A new discussion paper by Edward Cartwright and Anna Stepanova, KDPE 1506, March 2015

**Non-technical summary**

There are many important contexts where ‘success’ requires a critical amount of activity. Consider, for example, a political party deciding whether to adopt a policy which is socially efficient but, for some reason, unpopular with voters. The policy will be enacted if and only if enough party members are willing to back it. Individual members face a difficult choice: the policy is socially efficient and so they would want to back it, but to do so would risk the wrath of voters. Potentially we could end up with an inefficient outcome where members shy away from backing the policy.

The scenario we have just described above is, in the terminology of game theory, a binary threshold public good game. In the current paper we study a particular type of threshold public good game called a forced contribution game. In this game all group members are ‘forced’ to contribute if sufficiently many members ‘voluntarily’ contribute. In the context of our earlier example, this would be to say that all party members pay the cost of an unpopular policy if the party enacts the policy.

Our interest in the forced contribution game stems from prior evidence that enforcing contributions increases inefficiency. In particular, we know that in general, groups are relatively inefficient at providing threshold public goods. Some prior experimental studies, however, have shown that high efficiency is obtained in forced contribution games. Our objective in this paper is to explore in detail, both theoretically and experimentally, the conditions under which enforcing contributions works.

In our theoretical analysis we contrast and compare three alternative models of behaviour: ordinal potential, quantal response and impulse balance. Ordinal potential says that group members will act to maximize aggregate payoff; this results in the ‘optimistic’ prediction of maximum efficiency. Quantal response is a model that allows for decision making ‘with mistakes’; it gives a ‘pessimistic’ prediction of low efficiency unless the return from the public good is very high. Finally, impulse balance theory assumes that people make decisions based on expected ex-post regret; here we get an intermediate prediction where efficiency depends on the return to the public good and size of the threshold. We complement the theory with an experimental study where the number of players and return to the public good are systematically varied in order to test the respective predictions of the three models detailed above. We find that impulse balance provides the best fit with the experimental data. This allows us to derive a simple expression predicting when enforced contributions result in high or low efficiency. Our predictions are consistent with the uniformly high efficiency observed in previous studies. We also find, however, that enforced contributions are not a guarantee of high efficiency.

Read the complete paper here.