POLI 100E, Interest Group Politics: Topics 3 and 4

The Collective Action Problem

1. To be successful, some endeavors require the collective
   efforts of many individuals.
   
   
2. Each individual has two options: (1) Contribute to the
   group enterprise; and (2) Do not contribute to the group
   enterprise.
   
   
3. In the simple case of 2 individuals this can produce
   the classic Prisoner's Dilemma.
   
   Classic Example: Two suspects are arrested and separated
   at the police station. The DA is convinced that the two
   are both guilty and offers to reward each suspect if he
   confesses. This produces the following strategic problem
   for the suspects:
   
   
   
   Which yields the "Payoff Matrix":
   

                               Prisoner 2     
                                ~C     C
                            -----------------
                         ~C |   1,1  10,.25 |  
                            |               |
              Prisoner 1    |               |  
                            |               |
                          C | .25,10  8,8   |  
                            |               |
                            -----------------  
   

   The Dominate Strategy for both prisoners is to
   Confess. However, Collectively, this is the worst outcome!
   
   David Hume's Marsh Draining Example.
   A marsh abuts the land of two farmers. If the marsh were
   drained each farmer would receive a payoff of 2. If one
   farmer drains the marsh by himself the cost is -3.
   If both cooperate and drain the marsh together
   the cost to each is -1.
   
   
   
   
4. The Problem of Collective Action:
   
   
   1. Coordination: How do you coordinate the actions
      of a large number of individuals? .. or .. How do
      you get them to contribute?
      
      
   2. Free Riding: If all the individuals gain something
      from the success of a group effort but some
      individuals do not contribute to the group effort
      itself, what do you do about it?
      
      "If the group goal is obtained, then every member
      of the group enjoys its benefits, whether he or she
      contributed to its achievement or not." (Shepsle
      and Bonchek, p. 226.)
      
      
5. Free-Riding:
   
   Suppose there are n individuals in a group and it takes
   only k individuals, k £ n, contributing to achieve
   some goal of the group. Let B be the benefit that every member
   of the group receives if k or more members contribute, and let
   C be the cost of a contribution by a member.
   
   
   
   Shepsle and Bonchek argue that:
   
   
   1. Holding n, B, and C fixed, the likelihood that there will be
      enough contributors declines as k declines.
      
      Their reasoning: With small k members may feel that their
      contribution is inessential so that "they feel liberated
      to make alternative uses of their efforts." However, the
      effect is non-linear. There is almost certainly
      a small (or not so small) number of people who "do the
      right thing" regardless!
      
      
   2. Holding k, B, and C fixed, as n gets large the likelihood
      of there being enough contributors declines.
      
      Their reasoning: As n gets large the psychological
      identification with the group becomes more
      tenuous ("in-group" feeling declines). (For example,
      an n of 100 versus an n of 10,000.)
      
      
   3. Holding n, k, and B-C fixed, as C gets large the likelihood
      of there being enough contributors declines.
      
      Their reasoning: As C gets large even though B-C
      is fixed, the psychological risk of contribution and
      fewer than k contributors becomes inhibiting.
      
      
   4. Holding n and k fixed, as B-C gets large the likelihood
      of there being enough contributors increases.
      
      Their reasoning: As B-C gets large -- that is, as B gets
      large relative to C -- then the importance of the group
      goal grows and people are prepared to take psychological
      risks to contribute.
      
      
6. Coordination:
   
   Shepsle and Bonchek use a version of a famous game
   from the 1950s -- the classic "Battle of the Sexes Game" --
   to illustrate the problem of coordination.
   
   In the original game, a man, player (a, and a woman,
   player (b, each have two choices for an evening's
   entertainment. Each can either go to a prize fight
   (a₁ and b₁) or to a ballet (a₂ and b₂).
   Following the usual cultural stereotype, the man much
   prefers the fight and the woman the ballet; however,
   to both it is more important that they go out together than
   that each see the preferred entertainment. (Note that this is
   not really a "battle"!) The man and woman have to make
   their decisions without communicating with each other.
   
   
   
   In Shepsle and Bonchek's illustration of the coordination
   problem a particular member of a group has to choose
   between going to a ballet or an opera. The group must
   unanimously choose the same option for a payoff of B
   to be awarded to each member. Otherwise everyone gets
   the smaller payoff, b. However, from the point of view
   of a particular member making a choice without
   a knowledge of what the other members are doing,
   the situation is the same as the "Battle of the Sexes" game.
   
   
   
   Note that Shepsle and Bonchek are assuming that:
   
   B_i,Opera = B_i,Ballet for all i
   
   so that this is a symmetric form of the "Battle of
   the Sexes Game."
   
   This seemingly intractable situation can in fact be solved
   through repeated play. For example, if the opera
   vs. ballet choice is made every weekend then if
   the group members start alternating between going to
   the opera and going to the ballet then it will not take too
   many weekends for the members to figure out that next
   weekend must be the opera weekend and the weekend after
   that is the ballet weekend.
   
   A more realistic situation is where preferences are
   heterogeneous, that is, the utilities that members get
   for the two activities vary. Let
   
   B_i the benefit player i gets from going to the Opera, and
   b_i the benefit player i gets from going to the Ballet
   
   Then, for two players i and j it is possible that:
   
   B_i > b_i and
   B_j < b_j.
   
   In this situation it is doubtful that repeated play will
   solve the problem.
   
   
   
   In this more realistic situation a group will typically
   institutionalize a solution.