How to determine which phoneme a group of allophones realizes?

Question

This question is related to this other one, about the difference between Phonetics and Phonology.

I can understand the difference between the two subfields as well as what it means to produce phonetic and phonologic transcriptions. Simply stated, the phonetic transcription deals with the surface representation, whereas the phonemic one deals with the underlying representation. But how does one determine what is the underlying representation? For example, in English, [r] and [ɹ] are considered variants (or allophones) of the phoneme /r/. But what is so special about /r/? Why can't we say that these two sounds are variants of the phoneme /ɹ/, instead? Of course, this is just one example. It can be extrapolated to any pair of allophones, such as [p] versus [b] in Korean or [d] versus [ð] in Spanish, etc.

Answer 1

You're absolutely right - the choice is completely arbitrary. Generally, before the publication of The Sound Pattern of English (Chomsky & Halley 1968), whichever underlying representation required the fewest number of rule derivations to produce the output forms was chosen, i.e., whichever was the most elegant.

For example, the following rule set describing (simplified) Korean stop allophony:

/p/ -> [b] / V_V
/p/ -> [p] / otherwise

Would be preferable to:

/b/ -> [p] / #_
/b/ -> [p] / _#
/b/ -> [b] / otherwise

Post-SPE, sound segments were reanalyzed as bundles of features - for example, [p] is shorthand for:

[-voiced
  labial
 -sonorant
 -continuant]

In SPE phonology, all features in the phonetic form of a segment are specified. However, the phonemic form omits features that are derived through rules - this is known as underspecification. For example, in SPE phonology:

[ labial      -> [+voiced] / [+voiced] _ [+voiced]
 -sonorant
 -continuant]

Note that only the modified features are written after the -> arrow, and that only relevant features in the surrounding environment are written after the /, rather than whole feature sets.

Answer 2

@AlekStorm's answer is pretty good, but I'd say that in practice there are at least two ways linguists decide which form is underlying.

1) If you take two allophones, say (using relatively broad transcription) [t] and [ɾ]. You could, rather tediously, list all the contexts where [t] shows up, and all the contexts where [ɾ] shows up. Then, you can so some set operations. Call T the set where [t] shows up and D the context where [ɾ] shows up. It should be the case that T-D is a relatively small set of contexts, and D-T should be empty. In this case, [ɾ] has a restricted distribution, so the features of [t] could be considered underlying. This is similar to the elegance of description from @AlekStom's answer. Of course, in practice it will happen that neither A-B nor B-A is empty, and then everything gets more complicated.

2) You can check to see if one allophone "behaves" as if it were the other. As with [t] and [ɾ], the diagnostic would be

• Does [t] ever behave as if it were a voiced, lenis segment?
• Does [ɾ] ever behave as if it were a voiceless segment?

In fact, in many dialects [ɾ] does frequently behave as a voiceless segment, triggering changes in quality of its preceding vowel. For example, in Canadian English and some other dialects, there is the following distinction between write and ride.

raɪd   (ride)
rʌɪt   (write)

When adding on the morpheme -er, the /t/ in writer is flapped.

raɪɾɚ   (rider)
rʌɪɾɚ   (writer)

This case has the additional complication that both the [d] and the [t] are neutralized to [ɾ]. However, you could still argue that the vowel difference between [aɪ] and [ʌi] is triggered by voicelessness, so that the underlying form of the [ɾ] in writer is behaving as a voiceless segment.

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But, like I said, heuristics like these are not applicable to all analyses, and there are certainly underlying forms which have been posited on flimsy evidence. And thank god, because that means that linguists' work is not done!

Answer 3

It's not arbitrary, and while the ease of rule-writing is certainly a consideration, this is not what determines which sound is the phoneme and which sound is the allophone. To re-use @Alek Storm's first example:

/p/ -> [b] / V_V

/p/ -> [p] / otherwise

It's true that this is a simpler analysis than trying to instead account for [b] becoming [p] in a wide range of environments. But, the actual reason why [b] is a variant of [p] is because [p] can occur anywhere, while [b] can only occur in a specific phonetic environment. That is, the voiceless bilabial plosive only becomes voiced when it occurs inter-vocalically, because the voicing of the surrounding vowels carries across to the otherwise voiceless plosive. So, when you start to find phones which seem to be variants of the same sound, you need to look at the environments they occur in to work out which phones have plausibly been affected by the surrounding phones, and which phones seem to be robust in a range of environments.

That said, there are languages which permit a lot of 'free variation' (allophones that don't seem to arise through phonetic conditioning), in which case linguists might choose 'the phoneme' based on frequency, ease of explanation, or familiarity with one type of sound over another. But, in many analyses noting 'free variation', there do turn out to be phonetic factors governing the variation.