Introduction

We now understand these problems from Arrow's and Sen's theorems, Simpson's Paradox, gambling, economics, inefficiencies of complex, decentralized systems, and on and on. The paradoxical behavior reflects the inadvertent loss of crucial but available information about how the disjoint parts are related. Worse than being “lost,” this information can be purposely dismissed whenever we use or design procedures — whether decision, economic, or statistical — which emphasize the “disjoint parts” over the “whole.”

As illustrated, by understanding why problems occur, a wide selection of unexpected examples from a variety of areas can be discovered. Quite frankly, by now, we should view with suspect any conclusion from any subject area which involves the surgical separation of “parts” from one another. Definitely worry when this separation is advertised in terms of noble intents such as “efficiency” or preserving the “integrity of the outcome.”

A more ambitious goal is to find resolutions. At least in principle, we know how to do this; reintroduce the lost information. But, how? To provide guidance in doing so, I tackle the obvious challenge of showing how not to, and then how to, circumvent the fundamental difficulties imposed by Arrow's and Sen's theorems.

To start, recall that Arrow's theorem requires a sufficiently heterogeneous society; this causes the Arrovian procedures to lose information about the rationality of the voters. So, to find a useful resolution, maybe we should design ways which avoid highly heterogeneous settings, or which require — in a “to-be-determined” manner — the decision process to use the previously dismissed information.