I told you

5/01/2010 04:12:00 am / The truth was spoken by Rich /

From 'the Underground Economist' Tim Harford's column in the Financial Times:

Yet, I am reminded of Kenneth Arrow – the youngest and perhaps most brilliant of all the Nobel laureate economists – and his “general possibility theorem”. Arrow’s theorem – more popularly known as the impossibility theorem – explores how individual preferences could be lumped together to express the preferences of society.

To get a rough idea of the proof, first let’s agree that if A is unanimously preferred to B, society must be assumed to prefer A to B. We can then prove (I won’t – but it can be done) that we can shrink the size of this decisive group regarding A and B from “everyone” to a single decision-maker. In other words, “society’s preference” between A and B ends up depending on some particular individual. Finally, it can be proved that if an individual is decisive as far as A and B are concerned, she ends up being decisive over all possible outcomes. In short, the only “social preference” is the whim of a dictator.

Arrow’s theorem is often interpreted as meaning that no voting system can ever reliably reflect society’s real preferences. It actually means something much more profound: that it is nonsense to even speak of society’s real preferences. In an election week, this puts democracy in its proper place: it is indispensable, but let’s keep a sense of perspective, shall we?



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