Shortly after the tragedy at Stoneman Douglas high school, the figure $1.05 had been popping up quite frequently — especially in connection to Florida senator Marco Rubio. It turns out that Rubio, staunchly pro-gun, had received $3,303,355 worth of electoral help from the NRA. With a little bit of math, we can divide that number by the number of students in the state and come to that sum: $1.05.


The clear insinuation is that $1.05 is the worth of a Florida student’s life to Rubio and the NRA. After all, to them, he is voting against their interests and in line with the source of the 3,000,000-ish dollars.

The logic makes sense. There’s only one minor problem. It’s completely wrong.

I get the sense that you’re skeptical. Or, at least, I’m guessing that you are based on experiences I’ve had in reality; I have no real epistemologically sound basis to assume that you expressed skepticism at the last paragraph but it permits me an acceptable segue. For all I know, you totally believe me. But I’ve already committed to the bit so if you do believe me, please pretend that you don’t for the next couple paragraphs.



Anyways, I get the sense that you’re skeptical. I’ve tried to explain more often than I care to remember that lobbiests don’t actually buy politicians. I’ve told family, friends, people on the bus on my way to work. If I had a nickel for every time someone dismissed my explanation due to overwhelming skepticism, I’d have more money than the NRA.

Honestly, I can’t blame you. We’re inundated with stories of corrupt politicians all the time. The politician as whore-to-monied-interest trope has literally been around as long as there has been politicians. And it’s reinforced pretty heavily by a number of mainstream media outlets. When you have news stories reporting “here are the Florida politicians who receive money from the NRA” just when something anathema to the organization’s stated goals is floated in the public discourse. The insinuation is more transparent than a leptocephalus.

I’m not going to try and convince you with academic journal articles. I’m not going to try and assuage your skepticism by insisting no, really, politicians are actually people and thus have personal ideological predispositions just like you or I. Instead, I want to try a different tack. Screw it. Let’s assume the worst.

Let’s go ahead and assume that interest groups only care about their bottom line. That buying politicians is totally a thing that can happen. That there may be people wed to their ideals, but that there also exists a class of people who are so mercenary and greedy that they will just acquiesce to the highest bidder. Basically, let’s just assume that all the worst things you believe about how policy is made in America is correct and go from there.

Here’s the kicker: Even provided that all of this is true, interest groups still wouldn’t try to buy politicians. If only for the reason that it’s actually cheaper not to.

The Theory

My rationale is going to rely on some quasi-formal thinking and that means using some letters instead of numbers. I promise though, it’s actually easier to understand it this way. I’m not going to claim to “prove” it to you because I’m not that good with formal logic — but I do hope to levy a logically sound and convincing argument.

Let’s imagine that people can be divided along a continuum between ideologues and mercenaries. Pure ideologues will never change their mind no matter how much money you try to throw at them and pure mercenaries will, as the name implies, will captitulate to whoever offers them more — even if it’s a pittance. There are lots of ways to imagine this relationship. Here’s how I think it looks.

I call the left axis here the “cost of conscience.” Basically, how much dough it’s going to cost to make people go against their principles. For pure ideologues (on the left) it’s a lot of money — perhaps even infinite amounts — because they refuse to abandon their beliefs. For pure mercenaries (on the right) it’s no money at all; they go where the money does. This is our stereotypical politician. The person who believes in nothing but lining their own pockets.

Let’s say that you have two lobbying firms and they really want to get a law passed. Since this post was inspired by gun control, let’s keep with the motif. We’ve got Guns Are Awesome (GAA)…

And then we’ve got Guns Are Dumb (GAD)…

Both of them are hoping to get a law that will increase the money going to them and that the law has some some worth to them (“w”). We’ll say that it’s a million dollars, but the variable means that it could be more or less. If GAA’s law passes they get a million dollars at GAD’s expense. Likewise, if GAD’s law passes, they get a million dollars at GAA’s expense.

GAA and GAD are looking to get someone in office. Doing this is going to cost them time and money; congressional races ain’t cheap. There are 3 kinds of costs that’ll come with trying to get the law passed: Recruitment costs, or the costs of finding someone willing to mount a run; Campaign costs, how much it’s going to take to get someone in office; and Vote-Influencing costs, how much it’s going to take to get them to vote your way. We’ll call recruitment costs “A”, Campaign costs “B”, and Influencing costs “C”. Together (A+B+C) they equal the total cost (“T”) to get the law passed.

Because GAA and GAD are concerned for their bottom line, they’re never going to put more money into a law than it’s worth. They may invest $999,999.99 but they won’t invest $1,000,000.01.

Let’s assume for the moment that they manage to get a mercenary candidate elected. And let’s also assume that they put in the same costs for “A” and “B”. (Actually, this isn’t that much of an assumption. It can be demonstrated that spending the exact same amount of money is a sub-game perfect equilibria when both organizations have the same pot of money. That amount, by the way, is $0. Which is basically a fancy way of saying that they’re not going to waste money on voting for someone just to have the other group outbid them as a direct consequence.) So now, all that’s left is to sway the newly-elected member of congress.

GAA puts in $1,000. GAD puts in $2,000. GAA adds more to make their total contribution $4,000. GAD goes to $999,999.99

That’s not an unjustified assumption. Work in optimal auction strategy (and, yes, that’s actually a thing) shows that the equilibrium strategy for cases like this is for both parties to bet infinitesimally close to their perceived value of the object. In this case it’s a person’s vote as opposed to an actual tangible object but the same principle applies. So they’ll bet virtually everything because a 1 cent gain is worlds better than a $1,999,999.99 loss.

Knowing this, it’s really going to depend on who gets to roughly a million dollars first. Or, in our generalized notation, who reaches just shy of w. Which, assuming that they’re rational actors, really means who gets to make the first offer. Either way, the winner’s only getting pennies on the dollar. And that’s only if they win. Because the loser’s out nearly $2 million, and because there’s only a %50 chance that they’ll get to go first, their “expected utility,” over the long term, is -$999,999.99 Or, once again looking at things generally, the expected utility is:

There’s got to be a cheaper way, right? And there is! Elect an activist.

Remember that L-looking chart a bit earlier? Recall that it told us how much money it would take for them to go against their conscience? All GAA (or GAD) would have to do is find someone who’s cost of conscience is higher than the expected worth of the vote.

That way, they know that there’s no way that they could be bought once they get elected. And since the competing firm will not spend more to swing a vote than the vote itself is worth, they know that they won’t be pushed into a bidding war.

Let’s say that it costs both the winner and loser of the election $100,000 to recruit and elect candidates. The expected utility is muuuuch better in this case. Provided that my back of the envelope calculations are correct (or, to be literal, my back of the local school newspaper calculations), the expected utility in this scenario is now -$100,000. That may be a loss, but it’s preferable because .

Here’s the kicker: It doesn’t matter how much that amount is. It could be $100,000, $500,000 or $900,000. So long as it is less than that closest faction to $1,000,000, both parties are winding up better than they had before. Further, that expected utility reflects there being a perfect equal chance of both parties getting their way. That isn’t how it is in reality, meaning that the expected utility for one group will trend higher and higher.

A Couple Caveats

I started this article rebuffing an overly simplistic view of how politics works in the United States. I moaned and complained about how it didn’t present an accurate picture of US politics. In response, I concocted and presented what is ultimately (behind the veneer of authoritative words and symbols) an equally simplistic view of how the political world works with its own equally wrong consequents.

The big thing that I want to caution is that this model should not be read as to suggest that bribery and corruption never happens. These things do occur as point of fact — and model as it stands now does not consider the cases of these bad apples. Further, it should not be taken as meaning that the money spent on campaigns and the like don’t impact the legislative process. They absolutely do. Money provides access. Access increases the likelihood that something favorable is going to get written into law. There are very grave concerns about the amount of and the ways that money allowed to work its way in our system. All this model does is show that politicians unquestionably kow-towing to the owner of the fattest pocketbook isn’t one of them. At least not from a systematic perspective.

In addition to that thematic issue, there is also a technical one. Astute readers will note that this seems to merely be pushing the issues of bidding down to the electoral level. Assuming that there’s a roughly 50/50 chance that either GAA’s candidate or GAD’s candidate is elected, we’re still looking at the exact same formula as above. It’s just now, instead of the recruitment and campaign costs being zero and the vote-buying being huge, it’s the inverse. We’re just pushing the “auctioneering” earlier in the process.

Said readers would be absolutely correct. In fact, it’s why tons of money gets dumped into competitive races. However, that equivalence only holds if the district doesn’t have something analogous to it’s own “cost of conscience.” That is, it assumes that the public is going to naively back the side with the most money poured in. Realistically, it’s going to be more of an “inertia” cost where the second actor will have to spend extra money to cancel the effects engendered by the first actor.

Regardless, the equivalence would only hold in the most purely competitive district possible. But the vast preponderance of political districts (at various levels of government) aren’t that ideologically competitive. There are far more “safe” seats than there was a decade or two ago. So what would happen mirrors a lot of what is happening now: More money being spent in ideologically commiserate areas than areas with a different ideological base but the most money being spent in areas with competitive races.

The fact that the outcomes of this model coheres so well with the real world suggests that there is some truth to the principle driver. Even assuming the worst, it’s easier (and cheaper) to simply support ardent believers instead of bankrupting oneself trying to persuade ideological mercenaries.🔷

(Note: This is a companion piece to a video I made for the Professor Politics YouTube channel. It’s not necessary to watch the video in order to understand the piece, but it does provide a nice, less technical overview of the ideas that are discussed in this post.)

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(This piece was first published on Medium.)

(Cover: Twitter/@marilynicmas - MSD student @Sarahchadwickk with a $1.05 price tag, which are being passed out at #MarchForOurLives. The price represents the number of students in Florida divided by the amount of money Marco Rubio has taken from the NRA, 24 March 2018.)