Which Beat Gets the Night Constables?
Two months of night-theft data from a semi-urban kotwali area are placed before the circle officer. Beat 4 recorded 42 shop thefts in the period; Beat 2 recorded 26. Beat 4 has about 900 shops and 18,000 residents. Beat 2 has about 300 shops and 6,000 residents, and also contains the district bus stand. Each beat currently gets one night constable and one home guard, and the circle officer has exactly two additional night constables to place before the weekend. The probationer at the table argues: "Beat 4 has the highest count, so both extra men must go to Beat 4." The station diary shows that Beat 4's thefts cluster between 2 a.m. and 4 a.m. and are mostly of shutter locks, while Beat 2's cases are largely bags and mobile phones lifted at the bus stand between 8 p.m. and 11 p.m. Two Beat 2 shopkeepers separately told the beat constable they did not report a break-in last month because "the thana would ask for money".
1. On the figures given, which beat carries the higher shop-theft intensity? Does the arithmetic support the probationer's conclusion?
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Convert counts into rates before comparing anything. Beat 4: 42 thefts in 900 shops = 4.7 per 100 shops; against population, 42 in 18,000 residents = 2.3 per 1,000. Beat 2: 26 in 300 shops = 8.7 per 100 shops; 26 in 6,000 residents = 4.3 per 1,000. On both denominators Beat 2 is roughly twice as theft-prone as Beat 4, and it additionally carries the bus stand crowd that Beat 4 does not have.
The probationer's reasoning error is denominator neglect: a raw count mostly measures how many shops and people a beat contains, not how unsafe it is. Beat 4 looks big, not dangerous. His conclusion therefore does not follow, and accepting it would permanently over-police the busiest beat while under-policing the beat where each individual shop is most likely to be hit. The count is not worthless - 42 victims is still 42 victims, and Beat 4 clearly needs cover - but "highest count" cannot be the stated reason for the deployment, and the circle officer should say so in the briefing rather than quietly doing the right thing.
2. The two unreported Beat 2 break-ins have surfaced. How does that change the comparison, and what single verification step would you take before reallocating?
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The comparison is now a floor, not a measurement. Beat 2's true numerator is at least 28, and the two missing cases are not random: they are missing for a reason - fear of the thana - which means under-reporting is probably concentrated exactly where the rate is already highest. So the observed gap of 26 against 42 understates Beat 2's load rather than overstating it.
That has a second consequence, and it is the more serious one: if a beat constable's conduct is suppressing complaints, the data set being used to plan deployment is itself contaminated, and a Plan based on it will keep reproducing the same blind spot.
The one verification step before reallocation should be a fifteen-minute reconciliation at the traders' association: match the association's own incident list against the FIR register for the two months, and check the Beat 2 constable's visit register and the bus stand CCTV log for the same nights. That tests both the missing cases and whether Beat 2's recorded 26 is real. Adopt "thefts per 100 shops per month" as the working metric in the crime meeting so the same error is not repeated next month.
3. Set the deployment of the two extra constables on reasoning, and name the reasoning error you would flag at the briefing.
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The two beats do not have the same problem, so they should not get the same answer.
Placement: one extra constable on the Beat 2 bus stand between 8 p.m. and 11 p.m., the band in which bag and phone lifting actually occurs; one extra constable on Beat 4 between 2 a.m. and 4 a.m., where the shutter-lock series has its window, with instructions to build a series-offender list because a single repeat offender with one method can inflate a beat's count without the place being dangerous.
Reasoning error to name: denominator neglect - comparing absolute counts across populations of very different size, when the question is risk per shop and per resident. Naming the error matters because the probationer is not wrong about Beat 4 needing cover; he is wrong about why, and he will make the same mistake with other data next week.
Two riders for the order: an honest note that Beat 2's figures may be incomplete, and a separate written reference of the shopkeepers' allegation about demands for money, since a patrol plan cannot be built on a register that may be being suppressed.