hypotheses for why people on the margin make step-function-y decisions

The scenario we are discussing:

Alice and Bob both have a collection of decisions to make, which result in income input and output. All her decisions trade a quantity q_X of an entity X for an amount of money m. Alice starts with an amount M_A, and Bob starts with M_B; each make a series of trades, which are given by T_A: Q_X -> M.

T_A(q) ~= floor(q)*f(q) , where f(q) monotonically increases

T_B(q) ~= f(q)

The real reason we're even talking about this, of course, is because we're trying to figure out how intelligence - i.e. approaches to solving a resource allocation problem, or any other - might aggregate across populations, or across time. A good general persepctive on why this problem might be a problem comes from Mullainathan & Shafir , who discuss the idea that the aggregation mechanism that applies to the decisions made by the poor might be crucial architecture of the poverty trap; as opposed to being transparently caused by the harmful tendencies possessed by poor individuals themselves, or the circumstances and institutions that determine and limit the opportunities afforded to the poor.

So: an atomic decision, iterated over time; or, an atomic decision, made by every member of a crowd.

In the former case, we ask after the stocks and flows: what values are changing? Early decisions affect the context in which late ones are made, and the cleverest approach will stabilize on a time graph of some sort; from which other graphs, that try to capture the policy being followed, might derive.

In the latter, we ask after what game the crowd is playing. What are the strategic interactions? What outcomes are salient to every member? What does each member prefer? What can they enforce, under the circumstances? In order to enforce it, who must they cooperate with, and how?

The game itself acts as the aggregation mechanism in that case. A collective of people can be superadditive or subadditive no matter what they choose, if the rules they are playing by choose to enforce it. How knowledge aggregates across that collective will naturally depend on whether competition or collaboration is viable in context.

In the above example, therefore, we must ask ourselves: why does Alice behave this way? And our answers must allow us to construct a gears-level model for how Alice's behaviour follows from her circumstances, without "explaining away" her "individual" considerations...that is, the things that follow from Alice's circumstances uniquely, within which she may be a bounded reasoner and capable of errors in judgment, but is nonetheless best situated to determine approaches to, must be parametrized in order for us to construct a general model; and the model we construct must also allow us to examine how Alice's errors might propagate and amplify, if only to ensure that we are mitagating them, rather than amplifying them in turn.

Something something my head for statistics is not clear at the moment

This is a thing we have to return to once we have a better understanding of what it is we're even alleging.