Disclaimer. Don't rely on these old notes in lieu of reading the literature, but they can jog your memory. As a grad student long ago, my peers and I collaborated to write and exchange summaries of political science research. I posted them to a wiki-style website. "Wikisum" is now dead but archived here. I cannot vouch for these notes' accuracy, nor can I even say who wrote them. If you have more recent summaries to add to this collection, send them my way I guess. Sorry for the ads; they cover the costs of keeping this online.
Baron. 1997. Political action versus voluntarism in social dilemmas and aid for the needy. Rationality and Society 9 (3): 307-326.
There are cases in which rational political actors would choose to engage in costly political action (to compel everyone to behave a certain way) rather than voluntary individual cooperation (to behave that certain way myself).
For example, an individual fisherman might be unwilling to not fish a certain area (to prevent overfishing), but he might support a politician advocating legal (coercive) restrictions on fishing in that area. The fisher recognizes that his individual voluntary action (not fishing in the area) will be individually costly but have little effect on the overfishing problem; at the same time, he knows that coercing everybody to not overfish will be individually costly (he can't fish the area) but it will solve the problem.
Baron describes two typical situations in which people must choose between individually cooperating and petitioning for social cooperation: the social dilemma and the issue of aid to the needy. The only difference between these cases is that in the former the beneficiaries are the same people as the cooperators, while in the latter they are different.
According to Baron, political action has some fixed cost, A. We can think of this as the cost of expressing our political attitudes. If A is small enough, it is rational to express support for social cooperation, even when one is not willing to cooperate spontaneously. But why would a person bear the cost of voting for something they would not spontaneously cooperate with? Well, the cost of voting might be smaller that that of cooperating, but then the potential benefit of voting is greater than that of cooperating. Baron argues that as N increases, the cost of cooperating rises slightly, while the expected benefit to the group increases dramatically.
He also deviates from classical utilitarianism by presuming that an individual's personal utility counts more to that person than does the utility of others. Thus the cost of voluntary cooperation is multiplied by this self-regarding factor, while the expected benefit of social cooperation increasingly outweighs it as N increases. Specifically, political action should be preferred to spontaneous cooperation, given a large N, if (W-1)C exceeds WA, where W is the self-regarding multiplier. The case of aid to the needy is the same, but here the net benefit comes from the fact that money confers greater benefit to poor people than to rich people, rather than from the game-theoretic benefits of cooperation itself. Note that here we must presume strict utilitarianism, in which there is no differentiation between contributors and beneficiaries, which seems to at least weakly contradict his assumption of W (which is, he admits, an assumption of bounded self-interest). He modifies the proportion of beneficiaries to contributors and finds that this has an effect on social choice: voluntarism would be used more often for small classes of beneficiaries.
He also modifies the N and W parameters. In the first case, he finds that the simplifying assumption of P=1/N (where P is the probability of political action succeeding) holds when P is understood as a dilution factor, but must be altered to describe voting. It implies that as N increases, my ability to act successfully (cast the decisive vote) goes down; in its modified form, as N increases the relative advantage of political action over spontaneous cooperation increases as well, since P depends on N.
If W is 1, and the person is a perfect utilitarian, then the utilities of spontaneous cooperation and political action are NB-C and PN(NB-C); that is, the group benefit minus the personal cost, and the group benefit minus the personal cost times the chances of political success, respectively. So if P=1/N the two options are equally good (remember that NB is greater than C, so they are not just "equal"). If W is infinite, the two options are equally worthless, since neither approaches the benefit I derive from doing nothing. So for political action to be preferred to voluntarism W must be greater than 1 but less than infinity. Going back to our equation: (W-1)C is greater than WA. As W increases, the minus 1 matters less and less, so the higher the relative utility of political action. Political action is sometimes preferable because we are somewhat selfish, and can avoid paying the full cost of political action unless it succeeds, as it has little effect.
Baron is recuperating the logic of supporting a cause politically while seemingly against it economically, which he sees as justifiable in many cases. In a social dilemma experiment he created, fishermen justified their personal overfishing by claiming it would not have an effect on the whole, while at the same time supporting a rule that would make everyone cut back. They did not realize that their individual political support would have about as little an effect on the outcome as their individual overfishing. This seeming contraction is often a successful strategy, given the following assumptions:
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