The Bomb Party

• Doctor Fischer Of Geneva - James Mason, Alan Bates 1984$24.99USVHS

• Doctor Fischer is a rich Swedish industrialist whose own bored and cynical attitude to life is partly lightened by his occasional chateau party. Here, his guests are tested to the limits of greediness.

• Dr. Fischer has an unusual hobby - to expose human greed. How much humiliation will his fellow man endure enticed by valuable presents? Dignity for money! Death for money?

cast: James Mason .... Dr. Fischer /Alan Bates .... Alfred Jones /Greta Scacchi .... Anna-Luise Fischer /Cyril Cusack .... Steiner /Barry Humphries.... Richard Deane.Country: UK Language: English Colour

The Bomb Party

The Bomb Party• "Dr Fischer of Geneva" began life as a short novel by Graham

Greene. Written in 1980 (Greene died in 1984) it is a dark satire. Dr Fischer (James Mason) is a multi-millionaire, his fortune founded on human hygiene. At regular parties he surrounds himself with acolytes, all rich, all prepared to go through humiliation for one of Fischer's gifts. Fischer is cold, cruel, manipulative.

• Fischer's daughter Anna-Luise (Greta Scacchi) is a gentle creature abhorring her father's attitude and more particularly the attitude of those acolytes of Fischer (she calls them "toads"). She falls in love with and marries Alfred Jones (Alan Bates), an Englishman who has suffered tragedies (a childhood war mutilation; the loss of his wife and child) and is immune to Fischer's attempts to corrupt him.

• Determined to prove that even the most righteous person can be bought, Dr Fischer plans an ultimate party with a strange and diabolical twist. The party favors contain one of two things--a cheque for $5 million Swiss francs, or a lethal bomb.

The Bomb Party

Imagine that you are invited to a party where all six guests are obliged to pick a cracker from a barrel. Your host tells you that five of the crackers each contain cheques for extremely large sums of money but the remaining cracker contains a bomb that will kill the person that pulls it.

The Bomb Party

Imagine that you are invited to a party where all six guests are obliged to pick a cracker from a barrel. Your host tells you that five of the crackers each contain cheques for extremely large sums of money but the remaining cracker contains a bomb that will kill the person that pulls it.

One of the guests stands and, while pausing to gather courage to approach the barrel is beaten to it by another, Mrs. Montgomery, who runs to the barrel first. Greene writes: “...Perhaps she had calculated that the odds would never be as favourable again.

Belmont had probably been thinking along the same lines, for he protested, ‘We should have drawn for turns’.”

When Mrs. Montgomery pulls her cracker there is a small pop and a cheque for five million francs falls out. Belmont then pulls a cracker and also wins a cheque.

The Bomb Party

The story continues:

“’What about you Jones?’ Doctor Fischer said. ‘The odds are narrowing.’

‘I prefer to watch your damned experiment to the end. Greed is winning isn’t it?’

‘If you watch you must eventually play - or leave’

‘Oh I’ll play I promise you that. I’ll bet on the last cracker. That gives better odds to the Divisionaire.’ "

(Jones has been contemplating suicide for several days and also pities the Divisionaire, who, despite his high military rank, has never heard a shot fired in anger and has been cruelly taunted by Doctor Fischer for having no record of any act of bravery.)

The Bomb PartyThe story continues:

“’What about you Jones?’ Doctor Fischer said. ‘The odds are narrowing.’

‘I prefer to watch your damned experiment to the end. Greed is winning isn’t it?’

‘If you watch you must eventually play - or leave’

‘Oh I’ll play I promise you that. I’ll bet on the last cracker. That gives better odds to the Divisionaire.’ "

(Jones has been contemplating suicide for several days and also pities the Divisionaire, who, despite his high military rank, has never heard a shot fired in anger and has been cruelly taunted by Doctor Fischer for having no record of any act of bravery.)

Then the third cracker is pulled by another guest and turns out to contain two million francs. This leaves three crackers and two guests, Jones and the Divisionaire, who is realising that he is too afraid - too cowardly - to take the risk:

“’I haven’t the courage. I should have gone to the barrel first, when the odds were better.’”

The Bomb Party

The comments of the characters at the bomb party imply that the longer you wait your turn to pull a cracker the more dangerous the risk becomes. Is this correct reasoning? What can be done to maximise the chances of winning two million francs while at the same time minimising the possibility of being blown up?

The Bomb Party

The comments of the characters at the bomb party imply that the longer you wait your turn to pull a cracker the more dangerous the risk becomes. Is this correct reasoning? What can be done to maximise the chances of winning two million francs while at the same time minimising the possibility of being blown up?

While Doctor Fischer is correct when he says that the odds on winning are narrowing after the first two crackers have been pulled, this is conditional on neither of them containing the bomb. If the bomb had been detonated by the first guest to take the risk, the others could have pulled the remaining crackers secure in the knowledge that they would benefit financially rather than be exploded. The longer you wait your turn the odds on survival shorten providing the bomb cracker is not pulled. The longer you wait the more likely it is that someone else will pull the cracker before you.

Doctor Fischer and his guests appear not to have taken this factor into account in their reasoning. The first guest has a 1/6 chance of pulling the lethal cracker and a 5/6 chance of surviving. The second guest has a 1/5 chance of survival if the first guest does not blow up; the chance of the second guest surviving are therefore 1/5 x 5/6 = 1/6. Similarly the chances for the third guest are 1/4 x 4/5 x 5/6 = 1/6. In fact, the position of a guest in the queue does not affect the probability of survival.

The Bomb Party

Nonetheless, our experiments confirm that the illusion of an advantage in going first is held by many subjects; only a minority correctly affirm that all positions are equally likely to draw the bomb. We investigated this by describing the situation to a group of seventy seven psychology undergraduates. We asked them to imagine that they were guests at a bomb party before any crackers had been pulled.

Q: Would you rather go 1st, 2nd, 3rd, 4th, 5th or last?

1st 2nd 3rd 4th 5th 6th ‘Any’ 40% 12% 4% 0% 0% 42% 3%

The Bomb Party

Nonetheless, our experiments confirm that the illusion of an advantage in going first is held by many subjects; only a minority correctly affirm that all positions are equally likely to draw the bomb. We investigated this by describing the situation to a group of seventy seven psychology undergraduates. We asked them to imagine that they were guests at a bomb party before any crackers had been pulled.

Q: Would you rather go 1st, 2nd, 3rd, 4th, 5th or last?

1st 2nd 3rd 4th 5th 6th ‘Any’ 40% 12% 4% 0% 0% 42% 3%

Q: Which has the best chance of surviving? (Experiment 1)

1 2 3 4 5 6 Equal Don’t ‘Firstknow

or last'

48% 0% 3% 0% 0% 19% 23% 4% 3%

The Bomb PartyNonetheless, our experiments confirm that the illusion of an advantage in going first is held by many subjects; only a minority correctly affirm that all positions are equally likely to draw the bomb. We investigated this by describing the situation to a group of seventy seven psychology undergraduates. We asked them to imagine that they were guests at a bomb party before any crackers had been pulled.

Q: Would you rather go 1st, 2nd, 3rd, 4th, 5th or last?

1st 2nd 3rd 4th 5th 6th ‘Any’ 40% 12% 4% 0% 0% 42% 3%

Only 3% of subjects said that they had no preference for a particular position in the queue. Although first and last positions are roughly equally popular choices, different justifications are offered for each. When asked why they had chosen as they had, a common reason for those who went first was that they had a better chance of surviving. However, this was not a common reason for those who said that they preferred to go last. Those choosing to go last mentioned two main arguments. One was that if the bomb had not gone off they would always refuse to actually pull a cracker and run away, and therefore they could guarantee their survival.

The other common reason was that going last would ensure that one knew one’s fate - you would know what would happen to you before you pulled the cracker. (Though note that this defence overlooks the fact that you wouldn't know what happened to you until other guests pulled their crackers.)

The Bomb Party

To avoid subjects feeling that they could increase their chances of surviving by going last and then running away if a cracker hadn’t exploded, we repeated the study telling subjects that they had to pull a cracker and would be shot if they tried to run away...

Experiment Two: Running away is not allowed...Q: Would you rather go 1st, 2nd, 3rd, 4th, 5th or last?

1st 2nd 3rd 4th 5th 6th ‘Any’49% 4% 0% 0% 1% 32% 11%

The results are very similar to those for experiment one except that now last position is less popular...

The Bomb Party

What is the cause of the effect?

Communication problem?

Perhaps subjects assume that the experimenter is asking them which they would prefer - a party where no bomb has exploded and there are 6, 5, 4, 3, 2 or 1 crackers left. In this case the probabilities are 1/6; 1/5; 1/4; 1/3; 1/2 and 1. Although the text of the problem does not encourage or, strictly, permit this representation, might subjects perceive the problem in this way?

The Bomb PartyWhat is the cause of the effect?

The surprise paradox.There are some similarities between the bomb party and one explanation of the the so-called surprise test paradox (see Margalit and Bar-Hillel, 1983). The surprise test paradox emerges when a teacher tells her class that they will have a surprise test one day next week.

Quine (1953) offers an explanation of this paradox in terms of neglect of the possibility that the test has already occurred. In the surprise test paradox people seem to overlook the possibility that the critical event has occurred earlier and thereby require it to occur later. The bomb party also sees people finding it easy to overlook the possibility that the event has occurred earlier in time - though here people are reasoning forwards in time. In each case there seems to be a problem with finding a particular scenario so alluring that it becomes difficult to consider alternatives.

Monty Hall

The popular television game show Let's Make A Deal continues throughout the world -- forty years after its debut on the NBC Television Network on December 30, 1963!

Behind one of these doors is a car.

Behind the other two is a goat.

Pick the door you think the car is behind.

Behind one of these doors is a car.Behind the other two is a goat.

Obviously the car is not behind door 1.

But before I open door 2, the door you selected,I'm going to let you switch to door 3 if you like.

Again, pick a door you think the car is behind.

Behind one of these doors is a car.

Behind the other two is a goat.

LOSER!!

Recap: You originally picked door 2 and then switched to door 3.

The difficulties that these two problems cause have ben attributed to the operation of “subjective theorems” (cf. Shimojo and Ichikawa, 1989). One suggestion of a subjective theorem that people apply to probability is the uniformity principle (see Falk, 1992). This principle effectively states that when there area number of uncertain alternatives one should, in the absence of indications to the contrary, assume that they are all equally likely. This mistake was made by Leibniz (1678).

GOAT GOAT CAR

GOAT GOAT CAR

GOAT GOAT CAR

The Bomb Party

• However, the bomb party illusion is distinct from the fallacies triggered in these problems. The bomb party illusion violates the uniformity principle. People erroneously believe that the set of alternatives identified are not equally likely.

Now imagine that over the years Dr Fischer has actually held lots of bomb parties each one attended by different guests who have all pulled crackers. Sadly, at every party one of the guests was killed. Dr Fischer has been carefully keeping records of how many guests died in each position in the sequence. He has plotted a graph to show the results. Which of the graphs (A to E) below do you think most resembles Dr Fischer's graph?

A B

C D

E

Now think again. If you were at a bomb party and had to pull a cracker, which position do you think would have the best chance for surviving?

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The Bomb PartyThe bomb party illusion diminishes when subjects perceive it as a frequentist problem...Q: Which has the

best chance of surviving? (Experiment 3a)

1 2 3 4 5 6 Equal Don’t know

single event 88% 4% 0% 0% 19% 4% 4% 0%

frequentist* 50% 0% 0% 0% 0% 8% 38% 4%

If subjects are presented with the frequentist formulation before they tackle the single event version of the problem then the illusion largely diappears.

Q: Which has the best chance of surviving? (Experiment 3b) 1 2 3 4 5 6 Equal Don’t

know single* 15% 0% 7% 0% 0% 7% 67%% 7% event

Frequentist19% 0% 0% 0% 0% 0% 74% 4%

*These subjects had access to the frequentist formulation before giving judgments for the single-event version of the problem.

The Bomb Party

Experiment 4: Imagine you are a guest who has agreed to play at a similar party, before any crackers have been pulled. At your party though there are 100 guests and 100 crackers - 99 with cheques and one with a bomb. You must pull a cracker (Dr Fischer will shoot anyone attempting to run away):

1 2 3 10 50 100 Equal Don’t know

Which Prefer? 54% 12% 4% 4% 4% 13% 4%

Which has 36% 1% 0% 0% 3% 13% 41% 4%best Chance?

The Bomb PartyExperiment 5: Imagine you are a guest who has agreed to play at a similar party, before any crackers have been pulled. At your party though there are 2 guests and 2 crackers - one with a cheque and one with a bomb. You must pull a cracker (Dr Fischer will shoot

anyone attempting to run away):

1 2 Equal Don’t know

Which Prefer? 63% 34% 0% 1%

Which has 17% 13% 65% 4%best Chance?

The Bomb PartyGraham Greene's failure to perceive the situation correctly is perhaps more disturbing when one considers his experience as a young undergraduate. In his autobiographical book 'A sort of Life' Greene records that in the autumn of 1923 he had been reading a book which described how White Russion officers, condemned to inaction at the tail-end of the counter-revolutionary war, invented the game now known as Russion roulette as a means of escaping their boredom.

Greene found a revolver loaded it with one bullet and walked to a remote spot. He put the muzzle to his right ear and pulled the trigger. He describes the intense jubilation that was provoked by the tiny click that signalled his survival of the experience - looking at the chamber he saw that the bullet had now moved into the firing position. He remarks, "I was out by one". He played Russian roulette on other occasions but the thrill gradually diminished: "It was... during the Christmas of 1923 that I paid a permanent farewell to the drug. As I inserted my fifth dose, which corresponded in my mind to the odds against death, it occurred to me that I was not even excited: Iwas beginning to pull the trigger as casually as I might take an aspirin tablet. I decided to give the revolver - since it was six-chambered - a sixth and last chance. I twirled the chambers around and put the muzzle to my ear for a second time, then heard the familiar empty click as the chambers shifted."

Greene hints that he felt that six attempts at Russian roulette gives fate (God?) the casting vote as to whether he should continue to live or die. However the chance of surviving six games of Russian roulette (providing the chambers are spun each time) is just over 1/3. While Russian roulette appears to have been the inspiration for the bomb party, note that while the bomb party is a case of sampling without replacement, Russian roulette is a case of sampling with replacement.