Lamport logical clock: why event occurs in a process with smaller pid is treated earlier?

Question

In lamport's paper1, he define global local timestamp, which is composed of process id and local lamport timestamp.

This timestamp is used to order all the events in a distributed system.

The rule to compare two events is following.

My Question

Imagine we have two events, one happens in process 1 (P1), with local timestamp 9, another event happens in process 2 (P1), with identical timestamp 9.

Based on lamport's rule, the first one is earlier than second one.

C₁(9) => c₂(9)

But why?

From my understanding, it does't make sense. An event is treated earlier just because it is born in a process which has smaller pid?

Reference

1. Lamport, “Time, Clocks, and the Ordering of Events in a Distributed System.”