The rise of mega-donors has been an important storyline in the unfolding drama of the 2016 presidential election (for example, see here).  The presence of these donors in the political game (or at least their visibility) is partially the result of the Supreme Court’s decision in Citizens United.  But more interesting is whether the rise of these mega-donors has caused the explosion of seemingly viable (mostly Republican) contenders for the 2016 election.

The argument that Citizens United has caused the explosion in candidates is admittedly appealing.  As Steven Conn describes this argument in the Huffington Post,

…Citizens United has created a new dynamic within the Republican Party. Call it the politics of plutocratic patrons, and at the moment it is causing the GOP to eat itself alive.

Continuing, Conn notes that the argument

works something like this: With the caps lifted on spending, any candidate who can find a wealthy patron can make a perfectly credible run at the nomination.

I’ve added the underline because this is where “the math” gets interesting.  If by perfectly credible, one means, “capable of spending lots of money,” then yes, I agree.  That was actually always true: the right of an individual (i.e., a “wealthy patron”) to buy advertisements for any political issue/candidate has never been effectively curtailed.  Rather, the right of individuals to contribute without limit to organizations that can then do so has been, in fits and starts, regulated.

More importantly, though, the fact that anyone can do so now does not mean that wealthy patrons can guarantee that any candidate can make a “perfectly credible run” at the nomination.  As Conn notes, Foster Freiss is bankrolling Santorum’s 2016 bid.     …Does anyone think that Rick Santorum is a perfectly credible candidate for the GOP nomination?

Maybe Foster Freiss.

No, Rick Santorum is not going to win the GOP nomination.   Neither is Rick Perry. Neither is Chris Christie.  Neither is Carly Fiorina.  Neither is Bobby Jindal.  Of course, I might be wrong on any one of those five.  But I will assuredly be right on at least four.  In fact, if I wanted to type enough, I could be right about no fewer than 15 people who are currently running for the GOP nomination not winning it. (Evidence?  For the latest, see here.)

Simply put, if there are 16 “perfectly viable” candidates for the GOP nomination, then I’m throwing my hat in the ring, too.  WHY NOT?

Look, a wealthy donor can get you in the media.  That is easy, to be honest, if you have the money.  To be a credible candidate, you have to have a chance of winning.  Only one can win.  Lots can spend.  In social science, we often describe this kind of competition as an “all-pay auction.” In an all-pay auction, the highest bidder gets the prize after paying his or her bid.  All of the other bidders pay their bids and don’t get a prize.  It is a stinky, foul game.  (Kind of like running for the presidency.)

In the mega-donor world, the donors are now the bidders, and we are to believe that they want to create viable candidates through their monies spent.  But this is at odds with two points, one empirical and one theoretical.  The empirical point is that these mega-donors are often successful investors and businesspeople.  The theoretical point is that, when there is a single prize, the all-pay auction should not generally see any positive bid from more than two bidders.[1]

These mega-donors have the real-world experience to understand the theoretical point.  …So what are they thinking?

Aside from misunderstanding the game (which can not explain all of the 14 or so “out of equilibrium donors” under the simplistic all-pay model), there are two immediate explanations.  The first is vanity: these donors want to play with the “big kids,” have a roll in the hay with the DC cognoscenti, etc.  While I think that’s obviously got some purchase, it is both unsatisfying and seems too simple for billionaires.

Accordingly, the second is that some or all of these donors are playing the long game with the real contenders.  You see, what the all-pay auction analogy to multicandidate elections misses (among assuredly other things) is that the auction is actually for multiple prizes—each person’s vote is (slightly) differential in value to the bidder, because if it is not bought by me then it might go to various different candidates.

To make this concrete, suppose for simplicity that a donor supported some new candidate, “Charlie,” with money spent in a way that bought a bunch of votes exclusively from nativist (anti-immigration-reform) voters.  That would hurt some GOP candidates (such as Donny Trump, who is anti-immigration-reform) more than others (such as Jeb Bush). If I, as a mega-donor, am in favor of Trump not winning the nomination, supporting Charlie might be much more effective in the multicandidate, winner-take-all game of the GOP nomination fight than simply handing that same money to Jeb. (This is because I could take votes away from Trump—for Charlie—that Jeb could not steal away himself, thus causing Jeb to win because Trump loses votes.  This is another instance of the Gibbard-Satterthwaite Theorem.)

As Conn describes the picture, I completely agree with the main point: Citizens United might very well have unleashed a beast upon the GOP hierarchy (at least for now), because it is harder for the party establishment to control mega-donors, who can now be solicited for “simple checks” by super-PACs and 527 groups.  But, I disagree that this is because the new system increases the realm of “viable candidates.”  Rather, it simply lowers the prices of diversion, smoke, and mirrors in the nomination game.

Is that good or bad?  I’ll defer for now, but I’m perfectly willing to say that it’s neither.  It just changes the game—in the end, money matters, but votes matter more.  In other words, to paraphrase Mencken, though the ways may vary according to the institutional details, donors and voters will invariably get the government they want, and they’ll get it good and hard.

With that, I leave you with this.

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[1] This is a blog post, so I’m being quick about this.  But the basic idea is that the contestants have some common beliefs about their (generally differing) levels of resources (or valuations of winning) and, with few exceptions, the bidder who is capable and willing to pay the third-highest (or lower) price for the prize will not bid because he or she will not willingly sustain a bid that would win in equilibrium.