Paper: Arrow (1950)

19 pages in total. The theorem is popularized more by the 1951 book.
== Summary ==
=== I. Introduction (328-331) ===
* Par 1-2: mention 4 methods of social choice: voting, markets, dictatorship, and convention. He contrasts the latter two as not involving conflict of individual wills, with the former two as "methods of amalgamating the tastes of many individuals". Are the latter who collective modes of choice rational?
* Main question: "we ask if it is formally possible to construct a procedure for passing from a set of known individual tastes to a pattern of social decision-making, the procedure in question being required to satisfy certain natural conditions."
* Example of this failing: the paradox of voting: A \succ_1 B, B \succ_1 C \implies A \succ_1 C 
, and B \succ_2 C, C \succ_2 A \implies B \succ_2 A
, and C \succ_3 A, A \succ_3 B \implies C \succ_3 A. Then A wins from B, B wins from C, but C wins from A. So, the majority voting method here fails to produce rational collective choices. 
* Can we find other methods of aggregating individual tastes which imply rational behavior of the community (and which will be satisfactory in other ways)? If we adopt the identification of rationality with maximization of some sort, then the problem of achieving a social maximum derived from individual desires is precisely the problem central to welfare economics.Makes a nice note here that earlier welfare economics was based on cardinal preferences and was plagued by difficulties of interpersonal comparisons. It is noted that emphasis shifted to a weaker definition: Pareto optimality. But, this is not sufficient to make social choices, it is only preliminary to it.
* Voting and Kaldor's compensation principle are two social choice methods, but both suffer from the same problem outlined above: a paradox need not occur, but there are preference patterns which will give rise to inconsistent social choice patterns. Therefore, both must be regarded as unsatisfactory techniques for the determination of social preferences.
* "The aim of the present paper is to show that these difficulties are general. For any method of deriving social choices by aggregating individual preference patterns which satisfies certain natural conditions, it is possible to find individual preference patterns which give rise to a social choice pattern which is not a linear ordering."I'm fairly confident linear ordering here means total ordering in the mathematical sense.
=== II. Definitions and Notation (331-334) ===
==== II.1. A Notation for Preferences and Choice ====
==== II.2. The Ordering of Social States ====
=== III. The Social Welfare Function (334-339) ===
==== III.1. Formal Statement of the Problem of Social Choice ====
==== III.2. Positive Association of Social and Individual Values ====
==== III.3. Independence of Irrelevant Alternatives ====
==== III.4. The Condition of Citizens' Sovereignty ====
==== III.5. The Condition of Non-Dictatorship ====
=== IV. The Possibility Theorem for Social Welfare Functions (339-342) ===
==== IV.1. The Range of Possible Individual Orderings ====
==== IV.2. The Possibility Theorem ====
=== V. Some Implications for the Formation of Social Welfare Judgments (342-346) ===
==== V.1. Interpretation of the Possibility Theorem ====
==== V.2. A Reflection on the New Welfare Economics ====
==== V.3. A One Commodity World ====
==== V.4. Distributional Ethics Combined with Individualism ====