I'm sure you're right that the "third" in "Third World" refers to an order rather than a fraction.
I think the reason that "tiers" is used is probably historical. Although "Third World" is a relatively recent term it was coined from the much older expression "Third Estate" - "le tiers-état".
I imagine at the time when that term was created the language was rather different and "tiers" could be used to mean 3rd in sequence.
Thank you Alan for this excellent answer.
I was discussing this question posed by David with some French people yesterday as I have to admit I had never asked myself since in my mind it only designates a status and I learnt that there is another term 'le quart-monde'.
After a bit of research it appears that 'le quart-monde' was coined in 1969 to designate people under the threshold of poverty. It is wonderful to learn something new. If you are interested, take a peak at:
all in French I am afraid but good practice.
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