After doing some research, it appears there are two main orderings for dictionaries:
- Historical ordering. The first know usage is shown first, and then subsequent definitions follow.
- Frequency, or most common usage, is shown first.
Some dictionaries explicitly state which order they follow:
"For example, frequency information allowed the team to rank senses by importance and usefulness to the learner (thus the most common meaning should be put first)."
"(our Learner’s Dictionary gives the most common sense of a word first, and our Unabridged tends to give the oldest sense first)."
Oxford Unabridged Dictionary:
"As a historical dictionary, the Oxford English Dictionary explains words by showing their development rather than merely their present-day usages. Therefore, it shows definitions in the order that the sense of the word began being used, including word meanings which are no longer used."
The next helpful clue will be to actually check on some entries.
Merriam Webster's online dictionary has this for the word "abroad":
First Known Use of abroad
14th century, in the meaning defined at sense 2
and the word "bedlam"
First Known Use of bedlam
1522, in the meaning defined at sense 3
This is self-evident "proof" that the Merriam Webster online dictionary is not following historical order. Otherwise the oldest definition would be shown first in sense #1. Rather, the oldest definitions are appearing as the 2nd or 3rd item in the list.
Check the words "bedlam" and "abroad" in the other dictionaries. They also have that same most-common-definition at the number one position, rather than the earlier known use.
The archaic or original meaning follows later, if it appears at all.
So, for these online dictionaries:
- Cambridge dictionary
- Oxford dictionary
- Merriam-Webster dictionary
- Collins dictionary
- Word web dictionary
The ordering is not historical. Therefore, the evidence indicates a preference for frequency and common usage in determining the order.