“Tinker tailor soldier spy”

author: “Alexander Levakov”

date: “December 23, 2014”

Who can spy on the spies? John le Carre

Historical background

Tinker Tailor Soldier Spy is John le Carre’s novelization of his experiences of the revelations in the 1950s and the 1960s which exposed the Cambridge Five traitors, Guy Burgess, Donald Maclean, Anthony Blunt, John Cairncross and Kim Philby, as KGB moles in the British Intelligence services. http://en.wikipedia.org/wiki/Tinker_Tailor_Soldier_Spy

The problem

From the very beginning of his masterpiece Le Carre makes us no signal about who is a mole. On the contrary he lays out five persons as possible moles. So up to the end of the novel he unfolds step by step Karla’s double agent and gives us the name of the mole almost in the final. But is it possible, reading the novel, to make some assumptions or hypotheses about the mole? Sure we can do it by applying Bayes rule (theorem). http://en.wikipedia.org/wiki/Bayes'_theorem

Main assumptions

ttss

Oliver Lacon enlists Smiley and Guillam to investigate without the knowledge of the Circus, which is headed by Sir Percy Alleline and his deputies – Bill Haydon, Toby Esterhase, and Roy Bland – as any of these could be the mole. George Smiley after reading some materials and interviews comes to the strong conclusion that only three persons (Percy Alleline, Bill Haydon and Roy Bland) out of the four should be examined (tested) as candidates for the mole. As one can see Tinker, Tailor, Soldier is a clue in the name of novel. But on the eve of his great and final experiment with the telegram sent by Ricki Tarr from Paris to the Circus, Smiley is almost sure about the mole. Why?

Hypotheses

ttss-net

Right, we shall start. There are three possible persons to be the mole: H1 - Tinker (Percy Alleline), H2 - Tailor (Bill Haydon) and H3 - Soldier (Roy Bland). What are the prior probabilities for these hypothesis? Well, Tinker has the highest probability to be the mole as a rival and successor of Control - P(H1)=0.5. It means a priori Tinker has 50% chance to be the mole out of three. Tailor is the second one to be the mole, but a priori he has got less chance as a man standing in the shade of Percy Alleline power - P(H1)=0.3. And Soldier gets his P(H3)=0.2: \[P(H1) + P(H2) + P(H3) = 1\]

Next we should reconsider Smile’s theory about these persons after getting some more information about operation Testify planned by Control with the help of Jim Prideaux. The point is that Jim Prideaux had been very close friend of Bill Hayden, and Control after Jim fiasco got the clue for the possible mole Gerald. So Tailor as a second man on the top of Circus, very close friend of Jim and lover of Ann (Smiley’s wife) played very strange role while crisis in Czechoslovakia where Jim was caught and wounded.

So we assume P(S|H2)=0.9 - Bill Hayden got 90% conditional probability to be the mole Gerald as he was the only person besides Control and Jim being aware of the details of the operation Testify (Jim told him in spite of Control’s warning to keep secret), he knew about Jim arrest before arriving to the Circus although he was all night long with Ann (duty officer called Ann to find Bill’s whereabouts if possible) but he was puzzled by the news that Jim was shot (wounded) - Merlin did not tell him the whole truth. Very strange, isn’t it? We say more - Toby Esterhase knew about Tinker, Tailor code names. Who could tell him? Bill Hayden only!

As for Tinker and Soldier their role in the crisis with the operation Testify was very little if not minor (they did knew nothing) but they were involved in the active searching for Rickie Tarr (the man who got story about Gerald from Irina and transmitted warning to the Circus) and their position made Smiley to put them on the list. So we put P(S|H1)=0.3, P(S|H3)=0.1

Research question

Our goal is to calculate the posterior probability that the mole Gerald would be Tailor (Bill Haydon), given the fact that he is under suspicion to be the spy, in our notation, P(H2|S). Using the formula for Bayes’ theorem, we have:

where we have used the law of total probability to expand \(P(S)\). The numeric answer can be obtained by substituting the above values into this formula. This yields:

ph1=0.5
ph2=0.3
ph3=0.2
ph1+ph2+ph3

## [1] 1

psh1=0.3
psh2=0.9
psh3=0.1
ps=ph1*psh1+ph2*psh2+ph3*psh3
ps

## [1] 0.44

ph1s=ph1*psh1/ps
ph1s

## [1] 0.3409091

ph2s=ph2*psh2/ps
ph2s

## [1] 0.6136364

ph3s=ph3*psh3/ps
ph3s

## [1] 0.04545455

ph1s+ph2s+ph3s

## [1] 1

So we got the answer: Smiley, making the trap for the mole, was sure about 61% for Bill Hayden (Tailor) to be the mole Gerald. As we can see in the final of the novel Smiley was right but this discovery made him very unhappy about his own role as a cover for Gerald!

Conclusion

Although this example of Bayes Rule is for demonstration purpose only it can be used for estimates of insider threat not only in the Circus but in a real world!