There Is Disagreement About the Causes
j.p.birchallP0194869
T247
tma0224/5/95
Question 1.
1There is agreement that the deaths of 96 people at Hillsborough in 1989 was a tragedy and the safety of spectators at football stadiums must be improved. However before appropriate actions can be taken the causes of the disaster must be established.
There is disagreement about the causes.
One perspective is that this was a tragedy waiting to happen, there were clearly foreseeable factors :-
large crowds
limited turnstiles
narrow entrance
a spate of last minute arrivals
security fencing blocking escape routes
the police who were charged with crowd control responsibilities proved to be incompetent and their failure to redirect and control the melee was the cause of the disaster.
My own view of the problem rejects this analysis; blaming the police is akin to holding the police responsible for murders because they did not prevent them; the root cause was the anti social behaviour of the louts in the crowd. There has been a history of crowd trouble which no amount of expensive policing will cure. The problem is with :-
hooliganism and indiscipline at schools and in the home
political extremism
alcohol
lack of protecting sanctions
it is the breakdown of the moral values of a small minority in society which was the basic cause.
j.p.birchallP0194869
tma0224/5/95
2A MULTIPLE CAUSE DIAGRAM TO EXPLORE WHY 95 PEOPLE WERE KILLED AT HILLSBOROUGH IN 1989.
An alternative perspective.
2A MULTIPLE CAUSE DIAGRAM TO EXPLORE WHY 95 PEOPLE WERE KILLED AT HILLSBOROUGH IN 1989.
My own perspective. A complex mess with interconnections & feedback over history and not ‘cause & effect’ on the day as ‘effects were causes’ ...
j.p.birchallP0194869
tma0224/5/95
3From my own perspective the people that own the problem are the innocent spectators who risk their lives when they go to football matches, particularly if they can only afford to watch from standing enclosures.
Ancient cultural norms and standards of morality in the UK have inclined my own expectations towards the British propensity for orderly queues. This has been reinforced by my experience working overseas in alternative chaotic cultural conditions where neither orderly queuing nor armed police were solutions to problems of anti social behaviour.
A possible intervention point would be for supporters to persuade the stadium authorities to issue identity cards to bone fide fans and withdraw cards from the thugs whenever they are identified.
The hoped for outcome of this intervention would be the exclusion of the louts from watching the match and causing the trouble. However, unintended consequences could also result; theft of cards and illegal forgeries may become a source of income for criminals and the safety of the innocent spectator may become worse. Also welcome spectators may be excluded. For example, irregular visitors maybe be unable to watch a match if they had not planned ahead to get an identity card. Also there would be a severe administrative cost outcome from the initiative.
4The alternative perspective has the police as the problem owner. They are being paid to control the crowd, it is their responsibility.
In this case an appropriate intervention point would be using police horses to physically control the flow of spectators into the narrow Leppings Lane entrance.
The expected outcome would be to ensure the pushing and unruly behaviour was in an unrestricted area where pressure could not build up and cause deaths. However, the Sheffield police have a reputation of 'victimising' football hooligans and physical restraint may have resulted in riot making matters worse.
5Both diagnoses start from the problem of how to avoid crushing deaths and work back. There are similarities in that a chain causes and effects are involved. The main difference is that my diagnosis widens the boundary of the problem and looks at underlying behavioural characteristics of football crowds, identifying complex social problems.
The problem owners are very different. The majority of spectators are looking for trouble-free leisure enjoyment and have some choice about whether they go to matches. The police are paid employees and are expected to deliver a service. They are under pressure from public opinion and the sanction of the sack if they do not do something. A potential problem is that doing something may make matters worse.
My proposed intervention does not directly address these general problems. Identity cards at best would treat a symptom, hooliganism at matches, but would do nothing to stop the problem moving elsewhere. The innocent majority could still be vulnerable.
The alternative view is essentially practical and accepts the current behavioural profile of the crowd and seeks to ameliorate the problem by positive life saving actions through physical restraint by police. The intervention is relatively late in the sequence and is therefore likely to involve less unpredictable consequences.
The analysis has exposed the weakness of adopting a monocausal belief in complex human activity systems. Causes and effects 'fan out' resulting in a complex web of interaction. Neither causes or solutions are obvious. This is particularly important when adopting solutions; unintended consequences may make matters worse.
A complex mess with interconnections & feedback over history and not ‘cause & effect’ on the day as ‘effects were causes’ ...
j.p.birchallP0194869
tma0224/5/95
Question 2.MODIFIED INSURANCE MODEL
1The purpose of the modified model is to forecast the annual profit/loss when policy holder deaths vary from predictions. This forecast is to be used to assist in deciding the size of a contingency fund.
The assumptions are that the deaths will vary randomly with an equal probability of being accurate as the prediction, or one death more, or one death less.
The model is a stochastic static type.
The if...then...else statements for the number of deaths is:-
IF [the first one third probability of a random generator applies]
( checks if a random number between 0 and 1 is < 0.3334)
THEN [ increase predicted number of deaths by 1 ]
( if true then increase the number of deaths by one)
ELSE [IF [the third one third probability of a random generator applies]
( if false then check if arandom number between0 and 1 is > 0.6667)
THEN [ decrease predicted number of deaths by 1]
( if true the number of deaths is decreased by one)
ELSE [ leave predicted number of deaths as is]
( if false then the second one third probability applies & don't change the predicted deaths)
2The Framework formula required for C9 (for example) was developed in a separate frame as a sub-model with appropriate comments and kept as simple as possible. The initial formula developed was:-
Cell C10 contains the predicted number of deaths.
Cell C5 contains the random number generator.
Cell C9 contains the formula which derives the number of actual deaths.
@IF ( C5 < 0.3334,;checks if the random generator is ;< 0.3334
@sum ( C10,1 ),;if true display the value of C10 plus ;one
@IF ( C5 > 0.6667,;if false check if the random generator ;is > 0.6667
@SUM ( C10, -1 ),;if true display the value of C10 ;minus one
@sum ( C10, 0 );if false display the value of cell ;C10 unchanged
);ends the 2nd. random number check
);ends the 1st. random number check
The formula contains the @sum() which is not strictly necessary in this case because the predicted number of deaths is a given in C10, established at the start, ensuring C10 always contains a value.
The formula was tested to ensure there were no error messages and that the three possible values (C10+1, C10, C10-1) were returned in a random fashion and with equal probabilities. This was done by accumulating the occurrence frequencies of C10+1, C10 and C10-1 in display cells C11, D11 and E11 within the frame and checking that they were occurring with equal probability. After 600 recalculations the frequencies were 197, 201 and 202 which were considered satisfactory to validate the formula. This testing of the formula in isolation applied only to that part of the specification that demanded correct arithmetic for the generation of the randomised actual deaths with the desired probabilities.
The formula did not require debugging.
3The model itself was modified by copying the debugged and checked formula developed for C9 into cells D9 to L9 with appropriate reference cell modifications. I had an initial problem when I assigned a single random generator to a separate cell G5. The intention was to refer to this cell in each year's calculation. This proved unrealistic as the random deaths are required to be different each year, and making reference to a common G5 random number could not achieve this.
The debugging involved observing the initial behaviour of the actual deaths which identified a constant pattern of deaths either above, below, or on the predicted value every year. The error was stable and localised to the common G5 random generator. It was corrected by introducing a separate random generator for each year. The random generator in G5 was copied to cells C5 to L5, and the row 9 formulas adjusted to refer to these cells. The model was again tested by checking that cells D9 to L9 produced the same random results as the tested and debugged C9 formula. This was done by introducing display cells in row 21 which accumulated the probability frequencies for any specified formula in row 9.
The validation of the formula confirmed the assumptions about the variability of the death rate had been successfully modelled.
The model was then tested by checking the results against the specification. The annual profit was assumed to be the net cash flow. In the absence of data on other costs, (for example, depreciation, administration, commission, marketing and sales), this was considered appropriate for the stated purpose. The net cash flow fluctuated randomly during test runs as expected and it was clear that the key annual profit year was always the last year when deaths had mounted and the effects of reduced premium income, increased payouts, and eroded investment income had been compounded.
A print out of the modified model is attached Fig1., Fig.2. is a print out of the C9 formula.
4Key variables in the original model are the policy premiums and the associated assured sum and the investment income which varies with the interest rate. However, in the modified model the key variable is the random timing and number of deaths which have a major impact on annual profit. This is true even within the small plus or minus one per year variation which was modelled.
The variable which represents the model outcome is the annual profit, which was the stated purpose of the model in the specification.
The model will be used to investigate the maximum and minimum annual profit.
The model is a stochastic model (based on random input) which means interpretation of the results must be based on a statistically significant number of results.
The maximum profit can be expected in the early years when contributions are maximum and deaths minimum and when investment income is maximised for the following year. The model was run at random until the chance occurrence of minimum deaths were recorded in the first three years. It was unnecessary to run the model further as annual profits were obviously declining. In the first three years when deaths are the minimum in each year, i.e. 14, 15 and 17, the profit figures are:-
year 1year 2year 3
£3714£3710£2705
It was not necessary to do any further statistical analysis to establish when the profit is maximum. Furthermore the company are concerned about a contingency fund to cover annual losses.
To investigate the losses the model was used to accumulate the frequencies of final year profit figures. This was done using accumulators in cells F21 to O21 and assigning profit ranges to produce a frequency distribution as shown below.
Final year profit £'s sterling FrequencyCumulative
>-1000 1 1
<-1000to>-1500 28 29
<-1500to>-2000 82 111
<-2000to>-2500164 275
<-2500to>-3000183 458
<-3000to>-3500162 620
<-3500to>-4000161 781
<-4000to>-4500118 899
<-4500to>-50001011000
<-5000 0
A graph of the results is shown in Fig.3.
It is clear from the graph that losses are unlikely to be greater than £5000. This was confirmed by copying the model into a new frame and manually maximising the deaths in all years, in such extreme circumstances the loss in the final year was £4769. The best loss figure for the final year was also determined by minimising the deaths for all years, the figure was £491.
51)
a)From part 4 that the best annual profit is earned in the first year at £3714 when the actual deaths are minimum at 14. The maximum loss under the extreme circumstances of the maximum deaths every year from part 4 is £4769.
For any one year the profit variation is highest in the final year when the effects of the random deaths in earlier years is compounded. Thus the maximum and minimum profit/loss that can be expected in any one year will be in the last year were it can vary from a small loss of £491 to a big loss of £4769.
b)The contingency fund is a matter of judgement. From the frequency distribution a fund of £4000 would cover 78% of loss instances. £3000 would cover only 46% of instances. £4000 would be a reasonable contingency fund.
5 2)
The review of annual profit in this way is unrealistic as new business is ignored and policy holders deaths result in declining annual profit over the ten year period, resulting in the maximum profit in the first year and maximum loss in the final year.
Thus my advice to the company would be to use this model to asses profitability over the full period by analysing the cumulative cash flow.
Another model could be developed to reflect the annual position by including a statistical average for all current policy holders (new and old) and associated deaths.