Editing Rational choice model (section)

===Formal statement===
The available alternatives are often expressed as a set of objects, for example a set of ''j'' [[Collectively exhaustive events|exhaustive]] and [[Mutually exclusive events|exclusive]] actions:
:<math>A = \{a_1, \ldots, a_i, \ldots, a_j\}</math>
For example, if a person can choose to vote for either Roger or Sara or to abstain, their set of possible alternatives is:
:<math>A = \{\text{Vote for Roger, Vote for Sara, Abstain} \}</math>

The theory makes two technical assumptions about individuals' preferences over alternatives:
* '''[[Completeness (order theory)|Completeness]]''' – for any two alternatives  ''a<sub>i</sub>'' and  ''a<sub>j</sub>'' in the set, either  ''a<sub>i</sub>'' is preferred to  ''a<sub>j</sub>'', or ''a<sub>j</sub>'' is preferred to ''a<sub>i</sub>'', or the individual is indifferent between ''a<sub>i</sub>'' and ''a<sub>j</sub>''.  In other words, ''all'' pairs of alternatives can be compared with each other.
* '''[[Transitive relation|Transitivity]]''' – if alternative  ''a''<sub>1</sub> is preferred to ''a''<sub>2</sub>, and alternative ''a''<sub>2</sub> is preferred to ''a''<sub>3</sub>, then ''a''<sub>1</sub> is preferred to ''a''<sub>3</sub>.

Together these two assumptions imply that given a set of exhaustive and exclusive actions to choose from, an individual can ''rank'' the elements of this set in terms of his preferences in an internally consistent way (the ranking constitutes a [[total order]]ing, minus some assumptions), and the set has at least one [[maximal element]].

The preference between two alternatives can be:
* '''Strict preference''' occurs when an individual prefers ''a''<sub>1</sub> to ''a''<sub>2</sub> and does ''not'' view them as equally preferred.
* '''Weak preference''' implies that individual either strictly prefers ''a''<sub>1</sub> over ''a''<sub>2</sub> or is indifferent between them.
* '''Indifference''' occurs when an individual neither prefers ''a''<sub>1</sub> to ''a''<sub>2</sub>, nor ''a''<sub>2</sub> to ''a''<sub>1</sub>. Since (by completeness) the individual does not ''refuse'' a comparison, they must therefore be indifferent in this case.

Research since the 1980s sought to develop models that weaken these assumptions and argue some cases of this behaviour can be considered rational. However, the [[Dutch book argument|Dutch book theorems]] show that this comes at a major cost of internal coherence, such that  weakening any of the [[Von Neumann–Morgenstern utility theorem|Von Neumann–Morgenstern]] axioms makes. The most severe consequences are associated with violating [[independence of irrelevant alternatives]], and [[Money pump|transitive preferences]], or fully abandoning completeness rather than weakening it to "asymptotic" completeness.

<!--===Additional assumptions===
* ''Perfect information'': The simple rational choice model above assumes that the individual has full or [[perfect information]] about the alternatives, i.e., the ranking between two alternatives involves no uncertainty.
* ''Consistent Preferences'': The rational choice model assumes that preferences will remain consistent, in order to maximize personal utility based on available information
* ''Best course of action'': The simple rational choice model assumes that individuals are capable of calculating the best course of action and that they always intend to do so. 
* ''Choice under uncertainty'': In a richer model that involves uncertainty about the how choices (actions) lead to eventual outcomes, the individual effectively chooses between lotteries, where each lottery induces a different [[probability distribution]] over outcomes. The additional assumption of [[independence of irrelevant alternatives]] then leads to [[expected utility theory]].
* ''Inter-temporal choice'': when decisions affect choices (such as consumption) at different points in time, the standard method for evaluating alternatives across time involves [[discounting]] future payoffs.
* ''Limited cognitive ability'': identifying and weighing each alternative against every other may take time, effort, and mental capacity. Recognising the cost that these impose or cognitive limitations of individuals gives rise to theories of [[bounded rationality]].

Alternative theories of human action include such components as [[Amos Tversky]] and [[Daniel Kahneman]]'s [[prospect theory]], which reflects the empirical finding that, contrary to standard preferences assumed under neoclassical economics, individuals attach extra value to items that they already own compared to similar items owned by others.-->