The condition used in Property 1, namely that \(b\) and \(k\) must satisfy \(\phi\left(b,k\right)>0\), is fully characterized in the Appendix. Importantly, we show that it is not very restrictive.

Let us describe the incentives underlying Property 1. Increasing \(k\) changes the value of the contest for both pressure groups. Consider first lobby \(I\). If \(\delta\leq k\), because he pays \(\delta\) in court, increasing \(k\) changes nothing; if \(\delta>k\), because he pays \(k\) in court, increasing \(k\) reduces the value of the contest for him. Thus, following an increase of \(k\), the industrial pressure group has an incentive to exert less effort in the contest if and only if \(\delta>k\). Consider now lobby \(E\). Likewise, if \(\delta\leq k\), increasing \(k\) changes nothing, whereas if \(\delta>k\), increasing \(k\) reduces the value of the contest for him. However, as \(\delta\) is private information, lobby \(E\) can only anticipate the expected value of the contest. Thus, following an increase of \(k\), the environmental pressure group always has an incentive to exert less effort in the contest.

Clearly, when \(\delta\leq k\), these incentives jointly explain why the aggregate effort becomes smaller and why the probability of approving the product becomes larger, after \(k\) has increased. However, they are not sufficient to explain the rest of Property 1, because they then go in opposite directions and produce countervailing effects. If \(\delta>k\), both players want to exert less effort as \(k\) increases. As a result, the probability that the product will be approved, will increase provided lobby \(I\) proportionally reduces his effort less than lobby \(E\) does. Property 1 shows that this is indeed the case when \(b\) is large enough (i.e., if \(b>\left(1+k\right)/2\)). Finally, the way the expected social surplus varies as \(k\) increases, simultaneously depends on how the aggregate effort and the probability of approving the product change. On the one hand, the fact that the pressure groups exert less effort is socially beneficial. On the other hand, the probability that the product will be marketed changes in directions that may improve the expected social surplus or not. For example, the probability that the product will be marketed increases when \(\delta\leq k\), which is socially beneficial (because \(\delta\leq k\) and \(k<b\) implies \(\delta<b\)), but also when \(\delta>k\) and \(b>\left(1+k\right)/2\), which is socially costly for all \(\delta>b\). Despite this ambiguity, if \(\phi\left(b,k\right)>0\), Property 1 finds that overall, the expected social welfare is increasing in \(k\).