Who decides the phonemes of a given language and on what basis do they decide? Do the phonemes of a language change over time, if so, who changes them? I am extremely confused about this question because I can't find anything based on my google searches. Also, for example, English has the phoneme /aʊ/ but not /ɑʊ/ or /æʊ/.
One sense in which someone decides what the phonemes of a language are is when a linguist describes a language and proclaims what the phonemes of the language are (usually in some publication). Linguists use all sorts of logic to arrive at their list, and many linguists don't even subscribe to the concept "phoneme". Using the term "phoneme" is fairly specialized vocabulary – most of the time people talk of "the consonants and vowels" of a language. In written languages, there is a strong prejudice in favor of a tight mapping between written form and "phonemes", arising from the practice of explicating the written form of the language rather than explicating the spoken form (for example, it is not common to get descriptions of North Saami based on analyzed phonetic transcriptions, instead the written form is used and there may then be some discussion of how "lbb" is pronounced, vs. "lb"). After you filter out (linguistically invalid) influences of writing, what should be left is the distribution of phonetically-transcribed sounds and an analysis which eliminates some of those sounds. A classical test is the minimal pair test, where two distinct words are differentiated at the phonetic level only by choice of one sound versus the other. If you have such word pairs distinguishing [x, y] then you have established that those two sounds are not "allophones", which gets you in the direction of the sounds being phonemes.
However, a "phoneme" is not an actual sound, it is the distributional property of sounds. So you have to not just look at two specific sounds, you have to look at all sounds in the language. In American English, you can compare "seater" and "seeker" where the words differ only in the choice of [ɾ] vs [k], but you can't then conclude that /ɾ/ and /k/ are both phonemes. You can conclude that [ɾ] and [k] are phonemically distinct, but to conclude that /ɾ/ and /k/ are both phonemes, you have to continue the analysis by showing that [ɾ] enters into minimal pairs with all of the other sounds in the language. Given words like "weeper, Uyghur, wiener..." you can check off a number of other sounds as being distinct from [ɾ]. However, finding minimal pairs that prove that [ɾ] is a distinct sound from [t] or [d] is not possible – there are no such minimal pairs. As it happens, there is good independent evidence that there is a rule of (American) English that turns /t,d/ into [ɾ] in a particular context, which is claimed to be the source of all instances of [ɾ].
Linguists typically hold one of two theories about reduction of output sounds to phonemes. One is the phoneme-minimization theory, where if it is at all possible to eliminate a certain sound from the inventory of phonemes, you should do so, therefore "water" must be /watər/ or /wadər/, because that makes all instances of [ɾ] be the result of applying a rule. The other is the phonetic-closeness approach that says that the underlying form is the same as the phonetic form, unless there is good evidence to the contrary, and "let's you eliminate X as an underlying segment" is not evidence to the contrary. These theories are not really comparable, since the phonetic-closeness theory is based on a particular model of grammar with underlying forms and rules, whereas the phoneme-minimization theory is just based on modeling distribution in a corpus of data.
The main impediment to developing a theory of "phonemes" is that there are 30 million theories of language, and there only local agreement as to what a language really is composed of (are there rules? what do rules do? Do people just memorize pronounced forms or do they generate words from more abstract bits by applying rules). That's why we can't (all) say that the phonemes "are there" – that's a specific theory of language.
Another way to look at the question is, how do languages change so that English has the phonemes that it currently has. To answer that, you first have to solve the linguist's choice question: how do we know what the phonemes of English are? We then assume that children use the same reasoning as linguists use, so some people believe that children strive to eliminate phonemes, other people believe that children strive to find the simplest computational relationship between input and output. Historical linguists also know that the "phonemes" of a language change over time, for example the difference between [f,v], [s,z], [θ,ð] used to be the result of an allophonic rule turning the voiceless fricatives into voiced ones in a certain environment. Since the days of Old English, the language has changed and now we enough minimal pairs that we can decide that those are all separate phonemes. The historical question is, what brought about the change?
The best answer available (not just for that change in English, but generally) is that given a certain amount of evidence, a child would automatically give a certain analysis of the language. But if you change the evidence (if people start talking differently), then the evidence for that analysis weakens and children can entertain alternative analyses, such as saying that /s/ and /z/ are now distinct phonemes in the language.
Although we generally say that it's the child that makes this analytic choice based on how the surrounding population talks, it's also possible that adults (re-)make such a choice, that is, adults can change the analysis of their language, to some extent. So it's either the children, or the speakers, who make this kind of choice.
The linguists describing the language.
As user6726 mentioned, phonemes are a theoretical construct. We can't actually take quantitative measurements that prove that this is a
/k/ and this is a
/t/, unlike in e.g. articulatory phonetics.
So there are some linguists who claim Mandarin has only two vowels
/ə a/, and some who claim it has five,
/i y u ə a/, and some who say it has
/i y ɨ u e o a/. All of these theories can explain the data; they just go about it in different ways (for example, the people who like the two-vowel analysis claim that
[i y u] come from a sequence of a glide and a "null vowel").
So if you really wanted to, you could describe any language as having only two phonemes,
/1/, and then perhaps
[a] comes from
/01100001/ or something absurd like that. The question is, is this useful? Does it reveal any new insights, or make it easier to analyze the language? For the
/0 1/ analysis, the answer is "almost certainly not". And thus nobody actually analyzes languages that way.
For another real-world example, Proto-Indo-European is usually reconstructed as having three (or more) "laryngeal" phonemes, written *h₁ *h₂ *h₃. When these phonemes were first proposed, there was no direct evidence of them anywhere. But assuming them led to a strikingly elegant way to explain some strange vowel alternations, and so they were considered useful, and so they stayed. (Later, direct evidence was found for two of them with the decipherment of Hittite, but there's still no uncontroversial direct evidence of *h₁.)
For how they change, we know that languages change over time a bit like how organisms do: random mutations and such can get passed down through the generations within a community. And at some point, the old analysis of the phonemes may no longer be useful, and they need to be changed, or a new analysis needs to be invented. But there's almost never a clear-cut boundary, and linguists can (and do) often disagree about what phonemes a particular language or dialect has at any point in time.