The Arrow Impossibility Theorem by Amartya Sen
My rating: 4 of 5 stars

Why Nothing Works Right

The Nobel Prize-winning economist. Kenneth Arrow, died this past week. His famous Impossibility Theorem is, like many profound ideas, more talked about than understood. Sen's book is both a tribute to the man and an introduction this very disconcerting idea.

The Arrow Impossibility Theorem is arrived at through some tricky maths. But its conclusion is easy to state: In any group of people who have to reach a decision together but who have even slightly different preferences about where they want to end up, the decision they will reach is that which they all can accept but which none of them wants.

It applies to any group - electorates, markets, corporate boards, local councils, ad hoc committees, working parties, family meetings - wherever a choice among alternative courses of action is required. It applies even when, in fact especially when, members of the group are respectful and concerned about each other and the continued unity of the group. It is the default condition of all human deliberations.

The Theorem has been popularised as, among other things, the Abilene Paradox (https://www.goodreads.com/book/show/6... ) which is frequently mentioned but rarely explored by management consultants and experts in decision-theory. The full impact of its meaning has never really been appreciated either in the social sciences disciplines where it should be of paramount concern, or among the general public who deserve to know the inevitable consequences of decision-making in areas as diverse as democratic politics and corporate strategy.

The truth is that none of these decisions have any solid claim to representative rationality. The Theorem is not some quaint paradox that is of marginal importance to mathematicians. It is the WMD of collective choice, the granddaddy poisoner of political wells, the hydrogen bomb targetted on our pretensions of social rationality. The implications are profound, perhaps too profound to deal with. So the Theorem is largely ignored.

But we may have reached a point in both political and corporate life in which the Arrow Theorem can no longer be ignored. It is obvious, for example, that the national politics in the United States has cracked under just the kind of pressure Arrow predicted. Its principle electoral effect of dissatisfaction is growing. Frustration with democracy is intensifying. Acceptance of results wears increasingly thin as decisions disadvantage voters disproportionately.

The psychological effects are just as important. Continuous compromise promotes the sentiment of dictatorship, the strong man who can cut through messy democratic politics as the only real solution to the problem. Dictatorship can at least promise the satisfaction of some segment of society. Others may be tremendously disadvantaged but that's merely the price necessary to pay for coherence of action. It is to a sort of dictatorial sump that democratic attitudes deteriorate in a possibly inevitable progression.

In short, the Arrow Impossibility Theorem points to a fatal flaw in every form of social governance upon which we rely in civic and corporate life. It is a formulation of our social original sin. We are born into it without a choice. It sits in our somewhat smug society waiting for a chance to demonstrate its power. To date, no one has devised a convincing way to even mitigate its effects much less neutralise them. The least we can expect as the paradox bites deeper into social life is more vituperative party politics and more of Donald Trump.

Postscript: For a discussion of one promising approach to the Arrow problem see https://www.goodreads.com/review/show...

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