Pages

Friday, August 28, 2026

Bob Edlin: Game theory, conspiracies and the puzzle....

....of the way the media got a whiff of Penk’s plot

Sacked from the Luxon Cabinet for his role in the National caucus leadership challenge, the hapless Chris Penk – we are supposed to believe – was the sole plotter.

New Zealand first learned of this one-man conspiracy on August 12, after an emergency National Party caucus meeting and a secret confidence vote called by Prime Minister Christophe Luxon to address the speculation.

Four hours after the caucus meeting concluded, Prime Minister Christopher Luxon surprised reporters by publicly outing Penk in his dismissal statement.

Stuff this week reported:

Penk was sacked from Cabinet after Christopher Luxon named him as the culprit behind a failed challenge against his leadership. Penk later announced he would no longer be standing for Parliament at the upcoming election

And

Luxon, along with senior ministers, have insisted Penk was working alone, despite widely reported suggestions Erica Stanford and Chris Bishop were agitating against the prime minister.

PoO has been puzzled about how a whiff of a one-man coup attempt reached the news media.

When the NZ Herald and others first reported on the internal party discontent, the rumours and fevered “coup talk” had swirled around higher-profile MPs, such as Chris Bishop and Erica Stanford.

But according to the PM’s account of what transpired, Penk had been a one-man band, which means he must have done the leaking which triggered the media speculation.

This week he has declined to confirm or deny the Prime Minister’s assertion he was the sole plotter.

PoO was prompted to look at the botched Penk coup after reading an article titled The Cost of Conspiracy.

American economist Jon Murphy begins:

People conspire all the time. Firms collude. Politicians bargain behind closed doors. Militaries deceive their enemies. But other conspiracies are detected, or they do not last long. Why do some remain secret while others are revealed?

Murphy then says a simple game theory model can help illustrate that the probability of a conspiracy being revealed depends on the number of individuals whose cooperation is necessary and the incentives they face.

He invites readers to consider a simple model of a conspiracy (by “conspiracy,” the writer means two or more people working together to achieve some goal in secret).

Discretion is key to the conspiracy—it will be detected if somebody reveals what they’re trying to accomplish or how.

Readers must be braced for the argot of an economist:

We can model this as a simple probability model:

Pd=1 – (1 – p)N

Where:

Pd = the probability the conspiracy is disclosed

(1 – p) = the probability the conspiracy is not disclosed

N = the number of people in the conspiracy

Right away, we can see a key relationship: as the number of people involved in the conspiracy, N, rises, the probability of the conspiracy being disclosed increases exponentially.


For the sake of numbers, Murphy supposes a 95% probability that the conspirators stay silent.

Furthermore, he assumes each conspirator’s probability of disclosure is independent of each other and identical. (These are simplifying assumptions and not realistic ones, but they help demonstrate the core insight, and that insight isn’t changed by the particulars.)

The results:

Having two conspirators results in a 9.75% chance of the conspiracy being exposed:

With 10 people, that chance jumps to 40.1%.

With 50, the probability of exposure is 92.3%.


More generally, the model can be written as:

lim
n → ∞
[1 − (1 − p)N] = 1

In other words, as the number of people involved in a conspiracy increases, the probability that the conspiracy is exposed approaches 100%. Even a small number of conspirators greatly increases the probability of the conspiracy being exposed.


For a conspiracy to succeed, Murphy contends, either the timeframe or the number of conspirators need to shrink or the probability of breaking silence needs to increase.

He brings the Manhattan Project into considerations.

Some 130,000 people worked on what would become the creation of the atomic bomb. This project was carried out with absolute secrecy. (In fact, many “conspirators” did not know what they were working on until the bombs were dropped.) The N for this project was substantial, and that created risk. So, the federal government and the army worked to reduce the probability that any individual would divulge the secret. Reducing time was inherent to the project: there was a war on and there was pressure to finish the bomb before the Germans. What about (1–p)? We can think of p as a function of economic and social variables: incentives, monitoring, commitment to the cause, etc.

The federal government paid everyone working on the project, from the janitor to the top scientists, extremely well: sometimes four to five times what they could get in the private sector. This was especially true for minorities, who faced substantial discrimination outside the Manhattan Project. Furthermore, World War 2 had a strong patriotic component attached to it. Coupled with strong monitoring, the secrecy of the conspiracy remained.

The Manhattan Project demonstrates just how expensive large conspiracies are to maintain. That project alone consumed about 1.4% of GDP. We can think of that, partially, as the cost of secrecy. And that sort of expenditure is hard to hide. The Germans and Soviets knew we were up to something.


In the concluding paragraphs, Murphy says a conspiracy is an equilibrium, not a mystery.

Like any equilibrium, it survives only if the incentives of its participants support it. When someone alleges a conspiracy, the first question to understand how likely the conspiracy is to be a real one should not be “Could these people coordinate?” but “What incentives kept them coordinated and silent?”

On the flip side, to prevent conspiracies and prevent fraud, we can apply lessons from this model to create institutions that increase the transaction costs of undermining the system: create incentives that make secrecy all the more expensive. Of course, this is easier said than done. If designing incentives were easy, we’d not have these problems in the first place. But what I discuss here does provide a blueprint to help think through these incentives.


Applying this to the Penk coup attempt, PoO reckons we must suppose there was no conspiracy because there was no involvement of two or more fellow coup plotters.

But that does not explain how news of the plot was leaked to the media.

On the other hand, it is tempting to disregard the PM’s understanding of what happened and suspect that more than one MP was involved.

If that be so, it is worth thinking about the nature of the incentives to keep the plotters coordinated and silent.

Bob Edlin is a veteran journalist and editor for the Point of Order blog HERE.

No comments:

Post a Comment

Thank you for joining the discussion. Breaking Views welcomes respectful contributions that enrich the debate. Please ensure your comments are not defamatory, derogatory or disruptive. We appreciate your cooperation.