Consider an anarchist society in which there is no defense from bandits. (Olson argued that because of the public good/free rider problem, people in a large anarchist society would be unable to defend themselves from a powerful bandit. We can argue about that, but that point doesn't matter for where I want to take this argument.) Then there can be many bands of roving bandits who try to steal from people. Each gang has little or no incentive not to kill the goose that laid the golden egg because if they refrain from stealing "too much," another gang will take it. This is essentially the "tragedy of the commons" problem.
But now, says Olson, imagine that one tyrant manages to take over an area and provides defense from roving bands of bandits. He then becomes a stationary bandit. He'll steal a lot for himself but he now worries about the incentives of people in his territory to produce. He will take the maximum he can, but will think long run. He knows that as he raises tax rates, the incentive to produce falls and, therefore, the amount produced falls. He will maximize taxes, which equal the tax rate times the amount of output taxed. In other words, he will reach the top of the Laffer Curve. (I'm surprised, by the way, that Olson, who must have been familiar with the Laffer Curve, doesn't mention it on p. 469, the place where it would have been appropriate to reference it. I wouldn't be surprised if he actually did mention it but a referee or editor at the American Political Science Review insisted that the reference be cut. One cannot understand American academia without understanding the prejudices, snobbishness, and parochialism that are part and parcel of it.)
In short, while both the roving bandits and the stationary bandits steal, there will be more theft when there are roving bandits.
Where am I going with this? As regular readers of this blog know, I am politically active at a local level, fighting off seriatim the various attempts to increase taxes on the residents of Pacific Grove and of Monterey County. My allies and I have been quite successful. (See here, here, and here. For my long story about my first bit of successful anti-tax activism, see here.) The latest tax increase that we successfully fought off was a proposal for a new bond issue, financed by increased taxes on property owners. The money would have gone to Pacific Grove schools to buy computers, iPads for students, etc.
After we won, I happened to check the web site of the pro-tax side. The site is down now, for obvious reasons, but at the bottom of this link, you can see the list I saw on the other web site. What I noticed was interesting. Whereas I had expected to see the "usual suspects," that is, the various prominent local people who had lined up in favor of tax increases in the past, I saw some of them but very few. Almost all the supporters, to the extent I recognized the names, were teachers, school board members, and other employees of the school district. Noticeably absent were the mayor, members of the city council, and policemen. The one big exception was a retired police chief, but he is married to a teacher.
That was when the Eureka moment hit. It made sense that the "usual suspects" weren't listed. They want to tax Pacific Grove residents for their favored causes, one of the main ones being the huge pensions that the city council (illegally, it turns out) granted to police early in the last decade. If the police and firemen support this tax increase, that will make it harder to get a tax increase further down the road for those pensions.
But the people pushing for the tax increase for schools have different goals. They want to tax Pacific Grove residents for those goals. Thus we have multiple bandits. Each band of bandits wants to tax for its goals. But because each band does not have to worry (much) about how much is left for the other band to tax, each band goes for its favored tax for its favored cause. Multiple bandits are like roving bandits.
Daniel Kuehn, in the comments below, makes a good point. Yes, referenda do rein in the proclivities of those multiple bandits. But voting, informing, and getting out the vote are costly, and the people doing that, like my allies and me, are saving ourselves only our pro-rata share of the savings from preventing the tax. So we are creating a public good and, as Daniel and other economists know, there is typically underinvestment in public goods; those pushing the tax typically are getting a disproportionate share of the proceeds.