The theorem states that, absent restrictions on either individual preferences or neutrality of the constitution to feasible alternatives, there exists no social choice rule that satisfies a set of plausible requirements.

The Introduction contrasts voting and markets with dictatorship and social convention (such as those in a religious code).

Voting and markets facilitate social choice in a sense, whereas dictatorship and convention limit it.

Majority rule works for an individual selecting consistently among the 3 candidates but not necessarily for the "social choice" in any general sense.

Arrow asks whether other methods of taste aggregation (whether by voting or markets), using other values, remedy the problem or are satisfactory in other ways.

To answer the questions, Arrow proposes removing the distinction between voting and markets in favor of a more general category of collective social choice.

Topics implicated along the way include game theory, the compensation principle in welfare economics, extended sympathy, Leibniz's principle of the identity of indiscernibles, logrolling, and similarity of social judgments through single-peaked preferences, Kant's categorical imperative, or the decision process.

The book defines a few terms and logical symbols used thereafter and their applied empirical interpretation (pp.

So, the ordering is an "individual value," not merely, as in earlier analysis, a purely private "taste."

It is convenient for deriving implications to compact the first two of these options on the ballot to one, an "at least as good as" relation, denoted R: The above two properties of an ordering are then axiomatized as: connectedness: For all (the objects of choice in the set) x and y, either x R y or y R x. transitivity: For all x, y, and z, x R y and y R z imply x R z.

From this, conjunction ('and') and negation ('not') of mere pairwise R relations can (also) represent all the properties of an ordering for all the objects of choice.

But Arrow places the constitution in the context of ordinalist welfare economics, which attempts to aggregate different tastes in a coherent, plausible way.

A constitution might seem to be a promising alternative to dictatorship and vote-immune social convention or external control.

Absent deadlock, transitivity crowds out any reference to the status quo as a privileged default blocking the path to a social choice (p. 120).

Arrow proposes the following "apparently reasonable" conditions to constrain the social ordering(s) of the constitution (pp.

Arrow describes this condition as an extension of ordinalism with its emphasis on prospectively observable behavior (for the subset in question).

The book proposes some apparently reasonable conditions for a "voting" rule, in particular, a 'constitution', to make consistent, feasible social choices in a welfarist context.

The 1963 edition includes an additional chapter with a simpler proof of Arrow's Theorem and corrects an earlier point noted by Blau.

[6] It also elaborates on advantages of the conditions and cites studies of Riker[7] and Dahl[8] that as an empirical matter intransitivity of the voting mechanism may produce unsatisfactory inaction or majority opposition.

These support Arrow's characterization of a constitution across possible votes (that is, collective rationality) as "an important attribute of a genuinely democratic system capable of full adaptation to varying environments" (p. 120).

The theorem might seem to have unravelled a skein of behavior-based social-ethical theory from Adam Smith and Bentham on.

The large subsequent literature has included reformulation to extend, weaken, or replace the conditions and derive implications.