tullock paradox

Might the NFL accept the Tullock paradox?

The chairman of the National Football League’s health and safety advisory commission believes American football could ban helmets in the future.

The NFL has tried to reduce the risk of head injuries over the last five years and recently reached an almost $1bn legal settlement with ex-players suffering with head trauma.

But some experts think helmets give the players a false sense of security.

“Can I see a time without helmets? Yes,” said Dr John York.

“It’s not around the corner, but I can see it.”

There is more here, via Michelle Dawson.

The lobbyists themselves state the “Tullock paradox”

According to statistics United Republic assembled, the prescription drug industry spent $116 million lobbying for legislation to prevent Medicare from bargaining down drug prices — legislation that enabled drug companies to make an additional $90 billion annually. That amounts to an extraordinary 77,500 percent return on investment. Oil companies, in turn, had a return on investment of 5,900 percent, and multinational companies, 22,000 percent….

For example, the Carmen Group, a Washington lobbying firm, boasted on its Web site that for every dollar it collected in fees, clients got $100 in benefits.

I enjoyed the ROI visual presented here.  Of course the Carmen Group needs to explain why it is not raising its prices and the companies need to explain why they do not spend more.  Presumably the rate of return on additional lobbying expenditure is relatively low.

One part of the Tullock puzzle of high upfront but low marginal returns to lobbying may be answered by the article:

I asked a prominent Democratic lobbyist with just over $3 million in annual billings — who requested anonymity to avoid alienating his clients — about the difference between trying to win legislation and trying to block it.

“It’s significantly easier to block and impede,” he said.

Once you have blocked, you have blocked, and “more blocked” doesn’t necessarily make you better off, so you can end up at a discontinuity point.  This also may explain why the forces seeking to push new laws do not spend more.  Spending more, to try to get your way, may induce more offsetting investment from the “blockers,” who have access to a cheaper technology, so to speak.  Still, if they have a fixed cost for getting the blocking activity up and running at all, you may spend some small amount in the first place, enough to have influence but again with the knowledge that their blocking abilities put a discontinuity in the returns function.

The article, with much more useful information, is here, by Thomas Edsall.  Here are a few earlier MR posts on the Tullock paradox.

Addendum: Karl Smith comments.

The Tullock paradox: why is there so little lobbying?

Tim Harford writes:

…the economist Thomas Stratmann has estimated that just $192,000 of contributions from the American sugar industry in 1985 made the difference between winning and losing a crucial House vote that delivered more than $5 billion of subsidies over the five subsequent years.

That is one example of many.  Our government controls trillions, but lobbying expenditures are a small fraction of gdp.  One explanation, which Tim cites, is that our government is not for sale.  This is true for most major programs, such as social security.  Voters have the dominant say. 

But how about the details of smaller policies?  Why aren’t the benefits of those redistributions exhausted by lobbying expenditures?  My preferred explanation involves competition.  In principle, more than one coalition is capable of winning a political game.  If your winning coalition demands too high a bribe from interest groups, you will be undercut by another coalition able to deliver the policy for less.  Government is not a unitary agent.  This also helps explain, by the way, why democracy is stable rather than wracked by intransitive cycling.  If you just write down different voting profiles, it appears any winning coalition can be outdone by another (at least for a multi-dimensional policy space).  But if you add differential costs of organization to the mix, and make collecting the votes part of an explicit but imperfectly contestable market, you are much closer to getting a unique or near-unique outcome. 

Ideas in this post are drawn from a paper by Roger Congleton and Bob Tollison.  Here is a recent paper on the same topic.

Assorted links

More on Arrow’s theorem

Dirk writes:

I vote that this post deserves a follow up post with more clarification. If anyone is against this please express your vote with inaction. Us laymen would like to understand this a little better. For the record, the reason I got on a tangent about the law of large numbers was that I watched Boudreaux's lecture and understood it in terms of 3 parties but kept thinking if there were 3000 parties it was unlikely that exactly 1000 would have preference A, 1000 preference B, and 1000 preference C. I guess I'm used to thinking in terms of run-off elections and not the sort in the example. That is why I couldn't grasp why things should "collapse" back to an island situation where n = 2 or 3.

Arnold Kling comments as well and not everyone is happy.  

Return to the oft-neglected difference between intra-profile and inter-profile versions of the theorem.  Most commentators and expositors have in mind an intra-profile version of the theorem.  They set up an example of people and preferences and show how cycling or some other paradox of choice or voting is possible.  Observers then wonder whether this cycling is likely as the number of people increases, or as preferences change, and indeed sometimes it is not, as Gordon Tullock pointed out long ago and as Dirk above wonders.

That's interesting stuff, but those fun and practical-sounding expositions are not Arrow's theorem as Arrow wrote it up.  Think of Arrow's theorem as modal in nature: "Maybe there is no paradox with current preferences, but there exist possible preferences where everything goes screwy, under any decision rule satisfying a few criteria."  Arrow showed that claim is related to something like: "if we apply a specified decision-making procedure across all possible preference configurations, consistent application means the same person gets her way each time."

That's called Arrovian dicatorship, but it does not have to be either harmful or unjust or not even necessarily undemocratic.  It just means that one person — the same person — is always getting her first choice, across these modal worlds with differing preference configurations.

This more metaphysical and more originally Arrovian version of the theorem is perhaps why Arnold Kling finds it difficult to apply the theorem to practical problems.  It is not about the likelihood or relevance of cycling (though it is a jumping-off point for those analyses).  It is instead a deep result about the implications of consistency, combined with limited information about the value of ordinally ranked outcomes.

The intra-profile versions are still important.  For intra-profile versions of Arrow, start with Kemp and Ng (1976).  Here is a good summary article on that literature.  Samuelson, by the way, remained somewhat recalcitrant when it came to the theorem.

Allowing in even limited amounts of interpersonal comparability defuses the paradox, as shown by Kevin Roberts (ReStud, 1980) and Amartya Sen (see the essays in Choice, Measurement, and Welfare).  That said, interpersonability can lead to other paradoxes, as shown by Derek Parfit and his Repugnant Conclusion.  Paradoxes everywhere, and you must choose which ones to live with. 

I take the practical upshot of Arrow's interprofile theorem to be this: when you make a judgment, it is our assessment of the interpersonal comparisons (or intersport importance comparisons, for scoring a decathlon) which is doing all the work.  Be very careful with those. 

Neither Tullock nor Samuelson was happy with Arrow's theorem, especially when it came to practical implications, so it is fine if you wish to add your name to that list.  But I also think they each missed Arrow's point a bit and that of the major economists of his time he was probably the deepest thinker, albeit not the best practical thinker.

Should you vote?

Jordan Ellenberg says yes and offers some mathematics in response to Steve Landsburg. He sees a voter in a swing state as having a very real chance of being decisive. Economists, of course, are known for their long-standing insistence that your vote has virtually no chance of swaying an election.

My take:

This entire debate goes down the wrong lines. Let us start with a simpler question. Should you always make decisions by considering your marginal product alone?

Let’s say you were asked to join a firing squad of ten expert marksmen, all shooting at an innocent man, and so good they never miss. Still, they want a louder execution with eleven bullets instead of ten. In return they will donate five dollars to your favorite charity. Should you join and shoot?

Most of us would say no, even though your bullet has no chance of changing the final outcome. Once you buy this conclusion, it is easy to see why people might vote. Most moral judgments reflect some mix of estimated marginal and average products, not just marginal products alone. In part morality means the ability to take a longer-run, universalizable, or more rules-based perspective. So you need not feel guilty if the economist tells you not to vote. Maybe you are not rational in one sense of the word, but surely having a disposition to be moral can be justified.

That being said, voting may still be a mistake.

The best argument for not voting is the following: in lieu of voting you should earn extra income and donate it to the very poor. Or perhaps take the day off and work at the soup kitchen. After all, why should voting be the most important collective good you can contribute to? And even if voting has a special importance, maybe you should work harder, earn more money, and use the funds and your time to get other people to vote. Spend a day driving people to the polls rather than voting, for instance. [Or donate to the poor in India and write a blog? Alex]

It does not suffice to talk about doing both voting and charity; substitution at the margin is always possible. You might think that voting is relatively cheap, but so is helping Indian beggars.

Another argument against voting involves holding the meta-rational belief that you are unlikely to improve upon the collective wisdom of others. Your chance of figuring out how to help the poor probably exceeds your chance of picking the right candidate. Of course few people will admit this.

Overall I view voting as a selfish act, usually done for purposes of self-image. But this has some altruistic and some non-altruistic ramifications.

I fondly recall Gordon Tullock’s point: “The paradox is not why people vote, but why everyone doesn’t vote for himself.”