What languages together maximize the number of people you can speak with?

Question

This is not quite a “which languages have the greatest number of native speakers” question, nor quite a “which languages have the greatest number of L2 speakers” question, both of which are easily googlable and come up plenty of times when I try to google this question. Also, this question does not give me the answer I’m looking for: all of its answers focus only on native speakers or ignore the fact that there is overlap in L2 languages.

Say I’m a language learner who is choosing languages to learn to maximize the number of people I can communicate with. Good bets to learn seem to be Mandarin and English, with the former’s high L1 population and the latter’s high L2 population. But if I look at Cantonese, it’s not a good choice even though it may have a large number of speakers: statistically, most people who speak Cantonese also speak Mandarin, even though their Mandarin is likely an L2 or L3. So even though we’d both use a second language to do it, I could communicaye to them in Mandarin, which has more speakers. By this criterion, it’s inefficient to learn two languages with a large overlap in speakers.

My question is this: is there an ordered list such that, starting at the top, each additional language down the list maximizes new speakers who do not already speak another language higher on the list? I’m pretty sure English tops the list, with its high L2 population, but what comes after that?

Answer 1

There is a sortable list, with numbers for L1, L2 and L1+L2, for the top 44 languages. If you want 5 languages, that's (in order) English, Mandarin, Hindi, Spanish, Arabic, getting you to almost 3.9 billion people. Or, the top 2 gives you 2.5 billion. However, there is no control in this list for not speaking one of the other languages on the list, and you can assume that some L1 speakers of Mandarin are also L2 speakers of English. This is based on Ethnologue reporting – Ethnologue makes large number of informed guesses in the field, and does not do a house to house survey of the entire planet, so there's no direct data that would allow you to discount the English count because of the number of Hindi speakers who also speak English. The internet suggests that 10% of the Indian population speaks English, so you could reduce the count for Hindi speakers by 10%, which could change the ordering of Hindi and Spanish (unless (1) you think Hindi speakers are more likely to also speak English than Tamil and Bengali are or (2) you think that English is as commonly spoken as an L1 by Spanish speakers as English is for Hindi).

Answer 2

It is not a list, but if you develop skill for both an analytic and a synthetic language, your language capacity can become considerable. I understand the question is not about anything like a competition, who spoke with more people last week. : )
English would be an analytic language.
https://en.wikipedia.org/wiki/Analytic_language
Russian or Polish would be synthetic.
https://en.wikipedia.org/wiki/Synthetic_language
Russian has been given much connotation for the Eastern Bloc, so Polish happens to work, provided you do not try to refer for everything to religion ("business is business, tsar is tsar", or, there is what there is). : )
Both markets, for English as well as Slavic (altogether) languages, are immense.
https://en.wikipedia.org/wiki/Slavic_languages
For the Slavic market, Polish may not have as many L2 speakers, but it can help comprehension or translation, to many people in the former Eastern Bloc[1] and beyond; available comparison can be of value for a really different language, like English -- if your purpose is linguistic. Plus, Polish is Latin alphabet.
[1] I do not mean the people for any former nomenclature; Russian was obligatory in the Eastern Bloc, and many people continue to learn and speak it. Polish remains close, even mutually intelligible at times: it's a bit peculiar, but so has been the Russian-Polish history.