"Saying “we as a society” means one
of two things: “We who agree with the choice imposed on others,” or, “We
are irrational in this choice, and could as well have chosen something
else.” In other words, “we as a society” does not really exist, except
perhaps with respect to a few fundamental values on which unanimity
obtains."
The Paradox of Voting
“We as a society” does not exist
DECEMBER 03, 2013
by PIERRE LEMIEUX
Speaking about Obamacare, MIT economics professor
Jonathan Gruber said, “We’ve decided as a society that we don’t want
people to have insurance plans that expose them to more than six thousand
dollars in out-of-pocket expenses.”
What does it mean that “we” decide something “as a society”? It’s an
important question: This sort of statement gets used frequently as a
justification of government of intervention. When, in the same fashion,
Obama says
“
we as a nation,” he is just using a variation of the same _expression_
and talking like the average politician.
“We as a society” or “we as a nation” is generally used as an incantation
with no scientific meaning. If it has any ascertainable meaning, it means
“we who want to impose our current and perhaps changing whims on
others.”
The simplest interpretation of “we as a society” is that it represents
what a majority votes for. It would simply mean, we as a majority of
51 percent (or 60 percent, or 30 percent if we are talking of a mere
plurality). But how is the majority representative of society? What tells
us that another majority wouldn’t vote differently if the issues were
presented differently? Whose preferences exactly does the majority
represent?
That Median Voter
In certain cases, the majority represents the preferences of a small
group of voters, perhaps a single voter. The “median-voter theorem” shows
that if you have one voter (or one group of voters), whose preferences
are exactly in the middle of the distribution of preferences, he will win
elections.
For example, if the median voter prefers public expenditures to be $3
trillion, no politician can win an election against one who runs on this
proposal. Any politician who proposes to spend more or less will lose
more than 50 percent of the electorate to the one who stands exactly in
the center. The median voter theorem explains why a successful politician
has to “hug the center,” as
The
Economist
puts it to explain the recent gubernatorial elections.
Preference Aggregation
When, however, the electorate is polarized around two opposing stances,
the median voter theorem does not apply. More diverse individual
preferences, and a more diverse society, weaken the median voter’s power.
What happens in this case? Who is the majority? How does it behave?
These issues fall under the label of “preference aggregation,” within a
field of inquiry called social choice. The broad question is, how can the
preferences of votersor, more generally, of individuals in societybe
aggregated to produce social choices?
A little intellectual voyage will help us answer this question.
First, meet Jean-Antoine-Nicolas de Caritat, marquis de Condorcet
(1743–1794). Condorcet was a French mathematician, philosopher, and
classical liberal. Like many politicians, he became cross with the French
authorities under the Terror (the nastier phase of the French
revolution), was arrested on March 27, 1794, and died in jail a few days
later.
His death, however, had nothing to do with his 1785 book, Essay on the
Application of Probability Analysis to Decisions Made with a Plurality of
Votesexcept perhaps to the extent that he was not an intellectual
yes man. Condorcet was the first one to clearly isolate a strange
phenomenon that came to be known as the “paradox of voting”: even if each
voter is rational, the result of a vote can be irrational.
“Rational” in this context simply means consistent or transitive
preferences: If you prefer X to Y, and Y to Z, you will also prefer X to
Z. The Condorcet paradox says that even with rational electors, a
majority that prefers X to Y and Y to Z can prefer Z to X.
An example will make this easier to grasp. Suppose the issue is whether
the president should have more power over the budget (compared to
Congress), less power, or the same degree of power as now. Let P
represent the status quo, P- mean less power to the president, and P+
more power. Now consider an electorate composed of three voters: Alice,
Bob, and Charlie. Suppose that Alice prefers P- to P to P+, which we can
write as P->P>P+. We use symbols to economize on words:
“>”simply means “preferred to.” Like all other voters, Alice is
rational, which implies that she also prefers P- to P+. Assume that Bob’s
preferences are P>P+>P-. As for Charlie, his preferences are
represented by P+>P->P. Bob and Charlie are also supposed to
have transitive preferences.
It is easy to check that if our voters are asked to vote between P- and
P, the majority (Alice and Charlie) will choose P-. If the electorate
votes between P and P+, the majority (Alice and Bob) will choose P. Since
the electorate prefers P- to P, and P to P+, you would think that it
would prefer P- to P+ if presented with these two alternatives. But no!
You can check that P+ would win over P- with a majority of votes (Bob and
Charlie). The electorate is irrational even if each voter is
rational.
Other preference orderings will produce a rational electoral choice. But
the example shows that the paradox of voting can appear. “We as a
society” is more a casino roulette than a rational actor.
Cyclical Majorities
This theory explains many observable phenomena. It explains the
inconsistencies we often find in public opinion surveys. It may explain
why voters vote both for job creation programs and for minimum wages that
destroy jobs. It explains the votes on the Muscle Shoals hydroelectric
project in the U.S. senate in 1925. Over less than a week in January of
that year, and without any senator changing his mind, the U.S. senate
voted to refer the alternatives to a study commission instead of allowing
private development, then for private development instead of public
ownership, and then again for public ownership instead of a study
commission (see John N. Neufeld et al., “A Paradox of Voting: Cyclical
Majorities and the Case of Muscle Shoals,” Political Research
Quarterly, vol. 47, no. 2, 1994).
This is another example of the paradox of voting, also called “cyclical
majorities.” Voters -- U.S. senators in this case -- cycle between issues
without being able to reach a definitive decision.
Mathematician Charles L. Dodgson (1832–1898) rediscovered the phenomenon
of cycling a hundred years after Condorcet. Dodgson was also known as
Lewis Carroll, author of Alice in Wonderland and other literary
works. That such a creative spirit as Dodgson worked on cycling lends
more credence to the importance of the topic.
Our intellectual voyage now takes us to Duncan Black (1908–1991), a
Scottish economist who rediscovered the paradox in the mid-twentieth
century. When a numerical example he was working on showed an irrational
electorate made of rational voters, Black was deeply disturbed: “On
finding that the arithmetic was correct and the intransitivity
persisted,” he later explained, “my stomach revolted in something akin to
physical sickness.” He had to admit that his prior intuitionthat
rational voters produce a rational electoratewas disturbingly
wrong.
The final destination in our voyage is Kenneth Arrow, a Stanford
University economist who extended the opportunity for nausea to all
economists and political scientists who study the issue. In his 1951
book, Social Choice and Individual Values, Arrow mathematically
demonstrated that the discovery of Condorcet, Dodgson and Black was only
a special case of a more general theorem: Whatever the decision mechanism
used, a social choice cannot be both democratic and rational. If all
individual preferences are to count equally (and given a few other
axioms), a social choice must be either irrational or imposed by some on
others. For his work, Arrow (along with with John Hicks) won the 1972
Nobel Prize in economics.
The political implications are striking. Saying “we as a society” means
one of two things: “We who agree with the choice imposed on others,” or,
“We are irrational in this choice, and could as well have chosen
something else.” In other words, “we as a society” does not really exist,
except perhaps with respect to a few fundamental values on which
unanimity obtains.
http://www.fee.org/the_freeman/detail/the-paradox-of-voting#ixzz2mS6siB6h
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