Chapter 9 of Analyzing Politics  

K.A. Shepsle

 A Summary

Multiperson Cooperation

  • Groups consist of individuals who bear some cost or make some contribution in pursuit of a common goal. In the simplest form persons may either contribute or not contribute to the group enterprise. If the number of contributors is sufficiently large the goal is attained, if not, then the objective is not met. However, if the goal is attained, each member of the group benefits irrespective of whether or not they have contributed.
  • It is important to know what level of contribution is needed for attaining the goal.
  • In the case of unanimous contribution full participation is needed. There is a cost, C, and a benefit B from attaining the goal. If C>B then no one will contribute no matter how many other people might. If B>C then one of two things is possible:
  1. No one contributes. This is an equilibrium because if no one contributes the jth person would not reconsider her choice, as the payoff would only be –C. The choice between not contribute (getting 0) or contribute (getting –C) always come out in favour of not contribute.
  2. Everyone contributes. This is also equilibrium as the jth person would not reconsider contributing as the options are every contributes (getting B-C>0), or everyone except me contributes (getting 0).
  • Thus it is possible to be stuck in an equilibrium trap in which no one contributes even though all would be better off contributing. However, because everyone’s participation is essential and everyone knows this and knows everyone else knows it, it is likely that everyone contributing will be the outcome.
  • In the case of non-unanimous participation, of a group n at least k contributors are necessary. If fewer than k-1 of the group members are contributing, the jth person will not want to contribute as she will receive –C if she contributes when she would prefer just to receive 0 (by not contributing). In fact, only if exactly k-1 people are contributing is the jth’s persons contribution absolutely essential as the choices for her are not contribute (get 0) or contribute (getting B-C>0). This suggests there are two equilibrium outcomes:
  1. No one contributes. The jth person will not reconsider as 0>-C (payoff from not contributing greater than contributing when goal is not achieved).
  2. Exactly k people contribute. Those not contributing get B, and prefer this to contributing and getting B-C>0. Those contributing get B-C>0 which is better than any of them not contributing in which case they get 0. In other words exactly k individuals will have to believe their contribution is necessary, and that they and only they are likely to contribute.
  • Which outcome pertains will depend upon a variety of factors. If n is large as k is large relative to n then people know that a lot of support is needed, and will tend to believe their contribution necessary. Thus k or probably >k will contribute. As k reduces in relative size this pressure will disappear. Cooperation in other words is harder to achieve when it seem obvious that each individual’s contributions is probably inessential.
  • There may be some people who always prefer to do the right thing and contribute and thus if k gets really small the chances of success may again get better.
  • As n gets large the psychological identification with the group probably affects the utiles enjoyed from achieving the joint goal, and this makes cooperation less likely, as benefit that greatly outweighs the cost will make participation more probable. This is the same as if the C gets large.

 Olson’s Collective Action

  • Individuals are tempted to free ride on the efforts of others.
  • This is especially so if the individual is not very significant in achieving the group goal (k is small relative to n).
  • Olson claims that this temptation is an especial problem for large groups for three reasons:
  1. Large groups tend to be anonymous. This makes it hard to forge a group identity around which there will be pressure to contribute.
  2. Anonymity in the large group context means that the claim that no individual contribution is essential is more plausible. If lots of people contribute then the individual need not, if few people contribute then his efforts will make no difference.
  3. Enforcement is harder in larger groups. The slacker cannot be prevented from enjoying the fruits of the collective action. In anonymous groups it will not even be possible to identify those that have contributed from those that have not.
  • Small groups on the other hand are more personal and thus allow for interpersonal pressure. Individual contributions may make a real difference, and everyone knows who the slackers are. Punishment is thus easier to effect. Repeated play further enhances these features.
  • The same logic of large versus small also applies within groups, when less powerful members may free ride on the contributions of the most powerful in order to achieve the goal e.g. NATO.


  • We see instances of large scale collective action. How are these explained?
  • Groups achieve their goals by offering to individuals more than simply the benefits of achieving their goals. They receive these conditional on having contributed. So the motivational force for participation may in fact be these selective incentives, byproducts of the goal attainment. Groups that only provide the stated benefit will thus have a harder time organizing.

 Political Entrepreneurs

  • One additional observation made by Wagner to the Olson theory is regarding the role of political entrepreneurs. Group action is often sustained by not only selective incentives, but by the efforts of specific individuals, leaders, etc. These individuals receive a different set of incentives which accrue to them pursuant to organizing and maintaining an otherwise latent group.
  • In general this entrepreneur sees a prospective cooperation dividend, and for a price (votes, power etc.), or for a percentage of the dividend, the individual will bear the costs of organization, monitoring slack behaviour, and administering selective incentives.
  • Thus the idea of an institutional solution to collective action problems is introduced.
  • NB, some people may contribute irrespective of incentives, punishment, as to contribute conforms to their ideology or belief system or because they want to be a part of a social movement.

 Voting and Collective Action

  • A person has a preferred candidate out of a two horse race. She will receive a benefit B if he is elected. She incurs a cost –C which she must bear in order to vote (going to the polls, information gathering etc.). Again B-C > 0. This is a very simple application of the above logic. If more than 50% of the electorate vote for her candidate she receives B irrespective of whether she votes. As B is better than B-C she will not vote. If more than 50% of the population vote for the other candidate she can either receive 0-C or just 0 (voting and non-voting), so she will always choose to not vote. If both receive exactly 50% then she can break the tie in her favour. Assuming that if a tie occurs there is a coin toss to decide the outcome she now faces payoffs of 0.5B (expected value of lottery), or B. As B is better she will vote. If the other candidate gets 50%+1 vote she can vote and institute a tie meaning the lottery will be entered into. Thus she receives expected benefit of 0.5B rather than the no vote payoff of 0.
  • So only if there is a dead heat, or a loss of 1 single vote is it rational for her to vote in the election. The likelihood of there being a tie in the US election is infinitesimally small so it is very unlikely that a sensible person will conclude that they should vote. This is the case even when voting is very inexpensive for the voter.
  • When seeking to explain the prevalence of people voting Riker and Ordeshook claim there are experiential as well as instrumental benefits from voting – warm glow etc.



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