Should I have used a different word? Probably! But I will now proceed to a complex justification of my word choice anyway!
A lot of philosophy seems to be coming up with explicit definitions that fit our implicit mental categories - see Luke's post on conceptual analysis (which I might be misunderstanding). Part of this project is the hope that our implicit mental categories are genuinely based off, or correspond to, an explicit algorithmizable definition. For example, one facet of utilitarianism is the hope that the principle of utility is a legitimate algorithmization of our fuzzy mental concept of "moral".
This kind of philosophy usually ends up in a give-and-take, where for example Plato defines Man as a featherless biped, and Diogenes says that a plucked chicken meets the definition. Part of what Diogenes is doing is saying that if Plato's definition were identical to our implicit mental category, we would implicitly common-sensically identify a chicken as human. But we implicitly common-sensically recognize a chicken is not human, therefore our minds cannot be working off the definition "featherless biped".
This is the link between defining and predicting. Plato has proposed a theory, that when the mind evaluates humanity, it uses a featherless-biped detector. Diogenes is pointing out Plato's theory makes a false prediction: that people implicitly recognize chickens as humans. This disproves Plato's theory, and so the definition is wrong.
I suppose this must be my mental concept of what we're doing when defining a term like "self", which is what impels me to use "define" and "predict" in similar ways.
Was the irony intentional? If not that is just priceless!
Humans being what they are, when they define things it will inevitably tend to influence what predictions they make. Where a boundedly rational agent prescribed a terrible definition would be merely less efficient a human will also end up with biased predictions when reasoning from the prediction. Also, as you note, declaring a definition can sometimes imply that a prediction is likely to be made that the definition matches the mental concept while also carving reality effectively at it's joints.
The ...
Eliezer wonders about the thread of conscious experience: "I don't think that, if I were really selfish, I could jump off a cliff knowing smugly that a different person would experience the consequence of hitting the ground."
Instead of wondering whether we should be selfish towards our future selves, let's reverse the question. Let's define our future selves as agents that we can strongly influence, and that we strongly care about. There are other aspects that round out our intuitive idea of future selves (such as having the same name and possessions, and a thread of conscious experience), but this seems the most fundamental one.
In future, this may help clarify issues of personal identity once copying is widespread:
These two future copies, Mr. Jones, are they both 'you'? "Well yes, I care about both, and can influence them both."
Mr Jones Alpha, do you feel that Mr Jones Beta, the other current copy, is 'you'? "Well no, I only care a bit about him, and have little control over his actions."
Mr Evolutionary-Jones Alpha, do you feel that Mr Evolutionary-Jones Beta, the other current copy, is 'you'? "To some extent; I care strongly about him, but I only control his actions in an updateless way."
Mr Instant-Hedonist-Jones, how long have you lived? "Well, I don't care about myself in the past or in the future, beyond my current single conscious experience. So I'd say I've lived a few seconds, a minute at most. The other Mr Instant-Hedonist-Jones are strangers to me; do with them what you will. Though I can still influence them strongly, I suppose; tell you what, I'll sell my future self into slavery for a nice ice-cream. Delivered right now."