Undermining the Credibility of an Investigation - A Game-Theoretic Analysis

Let's suppose you were the subject of a serious criminal investigation.  Further suppose you were also a prominent and influential public figure.  You know a priori whether there's anything damning that the investigation may find.  Should you choose to use your influence to affect the credibility of the investigation?  Should you bolster the credibility or undermine it?  Let's take a game-theoretic approach.

Like almost all game theory analyses we'll construct a payoff matrix to guide our analysis.  I suggest one axis capture the eventual outcome of the investigation: evidence of wrongdoing found (guilty) vs. no evidence of wrongdoing found (innocent).  The other axis will capture the subject's three possible actions regarding using their influence: bolster credibility (bolster), do nothing (null), undermine credibility (undermine).

Payoff matrix for subject using influence to affect credibility of investigation - Empty
Bolster Null Undermine
Innocent
Guilty

We now need to consider each possibility in the matrix and assign a relative payoff.  The payoff value represents the utility of the scenario to the subject, that is, how much does the subject benefit based on the scenario represented by each cell.

I don't think it's particularly controversial to argue that any "Innocent" outcome will be good for the subject.  Better if the credibility has been bolstered, but slightly worse if the credibility is undermined.

Payoff matrix for subject using influence to affect credibility of investigation - Partial
Bolster Null Undermine
Innocent 20 10 7
Guilty

Again, it shouldn't be controversial to assume that a "Guilty" outcome will be bad for the subject.  Worse if the credibility is bolstered, but slightly better if the credibility is undermined.

Payoff matrix for subject using influence to affect credibility of investigation - Complete
Bolster Null Undermine
Innocent 20 10 7
Guilty -20 -10 -7

At a global view, it seems like the only reason to actively undermine the credibility of the investigation is if you believe the outcome will be "Guilty" as it will increase your utility.  That should be concerning to anyone paying attention to current U.S. politics.

I think there is one potential argument for modifying the "Undermine" payoffs.  If the undermining is an attack on the biases and motivations of the investigation, the supporters of the subject may see an "Innocent/Undermine" outcome as better than "Innocent/Null" because "even the biased investigation couldn't find anything."  A similar argument could be made about the "Guilty/Undermine" payoff.  The increased nuance becomes important if you think that the subject's actions are more directly tuned to either the supporters or opposers.

Payoff matrix for subject using influence to affect credibility of investigation - Supporters/Opposers
Bolster Null Undermine
Supporters Opposers
Innocent 20 10 14 0
Guilty -20 -10 0 -14

These supporter/opposer payoffs are probably up for much debate, but I think this is probably a good ballpark.

With an "Innocent/Undermine" outcome, opposers will use the attacks on the credibility of the investigation against the subject.  But, supporters will see it as stronger evidence of innocence ("even the biased investigation couldn't find anything").

With a "Guilty/Undermine" outcome, supporters will see it as "proof" that the investigation was biased and not valid.  Opposers will see it as an attempt to evade justice.

What's interesting is if the subject cares only about supporters then the only better possible outcome than undermining the investigation is to bolster an investigation that finds the subject innocent.  If the subject, knowing a priori the truth of their actions, believes that the likelihood of the investigation concluding "Innocence" is almost zero and cares most about their supporters' response then undermining the investigation becomes overwhelmingly the best action to take.

Does the President care so little about those who oppose him that he's willing to take another hit from them in the event that the Mueller investigation finds nothing?  Or is he expecting the investigation to find evidence of wrong-doing and he's laying the groundwork to salvage the only group possible?  Or is my analysis completely wrong?

2 thoughts on “Undermining the Credibility of an Investigation - A Game-Theoretic Analysis”

  1. The West Wing (tv) arrived at the same conclusion. When headed towards an investigation into whether President Bartlet lied to the American people about his health they decided their best course of action was to make sure the investigation was led by their harshest critics and not anyone that might be seen as sympathetic to their cause. Also, a common axiom I heard in school was that if you are the prosecutor, you want to go against the best defense attorney (not just for moral reasons) because a bad attorney might make it easier to win, but a bad defense attorney also makes it a lot more likely your case will get overturned, thrown out, etc.

    1. I understand that logic, they wanted a vicious adversary to show they had nothing to hide. But, Trump didn't encourage a tough investigator and Mueller is by no account an anti-Republican attack dog. And rather than saying, "Good, you'll see I've done nothing wrong." It's, "It's a politically motivated witch hunt, they are all biased, and can't be trusted."

      The West Wing version is actually bolstering the credibility, "Take your best shot." Whereas the Trump version is undermining it, "Even if they find something, you shouldn't believe them."

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