What arguments are there for "karma" -- that the agent inevitably experiences the result of their actions? There are philosophical arguments for e.g. 'emptiness', as evidenced by it having sections in philosophy encyclopedias. Whether or not you agree with them, probably depends on your language and pre-philosophical intuitions -- which is arguably the same for any philosophy. 

What about karma?


  And what he taught is not the version of karma popular in certain circles today, according to which, for instance, an act done out of hatred makes the agent somewhat more disposed to perform similar actions out of similar motives in the future, which in turn makes negative experiences more likely for the agent. What the Buddha teaches is instead the far stricter view that each action has its own specific consequence for the agent, the hedonic nature of which is determined in accordance with causal laws and in such a way as to require rebirth as long as action continues. So if there is a conflict between the doctrine of non-self and the teaching of karma and rebirth, it is not to be resolved by weakening the Buddha’s commitment to the latter.


Or again:


  He who acts is the agent (kartr); that which is performed (kriyate) is
  karma; and the agent of karma is the one who experiences the result of
  that performed karma. Without karma, an agent is not established.


The Inner Kālacakratantra, unknown page. 


  The law of karma is a fundamental principle of the Buddhist worldview.
  In brief, karma refers to the idea that intentional actions have
  consequences for the agent, in this life and in future lives; in fact,
  it is karma that leads to rebirth. Buddhists understand the law of
  karma as another manifestation of dependent arising
  (paṭicca-samuppāda), the law of cause and effect, whereby everything
  that exists arises due to specific conditions. In this sense, the law
  of karma is a sort of natural law, so that actions are naturally
  followed by consequences, not as the result of divine judgement. But
  they will follow: the Buddha emphasised that actions lead inevitably
  to appropriate consequences... The inevitability of karmic
  consequences is a large part of the way that traditional Buddhism has
  presented its ethical teachings. Evil actions, like killing, stealing,
  lying and so on, are bad karmas and will lead to rebirth in an
  unpleasant human situation or in hell.


Just trying to explain what the mainstream and traditional interpretation of karma is. I think the conventional argument is from authority and the authority of memories of past lives. These I don't find convincing. Can it be inferred from any other Buddhist doctrine, such as emptiness?



I was looking at the wild fox koan here, and this part struck me:


  Those who say "one does not fall into cause and effect" deny
  causation, thereby falling into the lower realms. Those who say "one
  cannot ignore cause and effect" clearly identify with cause and
  effect. When people hear about identifying with cause and effect, they
  are freed from the lower realms. Do not doubt this.


I think it seems to be saying that -- according to (the philosophy of) emptiness -- there is no escaping cause and effect because any cause is its effect.

But if we think about it, we don't --- or tend not to -- experience cause as effect. If we are going to, that's that, then the effect is somehow put off to another time: karma.
UPDATE based on the edited question with a suggested definition of karma.

While it is true that the Buddha taught that each and every volitional action has specific consequences this is most definitely not in opposition to the fact that repeated actions based on volitional thoughts can be habit forming. Indeed, consequences of a karmic action can be that it leads to further such actions.

If I were to tell you right now not to think of a pink elephant the chances are likely that you will do so in the immediate future. What's more, it is likely that many beings reading this will be thinking of pink elephants in a more distant future as a consequence of the pink elephant they are bringing to mind right now. I invite you to observe your monkey mind at work with its discursive thoughts and see if you can't trace the cause and effect consequence of each thought leading to others in a more or less continuous process. One moment of mind gives birth to the next and on and on.

Surrounding the definition in the Stanford Encyclopedia is a discussion of how karma and rebirth are in some tension with the Buddha's teaching on emptiness. I believe the correct conceptual understandings of emptiness, karma and rebirth resolve this tension.

This whole notion of the fruits of karmic action being delayed as some sort of puzzle is itself somewhat puzzling to me. In my very life I have observed that my actions can have far reaching consequences. Far reaching in time and space. What I have done or failed to do when I was young (decades ago) has manifested in the situation I am in now. Isn't that just obvious for you as well?

Asking where the consequence of a karmic action (that has ceased) is stored in time and space betrays the wish for a metaphysical explanation. And this metaphysical explanation leads to the doctrine of emptiness as it explains how things exist and how they do not. In what manner they exist and in what manner they do not. Asking where the consequence is stored (in time and space) betrays the idea that phenomena (including karmic actions) have substantial inherent own-being. They do not. That is explained and reasoned through by the teaching on emptiness that Nagarjuna has expounded.

The sutra below explicitly lays out that the Buddha says that the consequence is not stored in time and space. And it goes on to show that actions, consequences, death, birth, karma, are all void of own being. This is the teaching on emptiness. 

Believing that the teaching on emptiness somehow is problematic for dependent origination or the law of cause and effect is just wrong. In fact, it is quite the opposite as Nagarjuna has said in his famous treatise! Without emptiness - that is if things had their own-being - then actions could not be performed and there would be no cause and effect or dependent origination. 

Would encourage you to study Nagarjuna and trace his arguments if you can.



Although I am not certain about what your question actually is about I thought I'd share this passage from a rather obscure sutra that may help your mind:


  THE NOBLE SUTRA OF THE MAHAYANA DENOMINATED - "THE PASSAGE THROUGH
  EXISTENCES"
  
  Homage to all the Buddhas and Bodhisattvaas. Thus have I heard. Once
  the Bhagavant stayed in Rajagrha, in the Bamboo-Forest, in the place
  of the kalandakas, in the company of a group of one thousand two
  hundred and fifty bhiksus and of very numerous great Bodhisattvas.
  Then, the Bhagavant, while he was surrounded by many hundreds of
  thousands of his followers, looking at them, expounded the Dharma and
  expounded in its integrity the Brahmacarya beautiful in its beginning,
  beautiful in the middle, beautiful in its end, fair in its meaning,
  fair in its expression, without confusion, completely fulfilled,
  completely pure, completely immaculate.
  
  Then Sreniya Bimbisara, King of the Magadha country, going out from
  the town of Rajagrha, with great royal pomp, with a great royal force,
  went to the Bamboo-Forest where the Bhagavant was. On arriving, after
  bowing down at the feet of the Bhagavant and turning (around the
  Bhagavant) the right side towards him three times, Sreniya Bimbisara,
  King of the Magadha country, spoke thus to the Bhagavant : "O
  Bhagavant, how do actions, (a long time) after having been done (and)
  accumulated, a long time after having ceased, (re)appear in the mind,
  on being near the moment of death? All conditioned things (samskara)
  being void, how do actions pass without being annihilated?"
  
  So (the King) spoke, and the Bhagavant to Sreniya Bimbisara, King of
  the Magadha country, said thus : "O great King, just as for instance a
  man, in a dream while he is sleeping, dreams that he extremely enjoys
  himself with a beautiful woman of his country and, when he awakes from
  his sleep, remembers that beautiful woman of his country (he has seen
  in his dream) - what do you think, O great King : does that beautiful
  woman of the country, (seen) in the dream, (really) exist?"
  
  (The King) said : "O Bhagavant, she does not exist."
  
  The Bhagavant said : "O great King, what do you think : that man who
  ardently desires the beautiful woman of his country, (seen) in his
  dream - is he a wise man?"
  
  (The King) answered : "O Bhagavant, he is not - if it is asked why, O
  Bhagavant - because that beautiful woman of the country, (seen) in the
  dream, does not exist at all; and although he does not perceive her,
  (nevertheless) he goes on thinking of enjoying himself extremely with
  her. Thus that man, being deprived of her, has a destiny of sorrow."
  
  The Bhagavant said : "O great King, in the same way, an ordinary man,
  foolish, ignorant, on seeing with his eyes lovely forms, ardently
  desires those forms which are agreeable to his mind. While ardently
  desiring them, he becomes attached to them. On becoming attached to
  them, he feels a passion for them. On feeling a passion for them, he
  performs with his body, speech and mind,, actions that are born out of
  desire, hatred and error. And those actions, after having been
  performed, cease. And after having ceased, (those actions) stay
  neither in the east nor in the south nor in the west nor in the north
  nor up nor down - nor in any region of space. But, at any other time,
  at the moment near the instant of death, when the karma corresponding
  (to the life that is being concluded) is exhausted, at the (very)
  moment the last consciousness ceases, those actions (re)appear in the
  mind (of the dying man) - just as for instance the beautiful woman of
  the country (in the mind) of the man that wakes from his sleep. O
  great King, immediately after the first consciousness has ceased,
  there arises the series of consciousnesses, which corresponds (to the
  life that is beginning), and in which the ripening (of actions
  previously performed) will be experienced. O great King, although no
  element of existence (dharma) passes from this world to another world,
  nevertheless death and birth take place. O great King, the last
  consciousness which ceases is called 'death'; the first consciousness
  which arises is called 'birth'. O great King, the last consciousness,
  at the moment it ceases, does not pass to anywhere; the first
  consciousness, which forms part of the (new) birth, at the moment it
  arises, does not come from anywhere. If it is asked why, (I answer:)
  because of their lack of an own being. O great King, although the last
  consciousness is void (of the own being) of death, action is void (of
  the own being) of action, the first consciousness is void (of the own
  being) of a first consciousness, birth is void (of the own being) of
  birth, (nevertheless) actions do not perish. O great King, immediately
  after the first consciousness, which forms part of the (new) birth,
  has ceased, there arises without interruption the series of
  consciousnesses, in which the ripening (of actions previously done)
  will be experienced."


This sutra speaks directly to karma and how it ripens from moment to moment and life to life even though actions previously arisen have ceased and exist no where whatsoever in space or time and yet they ripen at later times and continue to produce fruit. The important point is that the manner and way this happens from moment to moment in this very life is the same manner and way it happens from life to life. There is no difference in extent or manner.

And note that the doctrine of emptiness is very definitely tied up with this ripening of past karma. Karma could not function without emptiness. Were things not empty, there could not be actions and the ripening of those actions. Understanding emptiness is indispensable in understanding how actions ripen and bear fruit and that is why it is said that emptiness and dependent origination go hand in hand.