Tag Archives: The Penalty Ceiling

Any finite penalty schedule has a flat region at the top where marginal deterrence fails. Raise the ceiling and you move the flat region; you don’t eliminate it. In multiplayer settings it gets worse: “you lose” stops being a punishment and becomes a strategic instrument — a tool for kingmaking, for tanking, for changing who wins rather than whether you do. Posts here are about what happens when the rules run out of room to escalate.

Trump, Cruz, Rubio: The Game Theory of When The Enemy of Your Enemy Is Your Enemy.

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I posted earlier about truels and how the current GOP nomination approximates one.  In that post, I laid out the basics of the simple truel (i.e., a three person duel), assuming that the three shooters shoot sequentially.  Things can be different when the three shooters shoot simultaneously.[1]  Short version: Trump and Rubio aren’t allies, but game theory suggests they should both attack Cruz, in spite of this.

This is arguably a better model for debates than the sequential version, in which candidates prepare extensively prior to debate, largely in ignorance of the other debaters’ preparations. Leaving that interesting question aside, let’s work this out.  I assume that the truel lasts until only one shooter is left, and that each shooter wants to live, and is otherwise indifferent.  I’ll also assume that the best shooter hits with certainty.[2] The probability that the second-best shooter hits his or her target is 0<p<1 and the probability that the worst shooter hit his or her target is 0<q<p.

When there are two shooters left, each will shoot at the other.  Not interesting, but important, because this implies that the worst shooter wants to shoot at the best shooter in the first round. In the first round, both the second-best and worst shooters shoot at the best shooter.  Either the first best or second best shooter will be dead after this (if the second-best and worst shooter each get to shoot before the first best shooter, but miss, then the second-best shooter will be killed with certainty). There is also a chance that the worst shooter will win in the first round: the best shooter kills the second-best shooter (probability 1/3), and the worst shooter kills the best shooter (probability q<1).

What does this say about the GOP race?  Both Rubio and Trump should be shooting at Cruz.  This is a simplistic model, and it ignores a lot of real-world factors.  But that’s why it’s valuable, from a social science perspective: if (and when) the behaviors of the three campaigns deviate from this behavior, we know that we need to include those other factors.  Until then, you see, in this world there’s two kinds of models, my friend: Those with just enough to capture the logic and those who need to dig for more things to include.  We’ll see if this one needs to dig.

With that, I leave you with this.

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[1]. For simplicity, I will assume that, if two shooters shoot at each other, then one of them, randomly chosen, will “shoot first” and, if he or she kits, kill the other shooter before he or she fires his or her weapon.  Note that, with this assumption, if shooter A knows that shooter B (and only shooter B) is going to shoot at shooter A, then shooter A should definitely shoot at shooter B.

[2]This assumption isn’t as strong as it appears. This is because the truel is already assumed to continue until only one player is left (note that it is impossible for zero shooters to survive, given the tie-breaking assumption).

The GOP’s Reality is Truel, Indeed

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A truel is a three person duel.  There are lots of ways to play this type of thing, but the basic idea is this: three people must each choose which of the other two to try to kill.  They could shoot simultaneously or in sequence.  The details matter…a lot.  I won’t get into the weeds on this, but let’s think about the GOP race following last night’s Iowa caucus results.  By any reasonable accounting, there are three candidates truly standing: Ted Cruz, Marco Rubio, and Donald Trump.  The three of them took, in approximately equal shares, around 75% of the votes cast in the GOP caucus.

The next event is the New Hampshire primary, and the latest polls (all conducted before the Iowa caucus results) have Trump with a commanding lead and Rubio and Cruz essentially tied for (a distant) second.  So, the stage is set.  Who shoots first?  And at whom?

The truel is a useful thought experiment to worm one’s way into the vagaries of this kind of calculus.  A difference between truels and electoral politics is that the key factor in a standard truel is each combatant’s marksmanship, or the probability that he or she will kill an opponent he or she shoots at.  What we typically measure about a candidate is how many survey respondents support him or her.  For the purposes of this post, let’s equate the two.  Trump is the leader, and Rubio and Cruz are about equal.

A relatively robust finding about truels is that, when the shots are fired sequentially (i.e., the combatants take turns), each combatant should fire at the best marksman, regardless of what the other combatants are doing (this is known as a “dominant strategy” in game theory).  Thus, if we think that the campaigns are essentially taking turns (maybe as somewhat randomly awarded by the vagaries of the news cycle and external events), then both Rubio and Cruz should be “shooting at Trump.”  This is in line with Cruz’s post-caucus speech in Iowa last night.

An oddity of this formulation of the truel is that it is possible that the best marksman is the least likely to survive.  This is true even if the best marksman gets to shoot first.

Is it current, or future, popularity? An alternative measurement of marksmanship, however, is not the current support, but the perceived direction of change in support.  After all, marksmanship is about the ability to kill someone on the next shot.

On this front, Rubio is currently the better marksman: his support in Iowa vastly exceeded expectations, while by many accounts (though not necessarily my own), Trump is the worst marksman.  If one buys this alternative measure, then the smart strategy for both Trump and Cruz is to “aim their guns” at Rubio.  We have a week to see who they each aim at.

Of course, a truel is a simplistic picture of what’s going on in the GOP nomination process. In reality, it is probably better to think that each candidate’s marksmanship depends on his (or her) choice of target.  Evidence suggests that it is harder for Trump to “shoot down” Cruz than it was for him to shoot down Bush.  Maybe I’ll come to that later.  For now, I’m still making sense of Santorum’s strategy of heading to South Carolina. For that matter, I’m trying to make sense of him being called “a candidate for President.”

With that, I leave you with this.

Going Down in Flames…To Rise Like A Phoenix (in the Primary)

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So, the Federal Government is once again approaching the debt ceiling.  Senate Minority Leader Mitch McConnell has said that he thinks that

“…for the president to ask for a clean debt ceiling, when we have a debt the size of our economy is irresponsible. So, we ought to discuss adding something to his request to raise the debt ceiling that does something about the debt or produces at least something positive for our country…”

What McConnell and his colleagues will discuss adding is a bit unclear at this point (though approval of the Keystone pipeline might be part of it), but Democrats are repeating President Obama’s earlier stance that there will be no negotiations based on the debt limit.

This seems like a stand-off in the making…or does it?

Setting aside the popular conception (with which I concur) that Congressional Republicans “lost” the previous fight on the debt ceiling, McConnell followed the above quote with the following statement:

“We’re never gonna default. The Speaker and I made that clear,”

Um, maybe this isn’t a stand-off in the making.  Maybe a “stand up, just to sit down?”  That’s not catchy, but it brings us to my point in this post.

I could argue that McConnell is pursuing a strategy of either looking “crazy” or trying to imply that he is “hemmed in” by his colleagues, as I have argued before regarding Boehner and his factious caucus.   But, I don’t think this is that.  Rather, McConnell’s unusual comments might be best understood as an attempt to send a costly signal to his constituents, as he is facing and already fighting a right-wing primary challenge by Matt Bevin.  I’ll quickly detail this argument.

Let’s suppose that McConnell is facing a primary challenge because some believe his conservative bona fides are lacking.  McConnell can scream as loud as he wants that he is as conservative, but Glenn Beck doesn’t think he’s good enough.

How can McConnell convince voters that he is a true conservative? Well, he can’t just say it—the voters he wants to convince with such a statement will understand that this is cheap talk.  He has to make the statement that he is “one of them” costly—it has to “pin him down” in some way.  This is tough to do with policy, given that he is the minority leader and his party does not control the White House.

So, my argument goes, he can publicly stonewall what is (hopefully) in the end a fait accompli—the debt ceiling increase—and take his lumps along the way.  This type of position will work only if it hurts McConnell in some verifiable way.  My too-clever-by-half argument is that he is setting exactly such a situation up for the voters who care to see that, at the least, he is willing to bleed for them.

His two statements above make it clear that (1) he is simply being difficult, and (2) he is willing to acknowledge that he will lose unless Obama is willing for some reason to compromise.  (Not saying Obama won’t—he might—but McConnell probably doesn’t know that Obama will.)

Arguably, by saying that he is going to try to drive a hard bargain on the debt ceiling while at the same time admitting he’ll ultimately support a clean debt ceiling increase,  McConnell has adopted a position of “I’m so conservative, I’m willing to fight A KNOWINGLY UNWINNABLE FIGHT FOR CONSERVATIVE `PRINCIPLES.'”[1]

To revisit the argument again before concluding, my point here is that McConnell was probably not speaking off-the-cuff: he is no idiot, and I believe he realizes that his position is internally inconsistent.  Most voters won’t care, but those who pay attention might, and the distinction between his statements and simply saying “awww, heck no—we aren’t going to give a clean debt ceiling increase” is that he purposely made clear that not only was he against default—he and Speaker Boehner have “made it clear” that “we’re never gonna default.”  That is, he explicitly pointed out that the GOP is very unlikely to get anything from this—and yet he’s willing to lose trying.

Because that’s just how flamboyantly conservative he is.

With that, I leave you with this.

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[1] I apologize if my distaste for this narrative offends you, dear reader, but I will not accept that even flirting with violating the full faith and credit of the Federal Government is consistent with any reasonable rendition of conservative principles.  Trust, reliability, sanctity of contract—hell, even the facile analogy between running the government and the responsible financial management of a family or small business—-all run squarely against using the debt ceiling as a bargaining chip. Full stop.  That said, as a political scientist, I do not think McConnell is playing dirty—procedural stopgaps are rightly the fitting and necessary last bastion of the minority party.  (See what I did there?  I can link filibusters and debt ceilings, because that’s the way I’m wired: namely, short-circuited.)

No, Seriously, That Was Such A Bad Idea, WE MUST DO IT AGAIN

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Another quote in this (still) excellent piece in the New York Times by Jeremy W. Peters, describing the resolution to the debt ceiling and funding showdown, stuck out at me:

The question so crucial to the Republican Party’s viability now, heading into the 2014 Congressional elections and beyond, is whether it has been so stung by the fallout that the conservatives who insisted on leading this fight will shy away in the months ahead when the government runs out of money and exhausts its borrowing authority yet again.

A key point in the compromise reached to resolve the current crisis regards the timing of the “two crises.”  The government is funded through January 15th, 2014, and the debt ceiling is extended through February 7th, 2014. Note that this compromise does two related things on this dimension:

  1. It does not put the “funding crises” on the same day, and
  2. It puts the less important one (federal government appropriations) first.

Peters appropriately asks whether the “next round” of this dynamic will be occasioned by different behavior by (say) the House Republicans.  But I want to focus on a logically prior question:

Why didn’t Congress pass something that delayed both of these past the 2014 elections?  That is, why did they simply kick the can a short way down the road?

On this question, my main argument/explanation for the delay/obstruction over the 16 days of the shutdown was one of signaling: members of the GOP (and arguably some Democrats) had an incentive to demonstrate their ideological commitments through costly (in)action.  The debt ceiling/default deadline represented arguably a Rubicon of sorts, one that allowed all members—or, at least, Boehner & Cantor—break the impasse by allowing a floor vote.  This is because the (perceived) true costs of obstructing any longer were sufficiently large that they even “true conservatives” would rather get kicked out of office than pay them, and accordingly, many stripes of conservatives (some more faithful, some less) could and would “pool” at this point and vote to end the impasse.  (This explains/is consistent with the push by some to claim that default was either not going to happen on October 17th or, even more amusingly, that default is not that big of a deal.)

To the degree that this signaling argument holds water, it also predicts that the last-minute resolution would involve just a small “kick of the can down the road,” as happened.  That is, to the degree that “the fight” was potentially a useful signal of legislators’ true ideological stances, “signing up for another one” must also be a useful signal.  This would change only if some other event intervenes to explain why ideologically pure individuals would shy away from the fight, allowing heterogeneous members to once again “pool” on agreeing to resolve the fight “permanently.”[1]

The delicious irony here is that the incentive to fight over fiscal responsibility, the latest round of which appears to have been a public approval loss for the GOP, is arguably part of the cause of the fiscal responsibility problem (at least with respect to debt ceiling and shutdown inefficiencies) itself.  This is in line with the frequently noted historical frequency with which, in spite of the fact that Congress can at any time stop having to take such “tough votes,” the debt ceiling has been increased over 90 times since World War II: these votes provide opportunities for members of various factions to attempt to “signal their true colors” by standing fast for a little while in the face of a “must pass vote.”

There’s more here, but it’s Friday.  So, I’ll signal my true type by grabbing a beer and leaving you with this.

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[1] I will leave aside for now the issue of plausible such events: one example, of course, would be a “grand bargain” that (say) cuts/controls entitlement spending in the future.

Winning At All Costs Will Make Winning Costlier (Than It Needs To Be)

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So, the shutdown continues.  Indeed, it seems to me that the collective conscience has accepted that the shutdown will continue until mid-October, when we can get a “two-for-one” CR-Debt Ceiling deal.  Kind of makes sense, in a sad way.

Anyway, the topic of today’s post is the uncomfortable position of Speaker John Boehner, who may very well want a clean CR. Or, more to the point, he might have truly wanted such an outcome before the shutdown.  There is at least a partial narrative to the effect that a clean CR would not pass.  The storyline is, as I alluded to in the previous post, is one of “ends against the middle,” in which liberal Dems want a “clean plus” CR that restores funding to the pre-sequestration levels[1] vote with tea-party GOP members who prefer people eating the goo out of each other’s heads to anything that might be seen as conferring legitimacy on collective governance.[2]

So, how to resolve this?

Well, I definitely don’t know for sure.  But I think the problem right now—to the degree that one thinks that the proper and properly lexicographic priority is to open the government—is entirely due to the Democrats’ stance on the CR.

Let’s be quick about this.  There is no discussion of what one might call a “CR minus,” which would (for example) fund the government at (say) 95% of the last FY’s levels.[3]

So, what Boehner needs here is a way out while saving face.  That’s basically what he is pleading for with respect to the debt ceiling. To me, Boehner is basically (and reasonably) saying “I’ll get the votes however I can, including from Dems…but I need to look like I got something out of this.”  It is important to note that, in politics, hypothetical wins and losses can count as much (if not more than) observed ones.

From a game-theoretic perspective, Boehner’s leadership struggle (as well as the reelection struggles of his more moderate copartisans) is based on the suspicion that he is not a sufficiently “true conservative.”  In signaling game terminology, Boehner needs some meaningful (“costly”) way to differentiate (“separate”) himself from Obama.

A side note: this argument can be related directly to the normal practice (at least in the US) of the winner of an election deferring his or her victory speech until the loser gives his or her concession speech, often preceded by a publicly announced “phone call” from the loser to the victor congratulating him or her on the victory and “a contest well fought.”

Here’s the deal: Obama (and arguably Pelosi) each have the opportunity to go VERY public and demand the moon.  Overplay the hand—demand not only a clean CR, but—-I dunno—a tax increase on the rich.  Let every Democrat who wishes to do so go public and disown this position as too extreme.  Then, have Obama/Pelosi sit down with Boehner and Cantor at the local Applebee’s, and come out with Pelosi and Obama mad as hell.  They need to say that Boehner won’t budge, won’t give into the strengths of their positions.  Maybe get Howard Dean to come up and give a “HEEEE-YAAHHH” for full effect.

Then Boehner takes the stage and says, look, this isn’t the thing we as good conservatives wanted here, but I think it’s time for us to come together and get to the real business of this nation.[4]  He turns and welcomes Reid, McConnell, and a few other Democrats and Republicans to the stage.  The Rules Committee brings the clean CR passed by the Senate to the floor with a closed rule, Boehner walks out smelling like roses with a solid 330-100 or so vote, and *POOF* the tea party is arguably neutered.

It has been said that the real value of the right to appeal in judicial systems is as a way for losers to “save face.” I really believe this.  Almost every collective decision has at least two components: the policy impact of the actual choice, and the reputational impacts on those who argued for and against the choice during the deliberations.  Incentivizing “fair dealing” sometimes requires the (policy) winners to “take a hit” on the reputational front.[5]

It would be sad and truly ironic if the Democrats take the “evidence” (at least strong folk belief) that the GOP overplayed its hand in 1995-96 so closely to heart that they end up overplaying their own hands in this one.

With that, I leave you with this.

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[1] Sorry to bring it up again, but remember sequestration?  Man, those were crazy times.  Like when we opened the fire exit for those dudes bringing burgers back from Hardees and almost didn’t get to walk in graduation!  Except, now it’s like, they got cold hot dogs from 7-11 and we ate them while watching Full House reruns.

[2] Too strong?  Oh, I don’t think so.

[3] The piecemeal approach being pursued by Boehner is an intriguing one, but I’ll leave that for later.  For now, I’ll simply say that such a strategy smacks of “politics meets the need to be seen as active meets the desire of Members of Congress to have their trash picked up.”  Or, more simply, “panic politics.”

[4] Which is, of course, Reality TV.

[5] Note that, in classical two-party electoral competition, “taking a hit” and “declining to pounce on an opportunity to win” are equivalent.