Some assembly required

What do games of chance, analyzing the spread of AIDS, gambling on football games, hedging on the market, appointment of congressional seats to states, and even strategic behavior have to do with this part-whole conflict?

I already explained why an array of important assertions — Arrow's Theorem, Sen's Theorem, as well as the difficulties experienced by pairwise voting, agendas, tournaments, conflicting comparisons, and even the search for consensus — reflect the loss of central, readily available information. Simply stated, by not using crucial information, the integrity of the outcomes cannot be ensured. Problems must be expected whenever information about the disconnected parts fails to characterize the connected whole.

The situation resembles those three feared words which can accompany a new purchase — some assembly required. Panic rushes in. Where is the instruction sheet? Without instructions explicitly explaining how the parts are related, without a guide to clarify how to put them together, the purchase can become an expensive pile of junk — a useless collection of parts collecting dust rather than meeting an intended goal. Similarly, as described in the last chapter, whenever a voting or decision procedure concentrates on the parts, it can unintentionally ignore the assumption that the voters have rational preferences. Lost is the instruction sheet describing how the parts — how each voter's ranking of the pairs — should be assembled. Since the properties of a procedure reflect its inability to use “connecting” information, we must anticipate results such as those of Arrow, Sen, and the free rider.