Q:

Why isn't accentuation recessive in ταμίαι? (Greek)

I have marked in green accentuation below which is not recessive, namely, in ταμίαι, πολῖτα, πολῖται, παρθένος, παρθένε, and παρθένοι.

Question:  Is there some general principle to explain the lack of recession in those words?
Background
By recession, of course, I mean what one sees in πόλεμος.  The accent wants to sit as far away from the end of the word as possible (given certain rules).
The lack of recession in παρθένος, I put down to, as it were, 'the word forming an exception.'  In a manner of speaking, I am assimilating this exception to that found in words such as ἀγορᾱ́, τῑμή, κριτής and ὁδός.  The accent just 'wants to' fall at the end.  I don't argue or try to explain it.  I only hope I'll remember.  In the same way, the accent just wants to sit on the penult in καρκίνος and παρθένος.
The pattern in ταμίᾱς and πολῑ́της however seems more tricky, for two reasons.

It almost seems as if the accent 'forgot to move' in the few places where it might have, each time (except in πολῖτα) because the word ended in -αι.
I don't find nouns in which the accent does move when it could (i.e. when the word ends in -αι).  In other words, the pattern of ταμίᾱς or πολῑ́της seems general.  For example, νεᾱνίᾱς (νεᾱνίαι) and δεσπότης (δεσπόται) follow that of ταμίᾱς.  ἰδιώτης (ἰδιῶται) and κυβερνήτης (κῠβερνῆται), that of πολῑ́της.  As yet, I have not found long vowel first declension words not conforming to one or the other of these two patterns (other than words like κριτής and ποιητής, in which the accent falls on the ultima).

Therefore my working hypothesis is that there is a subgroup level exception to recession for long vowel first declension nouns.  It would go like this:

First, let us set aside words accented on the ultima such as κριτής and μαθητής.  As for the rest, accentuation is recessive for these subgroups except where the word ends in -αι, in which case the accent 'forgets' to recede.

The question stated above really stands in for the following diffuse cluster of thoughts.

Am I OK to understand the two types of exceptions (word vs. subgroup level) as presented above?
If there is a subgroup level exception applicable to words such as ταμίᾱς and πολῑ́της, is there any higher principle of which that exception is an instance?
Even for words such as καρκίνος and παρθένος (and perhaps even ἀγορᾱ́, τῑμή, etc.), is there any circumstance to 'motivate' their non-recessive accentuation?

In general I am trying to 'motivate' these various types of exceptions to recession.

A:

You're actually going about this the wrong way. Although it's true that the accentuation of verbs is generally recessive, the accentuation of nouns (and adjectives) isn't; it's generally persistent instead. The accent will remain the same type and in the same location unless it's forced to move or change by, e.g., the quantity of the ultima or some special rule. The nominative singular form tells the base accent for a noun or adjective, and that accent doesn't have to go as far back to the beginning of the word as possible.
For example, for πόλεμος, the base accent is acute over the first ο in the antepenult; however, in the genitive singular, πολέμου, the diphthong in the ultima makes that syllable long; therefore, the accent can't remain on the antepenult but has to move to the penult – still as an acute in this instance. The base accent of παρθένος is an acute over the ε in the penult, and it can stay there in all forms of the noun. The base accent of ταμίας is acute over the ι in the penult; it can stay there in all forms except the genitive plural, where it must move because of a special rule that the genitive plural of all first declension nouns has a circumflex over the ω in the ultima.

