Limited Arbitrage, Gains from Trade and Arrow's Theorem

"The expression 'limited arbitragers' used to describe economies where only bounded, or limited, opportunities for gains are available to the traders from their initial endowments. This concept was rigorously defined in [4], [5] and shown to be central to the problem of resource allocation; it is also linked to the social diversity of the economy [7]. It turns out that a simple geometric interpretation can be given to limited arbitrage: here I show that it is equivalent to bounding the gains from trade, namely the sum of utilities increases which the traders can achieve from their initial endowments (Proposition 2, Section 1). From this geometry a somewhat unexpected new link emerges: a close connection with Arrow's impossibility theorem [1]. I establish that markets have limited arbitrage if and only in they have no Condorcet triples beyond certain utility levels (Proposition 3, Section 3). This means that on choices of great importance, irrational or intransitive behavior does not arise. Since Condorcet triples are the building blocks of Arrow's theorem, limited arbitrage appears to be at the core of social choice theory. The connection between limited arbitrage and the concept of no-arbitrage used in financial markets is discussed in Section 2.