Full agreement and the provision of threshold public goods

What is it about?

In a threshold public good game a public good is provided if and only if group members collectively provide enough for its production. This crucially means that group members have to coordinate their contributions. For instance, if the threshold is 125 then it is optimal for individual contributions to sum to 125, and not 124 or 126 or anything else. A seemingly simple solution to this problem is to split contributions equally. For instance if there are 5 group members and the threshold is 125 then they can each contribute 25. If, however, group members differ in how ‘rich’ they are then this solution may seem unfair. Instead one might favour, say, a proportional rule in which group members contribute in proportion to their endowment. Experimental evidence on threshold public good games shows that groups rarely coordinate on the equal split, or proportional rule, or any other solution. This leads to inefficiency with total contributions either below or above the threshold. So, why cannot groups better coordinate? We apply the concept of a collectively rational recommendation to see if there is a focal set of contributions in a threshold public good game. In the standard version of a threshold public good game we show that there is no collectively rational recommendation. This helps explain why groups cannot coordinate. A variant on the standard threshold public good is then considered in which the public good is provided only if there is full agreement on what each group member should contribute. Note that full agreement is a tough ask because everyone has to agree on what everyone else should contribute. We prove, however, that in this case there is a collectively rational recommendation and it is to split contributions equally. We argue, therefore, that groups may coordinate better if they are required to reach full agreement because the indirect benefit of their being a focal contribution overcomes the direct cost of everyone having to agree. We report results of an experiment designed to test whether a requirement to reach full agreement helps groups coordinate. We find that it does once group members have sufficient experience. This suggests that it can be beneficial to have tough criteria for the provision of public goods. For instance, in the European Union the need for all member states to agree is often seen as a barrier to decision making but our results suggest that in some contexts it can help. Essentially this is because every group member becomes critical to the outcome and this criticality concentrates minds on coordinating successfully.

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