified with its limits of error.
This is an entirely different question and it presupposes a rejection of Poincare's position.

The absolute indetermination of nature in respect of all the relations of congruence is replaced by the indetermination of observation with respect to a small subgroup of these relations.
Poincare's position is a strong one.

He in effect challenges anyone to point out any factor in nature which gives a preeminent status to the congruence relation which mankind has actually adopted.

But undeniably the position is very paradoxical.