Prof.
Bryan Caplan
bcaplan@gmu.edu
http://www.bcaplan.com
Econ
410
Week 2: The
Logic of Collective Action
I.
Fallacies of Group Action
A.
People often think in terms of groups acting to promote their group
goals.
1.
Workers/capitalists
2.
Oppressed minorities
3.
Women (and men?)
4.
Environment
5.
Northern business and the end of slavery
B.
Moreover, they often see groups pursuing their group-interest just as
individuals pursue their self-interest.
C.
But there is a fundamental difficulty in this popular perspective: it
amounts to a fallacy of composition.
Just because all members of group X would benefit if all members did
something, it does not follow that it benefits any individual
member to do so.
D.
Why? Because frequently the
benefits can be enjoyed just as well by people who did not pay the costs as
those who did. The benefits are
social, but the costs are private.
E.
Ex: Suppose one worker
decides to just stay home and watch TV while the other workers foment
revolution.
1.
Case 1: Revolution succeeds, all workers (supposedly) enjoy a brave new
world - including the couch potato.
2.
Case 2: Revolution fails, all workers continue to suffer under the
capitalist system - but at least the couch potato got to watch some amusing
television programming.
F.
Key insight: marginal thinking.
If the same outcome will happen whatever you do, then selfishly
speaking you might as well do personally benefits you, and quit worrying about
the big picture.
G.
Many people are appalled by this sort of thinking, but it is important
to keep the positive and normative elements separate. Maybe I do have a moral obligation to
contribute, but that does not show that it advances my self-interest to
contribute.
H.
We do need to be careful before we assert that there is no selfish
reason to contribute. As Olson
emphasizes, frequently there are "byproducts" and other
"selective incentives" that make contribution selfishly optimal.
1.
Ex: Trotsky on military discipline
II.
Individual Impact: Probability and Magnitude
A.
Saying that "The same thing will happen whatever you
do" is admittedly overstatement.
B.
It would be more precise to say "About the same thing will probably
happen whatever you do."
C.
In other words, you have to look at the probability you make a
difference and magnitude of the difference you'll make, and compare then
to your cost of acting.
D.
For example, it is possible that if you join the revolution, you will
change the entire course of history.
Possible, but not likely!
1.
Still, there are several famous assassins who changed the course of
history, and a lot of not-so-famous would-be assassins who came close.
E.
Similarly, if you give to starving children in Ethiopia, one more child
could be saved. That is a real
difference, but it is a tiny magnitude relative to the size of the disaster.
F.
More relevant to public choice: the probability a vote matters and the
magnitude of its impact.
G.
Voting increases the probability that your favored candidates wins, but
how much does it increase that probability?
H.
And even if your candidate does win as a result of your vote, how much
will policy change? As we will see
next week, competing politicians typically wind up favoring quite similar
positions.
III.
Calculating the Probability of Decisiveness, I: Mathematics
A.
When does a vote matter? At
least in most systems, it only matters if it "flips" the outcome of
the election.
B.
This can only happen if the winner wins by a single vote. In that case, each voter is "decisive";
if one person decided differently, the outcome would change.
C.
In all other cases, the voter is not decisive; the
outcome would not change if one person decided differently.
D.
It is obvious that the probability of casting the decisive vote in a
large electorate is extremely small.
Recent events in no way refute this. Losing by 100 or 1000 votes is a long
way from losing by 1 vote!
1.
You might however say that Bush did win by a single vote on the Supreme
Court! But that is a voting body
with only 9 voters.
E.
There is a technical formula for "guesstimating" the
probability of decisiveness. In
spite of the difficulty, it is worth pursuing this issue in depth. (If you haven't studied probability,
just make sure you get the main idea).
F.
Suppose there are (2n+1) voters asked to vote for or against a policy.
1.
Note: Assuming an odd number of voters avoids the picky problem of
ties.
G.
Then the probability that YOU are the decisive voter is the probability
that exactly n voters out of the 2n voters other than yourself vote
"for."
H.
Now suppose that everyone but yourself votes "for" with
probability p - and "against" with probability (1-p).
I.
Then from probability theory: _{}
J.
From this formula, we can see that the probability of a tie falls when
the number of voters goes up.
Why?
1.
_{} gets smaller as n gets larger
2.
_{} is less or equal to 1. When you raise a number less than 1 to a
larger power, it must get smaller.
(1 raised to any power is of course 1).
K.
Intuitively, the more people there are, the less likely one person
makes a difference.
L.
This formula also says that as the probability of voter support goes
above or below .5, the probability of a tie falls. Why?
1.
When p=0, _{};
when p=1, _{} too.
In between p=0 and p=1, this term rises to a peak of _{} when p=.5, then falls.
M.
Intuitively, the more lop-sided opinion on a topic is, the less likely
there is to be a tie. If everyone
agrees, a tie is impossible.
IV.
Calculating the Probability of Decisiveness, II: Examples
A.
What is neat about the above formula is that it allows us to say not
just how the probability of decisiveness changes, but how much. Let's work through some examples.
1.
Remember that the number of voters is (2n+1), not n.
B.
Example #1: The close
tenure vote. n=10, p=.5.
_{}, or 17.8%.
C.
Example #2: The easy tenure
vote. n=10, p=.8.
D.
_{}, or a little more than 1-in-500.
E.
Example #3: The close
county election. n=5,000, p=.51.
_{}, or a little more than 1-in-1000.
F.
Example #4: The moderately
close county election. n=5000,
p=.53.
_{}
, a little less than 1-in-8 billion.
G.
Example #5: The close
national election. n=50,000,000,
p=.501.
_{}
1.
For perspective: Imagine a lottery with a 1-in-100,000,000 chance of
winning. The probability of casting
the decisive vote is less than the probability of winning that lottery 11
times in a row!
H.
Example #6: The moderately
close state election.
n=2,000,000, p=.51. _{}
a chance smaller than 1 in 10^{-100}! (My calculator just says 0).
I.
Upshot: For virtually any real-world election, the probability of
casting the decisive vote is not just small; it is normally infinitesimal. The extreme observation that "You will
not affect the outcome of an election by voting" is true for all practical
purposes.
J.
Even if you were to play around with the formula to increase your
estimate a thousand-fold, your estimated answer would remain vanishingly
small.
1.
Ex: Adjusting for the Electoral College.
V.
Efficiency and Collective Action
A.
In collective action situations, the privately optimal level of
participation is extremely low; but high participation is often the socially
optimal outcome.
B.
Why? Frequently, everyone
benefits a little bit if one more person participates. The extra benefits for the participant
are small. But if you multiply them
by millions of beneficiaries, the total benefits will often still exceed the
total costs.
C.
The social efficiency of additional participation is not as clear for
elections, as we will see; but when people urge you to vote, perhaps they are
thinking that more participation is a public good.
D.
We can also think in terms of "public good for a group." Higher Albanian turnout may not be a
public good for everyone, but it might be a public good for Albanians.
VI.
Empirical Evidence on Collective Action Problems
A.
One way to get a feel for the logic of collective action is to see how
little participation in politics there is.
Survey of adult Americans from Dye and Zeigler:
Activity |
% |
Run
for public office |
<1 |
Active
in parties and campaigns |
4-5 |
Make
campaign contribution |
10 |
Wear
button or bumper sticker |
15 |
Write
or call a public official |
17-20 |
Belong
to organization |
30-33 |
Talk
politics to others |
30-35 |
Vote |
30-55 |
B.
Many experiments have been run to help improve our understanding of
collective action problems.
1.
Part of the design: Rule out "selective incentives" accounts
of apparently unselfish behavior.
C.
Standard design:
1.
I hand out a roll of 100 pennies to each person in the class.
2.
Then, people are allowed to secretly put any number of their pennies
into a jar.
3.
You personally get to keep the pennies you don't put in the jar.
4.
I count the number of pennies in the jar; then I distribute twice
that many pennies to the class, with each person getting the same share.
D.
What maximizes the total income of the class? 100% donation by everyone!
E.
What maximizes your private income? 0% donation! No matter how little you donate, you
still get an equal share.
1.
Caveat: This is only true if there are 3 or more players, yourself included.
F.
The first couple of times you do an experiment like this, you typically
get moderate to high levels of donation - 50-80%.
G.
Donation levels usually begin falling as you repeat the experiment with
the same group. After a while,
donation levels often fall to around 20%.
1.
For practical reasons, experiments usually only last a day or
less. So we can still speculate
about what would happen if people played this game 10 times a day for a
year. I would expect donation
levels to fall much more.
H.
Donation levels usually decline as the number of participants
rises.
I.
The less secrecy there is, the higher the level of donation.
J.
Conclusion: While the "logic of collective action" appears to
exaggerate the degree of human selfishness, cooperation in these experiments is
way below the group-income-maximizing level.
VII.
The Paradox of Public Good Provision
A.
People often appeal to the "logic of collective action" to
justify corrective government policy.
Public goods problems don't "solve themselves."
B.
Problem: Isn't monitoring the government to act in socially beneficial
ways itself a public good?
C.
Paradox: If citizens can voluntarily produce the public good of
monitoring government, why can't they solve other public goods problems without
government? And if they can't voluntarily
solve this problem, what reason is there to expect government to improve
matters?