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Democracy and the Arrow Impossibility theorem
The Economists, a weekly news magazine, published in London England, is often
considered the leading news magazine of the western world since it reports news not
from the US point of view. Articles in it are often quoted worldwide. In this week's issue
(7/14-20/07 p.45) it reports a news item concerning the conflict resolution in Beijing's
Jiuxianqiao (九仙桥??) neighborhood. Apparently this is an old run down neighborhood
in the midst of a trendy part of the capital. Private developer want to demolish the old
buildings and apartments for new luxury construction. But the residents, mostly retired
workers, have different opinions on the amount of compensations offered. Even though a
majority of the residents approved the plan in a "referendum" vote on June 9, the issue is
far from resolved among the developer, the local government, the residents, and the
media that report on the problem.
Ordinarily, such a local and relatively insignificant matter hardly warrants reporting in a
prestigious world news magazine. The main reason of its place in the Economists this
week must be the world's interest with the experimental democracy in China these days
This brings me to my blog this week.
Winston Churchill said famously that "Democracy is the worst form of government
except for all others". The Nobel prize winning economist, Ken Arrow, proved in the
50's his famous impossibility theorem on social choice which commonly known as the
impossibility of fair voting theorem.
Most of us who had any experience with voting know the unfairness of the majority vote
under certainly situation, particularly with respect to minority rights. Yet almost all
democratic system practices it despite its imperfection which of course is the source of
frustration aptly expressed by Churchill.
The Arrow theorem, roughly speaking, deal with the following universal problem. In a
society of human beings, each of us in principle has a set of preference with respect to
everything, such as, housing, health, traffic, jobs, etc. etc. The purpose of a society, any
society or system of government, is to amalgamate these individual preferences into one
social preference (or social choice or social policy) for all things ( housing, health, traffic,
jobs, etc.) for the entire population. You presumably accomplish this by some system of
voting, informal sampling of opinions, or even random choice. Arrow's result says no
such scheme exist if you want the social choice to satisfy a set of six eminently
reasonable requirements. In other word, no voting method of determining the correct
social choice is possible. One of the reasonable requirement is the non-existence of a all
wise God (or what Chinese called 仁君a benevolent emperor ). This may partially
explain why China had a emperor/dynastic systems of government for thousands of years.
However, here you are up against another political truism "power corrupts, absolute
power corrupts absolutely". History has proved again and again the truth of this
statement. We may be lucky to have a single仁君 for a finite duration, but how long can
s/he stay that way given human weakness. And in a dynasty of emperors where power is
inherited, how lucky can one get?
This gets us back to Churchill's remark and the Arrow's theorem. This is an imperfect
and complex world. We have an imperfect system of conflict resolution called democracy.
But it is the best we have. Laws, regulations, and system of government must be a living
adaptive thing tuned in to the local condition, custom, environment, and general
education level. Any attempt such as to export US democracy to Middle East without
change however well intentioned is doomed to failure.
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